WO2003019531A1

WO2003019531A1 - Method for multiresolution spectral analysis

Info

Publication number: WO2003019531A1
Application number: PCT/CA2002/001310
Authority: WO
Inventors: Pierre Guilmette; Serge Glories
Original assignee: G Ii Si Inc.
Priority date: 2001-08-27
Filing date: 2002-08-23
Publication date: 2003-03-06
Also published as: FR2828949A1

Abstract

The invention concerns a method for multilevel signal analysis for continuously obtaining constituting parameters in reduced number useful for continuous signal processing or routing . Parameters resulting from analyses on windows of different wavelengths are classified according to their type either by using transitional short windows for positioning medium and long windows, or by using medium windows to obtain amplitudes of elements on the peaks of medium spectra obtained or by using long windows to obtain frequencies on the long peaks of the long spectra obtained corresponding to peaks obtained on the medium windows.

Description

MULTIPLE RESOLUTION SPECTRAL ANALYSIS METHOD

SIGNAL ANALYSIS METHOD HAVING A TEMPORAL VARIATION

FIELD OF THE INVENTION

The present invention relates to signal analysis. More specifically, the present invention relates to a method of signal analysis comprising a variation of temporal order.

BACKGROUND OF THE INVENTION

Methods of analyzing a time-varying signal, such as for example an audio signal used to characterize it on a number of established parameters, are known in the art.

An example of such methods is the harmonic analysis, for example of the type of fast Fourier transform (TFR) over a window of determined length. However, such a harmonic analysis cannot provide all the information sufficiently precisely to contain all the information used to characterize a signal continuously. Thus, if a short window is used, the amplitude response of the TFR will be correct in that the window will be short enough to allow the detection of transients of the order of the length of the window. The frequency precision will however be poor, since the number of spectral lines is half the number of points in the window. Analysis on a single window is therefore suitable for most measurement and instrumentation applications, but not for applications in the field of signal processing. In addition, the analysis on a single window lends itself poorly to the regeneration of a processed signal, since it supposes a compromise as regards the precision at the levels of the amplitude (short windows) and the frequency (long windows) .

Harmonic analysis in the form of TFR as taught by the current state of the art, despite the fact that it is very instructive on the nature of the signal that it analyzes, is difficult to apply in processing, signal classification or routing. According to the prior art, other methods must often be used in parallel with the TFR in order to characterize the signal. These parallel or complementary methods include, for example, transforms including wavelets or highly specialized algorithms in the time field which can only be applied to specific functions.

A signal analysis method with temporal variation adapted to optimize the quality of the analysis both at the transitional and frequency levels and where the number of resulting parameters is minimized is therefore desirable.

SUMMARY OF THE INVENTION

The present invention relates to a multi-level signal analysis method making it possible to obtain, on a continuous basis, constituent parameters in reduced numbers and useful for continuous signal processing or routing. An object of the present invention is to analyze a signal comprising variations of temporal order so as to characterize it on a number of parameters established in such a way that the useful information on this signal is present and that the number of these characteristic parameters be reduced to a minimum.

The analysis process according to the present invention includes an appropriate processing sequence adapted to optimize the quality of the analysis at the level of the transitional response and at the level of the frequency precision.

More specifically, according to a first aspect of the present invention, there is provided a method of analyzing a signal comprising a temporal variation, the method comprising: a) sampling the signal at a total number of predefined sampling points; b) split the signal into successive first level analysis windows; the successive first level analysis windows being characterized by a first number of points from the total number of points; c) applying a frequency transform on each of the successive first level windows in order to obtain a frequency spectrum on each of the successive first level windows; d) using the frequency spectra of the first level windows in order to identify transitions in each of the first level windows; e) define successive second level analysis windows; the start of each second level analysis window corresponding to the start of a first level analysis window having the maximum of transitions among a predetermined number of successive first level analysis windows; the second level analysis windows being characterized by a second number of points from the total number of points; f) applying a frequency transform on each of the second level windows in order to obtain a frequency spectrum on each of the second level windows; the spectrum on each of the second level windows comprising peaks; and g) calculating amplitude and frequency values corresponding to the peaks on the frequency spectra obtained on each of the second level windows.

According to a second aspect of the present invention, there is provided a system for analyzing a signal comprising a time variation, the system comprising: a) means for sampling the signal at a total number of predefined sampling points; b) means for cutting the signal into successive first level analysis windows; the successive first level analysis windows being characterized by a first number of points from the total number of points; c) means for applying a frequency transform to each of the successive first level windows in order to obtain a frequency spectrum on each of the successive first level windows; d) means for using the frequency spectra of the first level windows to identify transitions in each of the first level windows; e) means for defining successive second level analysis windows; the start of each second level analysis window corresponding to the start of a first level analysis window level having the maximum of transitions among a predetermined number of successive first level analysis windows; the second level analysis windows being characterized by a second number of points from the total number of points; f) means for applying a frequency transform to each of the second level successive windows in order to obtain a frequency spectrum on each of the second level windows; the spectrum on each of the second level windows comprising peaks; and g) means for calculating values of amplitudes and frequencies corresponding to the peaks on the frequency spectra obtained on each of the second level windows.

The parameters resulting from the analysis are sorted and calculated in such a way that only the relevant elements are retained, that the elements preserved are greatly reduced in number and are of format easily usable for signal processing so that processes are facilitated and accelerated and that the storage or transport of parameters is facilitated.

It follows from the signal analysis method according to the present invention that the parameters which are provided by the analysis system describing the signal contain the information necessary for the characterization of the signal to be carried out by the additive combination of simple elements for high energy components or in a subtractive combination of complex elements filtered to reproduce weak and low energy components. The invention makes it possible to speed up signal processing processes by providing useful analytical elements, to speed up the remote transport of signal data and to provide signal parameters useful for their possible regeneration in real or deferred time. It allows more efficient storage on signal data, to choose the level of quality of signal reproduction and thus to obtain, if necessary, a significant rate of reduction of the data without loss of quality of reproduction or an additional rate of data reduction. on selectively removed items.

Other objects, advantages and characteristics of the present invention will become apparent on reading the following non-restrictive description of specific embodiments, given by way of illustration only with reference to the appended figures.

BRIEF DESCRIPTION OF THE FIGURES

In the accompanying drawings:

Figures 1A to 1C represent is a flowchart illustrating a method of analyzing a signal according to a preferred embodiment of the present invention;

Figure 2 is a graph illustrating the envelopes of a first oscillation of a signal for analysis purposes according to the method of Figure 1;

Figures 3A and 3B are graphs illustrating a sample of 8,192 points produced from a first oscillation sinusoidal generated from the envelopes of Figure 3;

Figure 4 is a graph illustrating the envelope of a second oscillation of a signal for analysis purposes according to the method of Figure 1;

Figures 5A and 5B are graphs illustrating a sample of 8,192 points produced from a second sinusoidal oscillation generated from the envelopes of Figure 4;

Figure 6 is a graph illustrating the envelope of a third oscillation of a signal for analysis purposes according to the method of Figure 1;

Figures 7A and 7B are graphs illustrating a sample of 8,192 points produced from a third sinusoidal oscillation generated from the envelopes of Figure 6;

Figure 8 is a graph illustrating the envelope of a fourth oscillation of a signal for analysis purposes according to the method of Figure 1;

Figures 9A and 9B are graphs illustrating a sample of 8,192 points produced from a fourth sinusoidal oscillation generated from the envelopes of Figure 8;

Figures 10A and 10B are graphs representing the sum of the oscillations of Figures 3A-3B, 5A-5B, 7A-7B, and 9A-9B constituting the sample to be analyzed; Figure 11A is a graph representing the first 256 points of Figure 10A corresponding to the first first level analysis window;

Figure 11B is a graph showing a weighting window for the top-level window in Figure 11B;

Figure 1 1 C is a graph showing the window of Figure 11 A weighted using the window of Figure 1 1 B;

Figures 12A to 12D are graphs representing the first level analysis windows after weighting of the sample to be analyzed in Figures 10A and 10B ('Fech') and after having undergone a TFR ('Spec');

Figures 13A to 13D are graphs representing the second level analysis windows after weighting of the sample to be analyzed in Figures 10A and 10B ('Fech') and after having undergone a TFR ('Spec');

Figures 14A to 14H are graphs representing the third level analysis windows after weighting of the sample to be analyzed in Figures 10A and 10B ('Fech'), after having undergone a TFR ('Spec'), after compression ( 'Fxe') and after the compressed sample has undergone TFR ('Spx'); and Figures 15A to 15D are graphs showing the oscillation envelopes obtained by the method of Figure 1 from the sample of Figures 9A-9B.

DETAILED DESCRIPTION OF THE INVENTION

A method of analyzing a signal according to a preferred embodiment of the present invention will firstly be described generally, then an example of application will be presented.

The analysis method according to the present invention comprises cutting a signal to be analyzed into analysis windows of determined lengths and combined in succession to ensure the continuity of the process.

According to the present invention, contiguous short TFR windows are used to detect the transitional nature of the signal, medium length TFR windows are used to provide information on the amplitudes of the elements and long TFR windows are used to provide element frequency information. The present invention thus makes it possible to use the algorithm in a large number of applications with several significant gains in the accuracy, continuity and reduction of the data.

More specifically, the method of analyzing a signal according to a preferred embodiment of the present invention comprises the following general steps (see FIGS. 1A-1C): a) sampling the signal at a total number of predefined sampling points; b) cutting the signal into successive first level analysis windows characterized by a first number of points; c) applying a frequency transform to each of the successive first-level windows in order to obtain a frequency spectrum thereon; d) use the first level frequency spectra to identify transitions in each of the first level windows; e) define successive second level analysis windows whose start corresponds to the start of a first level analysis window having the maximum of transitions among a predetermined number of first level analysis windows and whose length is a multiple of the length of the first level windows; f) applying a frequency transform to each of the successive second-level windows in order to obtain a frequency spectrum thereon; g) calculating amplitude and frequency values corresponding to the peaks of the frequency spectra obtained on each of the second level windows; h) defining successive third level analysis windows whose beginnings correspond to the start of second level analysis windows and whose length is a multiple of the length of the second level windows; i) applying a frequency transform to each of the successive third-level windows in order to obtain a frequency spectrum on each of them; j) calculating amplitude and frequency values corresponding to the peaks of the frequency spectra obtained on each of the third level windows; k) store in separate indexed registers each of the amplitudes and frequencies corresponding to the first of the third level spectra; for each of the following spectra:

I) check the frequency compatibility of each of the peaks of the 's' spectrum with each of the peaks of the previous spectrum; m) store in separate indexed registers each of the frequencies corresponding to the spectrum 's'; the peaks compatible in frequency with one of the peaks of the preceding spectrum sharing the same index as this peak; new indices not yet assigned so far being assigned to the frequencies corresponding to the peaks which are not frequency compatible; n) check the amplitude compatibility of each of the peaks of the spectrum 's' with each of the peaks of the previous spectrum; and o) store in separate index registers each of the amplitudes corresponding to the spectrum 's'; the peaks compatible in amplitude and in frequency with one of the peaks of the preceding spectrum sharing the same index as this peak; new indices not yet assigned so far being assigned to the pairs of amplitude and frequency values corresponding to the peaks which are not compatible in amplitude and frequency.

The parameters resulting from the analyzes on windows of different lengths are classified according to their nature, either by using the transitional short windows to position the medium and long windows, or by using the average windows to obtain the amplitudes of the elements on the peaks of the spectral means. obtained, or by using the long windows to obtain the frequencies on the peaks of the long spectra obtained which correspond to the peaks obtained on the average windows. On the peaks used as so many peaks are associated elements which allow continuous characterization of the signal analyzed in the successive order of the windows and the number of peaks obtained. So using the information collected the signal is processed from its constituent elements in the frequency field rather than in the time field.

The data received and characteristics of the continuously analyzed signal are representative of the shape of peaks on the different spectral lines of the windows of different correlated lengths. These peaks are associated to be, depending on their nature, characteristic single constituents or characteristic composite constituents. On a window, the additive combination of these elements makes it possible to reconstruct the incoming signal, to modify it, to store it, to classify it or to transmit it. The choice of taking certain specific peaks as single elements or several specific peaks combined into composite elements is made according to their own characteristics. These peaks provide information on the elements, their absolute amplitudes and natural frequencies.

The peaks can be compared with each other so that they are classified as simple elements for high energy peaks (high amplitudes) beyond an established threshold.

The peaks are compared with one another so that they are classified into composite elements for low energy peaks (low amplitudes) below a predetermined threshold when several peaks share a close frequency zone according to an established zone dimension. The simple and composite peaks, as they contain all the information on each window of the signal analyzed in continuity, fully describe the window in question which is a temporal portion of the signal in question. Successive windows thus fully describe the portions of the analyzed signal, and when these windows are contiguous, they describe the entire signal.

The parameters resulting from the analysis method of Figure 1 are identified by index links to elements in specific order and are correlated so that the evolution of the parameters and their variation over time are associated with the same indices of parameters and identified continuously with the same elements. The transformation of a time base to frequency is reversible and lossless, which allows the signal to be reconstituted by a re-synthesis device from the parameters thus ordered and grouped. The use of indexed registers ensures continuity in the processing or routing of the signal via the analysis parameters thus grouped.

According to the method of the present invention, only the significant spectral components are preserved, in frequency forms, of amplitudes and, if necessary, of phases, by eliminating the elements which do not correspond to relevant information and by retaining only amplitude peaks and collecting their respective frequency information and, if necessary, their relative phase.

The data of the peaks obtained to characterize the signal are allocated to indexed registers which, once identified on the basis of the peaks obtained from an initial analysis window, are representative of the evolution of the peaks on the successive windows, so that each register is associated with a peak in the window and a peak in each window according to which peak will be identified as compatible with the peak in the previous window.

Thus registers make it possible to follow the evolution of a peak on the successive windows by identifying the compatibility with respect to the greatest frequency proximity of a new peak of a new window with a given peak of the previous window put in a specific register. Thus, a certain number of indexed registers will make it possible to contain the peaks and to follow their frequency and amplitude evolution. It is therefore possible to follow precisely all of the simple and composite elements of a signal analyzed on successive windows.

The process of assigning registers for the peaks makes it possible to describe the signal not only on each window analyzed but to establish a temporal link of evolution between the successive windows and thus to precisely and dynamically describe the signal by providing precise information and signal dynamics on a minimum number of parameters. With this temporal correlation of the windows, the analysis process will be reversible like the inverse TFR but by containing more useful information on the signal: classification of the elements, links between the windows, frequency and dynamic variations, elimination of the irrelevant elements ( amplitude dips, noise thresholds, etc.).

The analysis process of Figure 1, using an allocation of registers according to pre-established criteria for the association of successive peaks such as frequency ranges, variations in amplitudes, thresholds to retain the choice of more elements or less important (especially on the levels), allows to obtain a dynamic information on the signal, on a precision and a class of basic parameters (amplitudes, frequencies).

Optionally, the phases can also be chosen by deducting these from the real and imaginary parts of the TFR performed. The type of treatment and its use of the analysis process can therefore be adapted and parameterized if necessary.

Harmonic analysis is used on windows of short to long lengths to obtain information on each section of a signal analyzed in continuity, where each section is converted into a harmonic analysis window whose TFR algorithm has the particularity transform the time base of the incoming window into a frequency base. This gives information on the energy content of the window on frequency bands covering the spectrum of the window. This energy content, which takes the form of a spectrum whose each point represents a band of the amplitude of the value of the point whose horizontal axis represents each frequency band in ascending order.

The number of points (bands) of a spectrum corresponds to the number of points of the analyzed window divided by two. For example, a window of 1024 points will give 512 frequency bands. The frequency of the bands depends. the window's sampling rate. For example, at a sampling rate of 48,000 Hz, 512-bands will cover a spectrum from 0 to 24,000 Hz, for a resolution of 46.9 Hz per band.

Each window that is analyzed is weighted beforehand so that the start and end of each window are at zero. This process is classic for TFR type harmonic analysis windows and different weighting windows can be used as needed, including: Hanning, Hamming, Blackman, Bartlett, Kaiser, Tukey, Lanczon, Blackman-Harris, etc. Depending on the needs and the desired precision, a window or the other will be used, either to obtain narrow bands, or for better amplitude precision, etc.

On each window analyzed, a spectrum containing the levels of the respective bands is obtained. A given spectrum has progressive values whose peaks indicate the energy bands of higher energies.

From the peaks and values on the neighboring bands, the peaks are determined to obtain the amplitude of the peak, but above all to obtain the frequency which must be determined with precision by averaging the bands around the peak. Once the peak values have been obtained, only these values are retained as significant elements.

The following function indicates a way to obtain with precision the amplitude values 'AMP' and frequency 'FRE' of each peak on selected spectra: np + nba

∑SPEC [n] (2 * nba) + l

* FBASE

or

'np' is the position of a ridge 'nba' is a predetermined number of spectral points used to evaluate said amplitude;

'nbf is a predetermined number of spectral points used to evaluate said frequency;

'SPEC [n]' is the value of the band 'n';

'FBASE'esl a base frequency.

The start of each pair of second and third level windows is associated with the start of the first level window with the maximum number of transitions.

The positioning of the windows that will be analyzed is therefore determined by the results of harmonic analyzes performed on short adjoining windows. Thus, each analysis window which will produce the information on the constituents, on their amplitudes and on their frequencies respectively on windows of medium and long durations, will be positioned following analyzes on the short windows.

The short analysis windows constitute the first step of calculation on a section to sample. They will be identified as first level windows.

The top level windows are 'ni' points and give 'Spec' spectra of 'n1 / 2' values, for example, 256 points. Beforehand the second level windows are predetermined with a certain length 'n2' which is a multiple '71 of the length of the first level windows. The multiple 'Z' gives the number of first level windows that will be analyzed for each second level window. The analysis sequence comprises different steps which are carried out in order on the basis of second level windows comprising 'Z' first level windows. This sequence is therefore carried out entirely for a given window, then for the following ones and this, advantageously, as the sample is read.

The first level analysis is performed on 'Z' short adjoining windows. A TFR is performed on each of these to then deduce, for 'Z' first level analyzes, the initial position of the second level window (average length - amplitudes) and third level (large length - frequencies).

A TFR function is applied to each first level window, according to the following function which will produce a 'Spec' spectrum from each 'FECH' window, which is a weighted window (of Blackman type or other) of 'n' points:

SPEC [0 .. (n1 / 2) -1] = TFR (FECH [0..n1-1])

On the first level analysis windows the data collected is used to observe the changes on the successive 'Spec' spectra, in this case the transitions, so that the second and third level analysis windows are aligned with the start of the first level windows with the largest variations.

To determine the nature of the transitions on the successive first level spectra, the respective amplitudes of the 'n1 / 2' frequency bands are compared individually on the successive spectra. A given spectrum is thus compared with the previous one. An example of calculation to evaluate the transitions on a given spectrum would be the sum of the absolute values of differences between the respective bands of the evaluated spectrum 'SPEC [s, n]' and the previous spectrum 'SPEC [s-1, n] \ the whole divided by the sum of the values of the spectrum evaluated. The calculation of transitions therefore follows the following equation:

"1

∑ | SPEC [s, n] - SPEC [s -l, n] \ vtrn ni

ΣSPEC [s, n]

"O =

On '71 compared spectra, the first level spectrum with the highest 'vtrn' value is the one with the most transitions. The start of the first level window with the highest 'vtrn' value is therefore chosen to be the start of the second and third level windows.

The second level windows with 'n2a' points are then analyzed. These windows will make it possible to deduce the amplitudes of the components of the signal and to carry out a summary calculation of their frequencies.

The second level analysis windows are chosen with dimensions of 'n2a' sample points. This number can be fixed and correspond to the reference value of 'n2' points which determined the ratio 'Z' between the windows of first and second levels. If, on the contrary, this number 'n2a' is chosen as variable, it will be chosen so that it is shorter on the first level windows whose transitional measures 'vtrn' are high so as to optimize the response to transient, and longer on the first level windows whose transitional 'vtrn' measures are low so as to allow detection of a larger number of elements.

As for the first level analysis, the second level analysis is performed on successive windows, but the position of these, determined by its starting point, is determined by the results of the first level analyzes, in the occurrence by choosing as the starting point the same as for the first level window which has the maximum of transitions (the value 'vtrn' higher) among '71 contiguous windows whose points cover 'n2' points.

A TFR function is applied to each second level window, according to the following function, which will produce a 'Spec' spectrum from each 'FECH' window, which is a weighted window (of Blackman type or other) of 'n2a' points :

SPEC [0 .. (n2a / 2) -1] ≈ TFR (FECH [0..n2a-1])

On 'n2a / 2' frequency bands, the second level spectra have a resolution 'RB2' determined by '(Sampling frequency / n2a)'. Each value of the spectrum is associated with a specific band. Sure each spectrum, the maximums are observed and, on a given spectrum, are retained the values beyond a threshold which is proportional to the maximum peak of the spectrum in question. Depending on the desired resolution, the peak detection threshold value is chosen, so that only values greater than 'AMIN' times less than the maximum peak value 'AMAX' will be retained. In the spectrum in question, the peaks which meet this criterion are used to calculate the amplitude values and their temporary reference frequency values.

The calculation of the amplitude and frequency values on the peaks of the second level spectra is carried out for each peak using the following relationships:

np + nbf

∑ (n) * SPEC [n]

FRE = n = np-nbf np + nbf * FBASE;

∑SPEC [n] n≈np-nbf or

'np' is the position of a ridge;

'nba' is a predetermined number of spectral points used to evaluate said amplitude;

'SPEC [n]' is the value of the band 'n';

'FBASE is a base frequency. The respective values of amplitudes and frequencies are thus obtained for each peak on a given second level spectrum. The peaks are classified in ascending order for each spectrum, ie each value of amplitudes and frequencies and, if necessary, of the phase of each peak.

On a given spectrum, 'q' values 'AMP' (amplitudes) and 'FRE' (Frequencies) are kept on a temporary register.

Third level windows with 'n3a' points will now be analyzed. These windows will allow the frequencies of the signal components to be deduced from the values calculated by the second level windows.

The third level analysis windows are chosen with dimensions of 'n3a' sample points. This number can be fixed and be the reference value of 'n3' points which is related to the length of the second level windows, ie 'n2'. This number 'n3a' can also be variable. It will then be chosen according to the variable length which will have been calculated on the second level windows, either double the second level window or other factor.

Each third level analysis is carried out on successive windows whose initial positions are the same as the second level windows.

A TFR function is applied to each third level window. The frequencies are calculated in the same way as in the case of the second level analysis, ie on interpolation of values around the peaks. On 'n3a / 2' points, the frequency resolution is of (Sampling frequency / n3a) on the spectra which will be obtained. As the frequency distribution of the spectrum is linear, this frequency resolution is insufficient in the low frequencies. In addition, a window that is too long will cause the detection of variations in components in amplitude or frequency to be weak. To overcome this problem of precision on low frequency components without lengthening the window, two separate analyzes will be performed on each third level window, a first analysis (standard) to determine the high frequency elements and a second analysis (extended ) to determine the elements of low frequencies.

If necessary, other extended analyzes can be carried out to, for example, determine the elements of medium and high frequencies. However, since the frequency distribution is linear, the precision is normally sufficient in the medium and high frequencies.

The third level 'Fech' windows are modified to eliminate elements of high frequencies when it is considered preferable to increase the resolution on low frequencies. The high-low frequency limit is fixed, for example, on a frequency which is a fraction of the maximum frequency, for example 1/4 of the bandwidth.

The process of modifying 'Fech' to enlarge the frequency resolution takes place in two stages. The first step consists in filtering each 'Fech' window by a low-pass filter whose cut-off frequency ('FC') is set to according to the frequency limit chosen. For example, a fourth-order 'IIR' type filter ('n = 4') can be used, i.e. the 'IIR' filter function on a 'Fech' window of dimension 'n3a', on each point between '0 'and' (n3a / 2) -1 ':

FFLT [θ .. (n3a / 2) - 1] = IIR (EECH [θ .. (n3 / 2) - 1_)

Order n \;

FC: Band limit j

The second step consists of compressing the 'Fech' window from 'n3a' to 'n3b' points, where the compression rate 'RF' corresponds to the ratio between the limit frequency 'FC and the bandwidth' FS ', then adding zeros before and after the compressed window to bring it back to the number of initial points 'n3a' or '((n3a-n3b) / 2)' zeros before and after.

'Fxe' represents the 'Fech' windows thus modified, i.e. on 'n' and 'm' at 2048 points:

0 \ n: 0 .. ((n3a - n3b) / 2) - l

FXE [n] = FFLT [m / RF] \ n: (n3a - n3b) 12 + (m 14) on m: 0..n3a;

0 | n: ((n3a - n3b)! 2 + n3b - \). . n3a

Each weighted 'Fech' window is transformed into frequency domain by a general Fourier transform on 'n3a' points of a 'Fech' sample window, giving a 'Spec' spectrum of 'n3a / 2' points where:

SPΕC [0 .. (n3a / 2) -1] = TFR (FΕCΗ [0..n3a]) Then, each modified window 'Fxe' is transformed into frequency domain by a general Fourier transform on 'n3a' points of a modified sample window 'Fxe', giving a spectrum 'SPX' of 'n3a / 2' points where :

SPX [0 .. (n3a / 2) -1] = TFR (FXE [0..n3a])

Third-level spectra on modified 'SPX' windows are used to calculate the frequencies of the peaks of low frequency bands, i.e. frequencies below 'FC. On 'n3b' frequency bands, the third level spectra 'SPX' have a resolution of '(Sample / (n3a * RF))'. Each value of the spectrum is associated with a specific band.

Third level spectra on unmodified 'Spec' windows allow the frequencies of peaks in high frequency bands to be calculated. On 'n3a / 2' frequency bands, the third level spectra 'Spec' have a resolution of '(sampling frequency / n3a)' hz. Each value of the spectrum is associated with a specific band. However, since the low frequency bands' FC and less are calculated from the third level spectra on the modified 'SPX' windows, only the bands corresponding to frequencies higher than 'FC will be retained, i.e. the spectral points between' ( FC / RF) 'and the upper band.

As for the second level analyzes on each spectrum, the maximums are observed and, on a given spectrum, are retained the values beyond a threshold which is proportional to the maximum peak of the spectrum in question, first on the spectrum of modified windows' SP and then on the spectrum of unmodified windows' Spec '.

The following relationships allow the calculation of amplitude values 'AMP' and frequency 'FRE' on the peaks of the third level spectra for each peak on 'SPX' and 'Spec':

For unmodified windows:

np + nba

ΣSPEC [n]

_{AMp =} n = np-nba,

(2 * nba) + l

np + nbf

Σ (n) * SPEC [n]

FRE = n-np-nbf np + nbf * FBASE

∑SPEC [n] n≈np-nbf

and, for modified windows

np + nba

ΣSPX [n]

_{AMp =! 1 =} __ _Z na

(2 * nba) + 1

np + nbf

∑ (n) * SPX [n] n = np-nhf

ERE = np + nbf * FXBASE;

∑SPX [n] n = np-nbf or

'np' is the position of a ridge;

'tii a' is a predetermined number of points of the modified spectrum used to evaluate said amplitude;

'SPEC [n]' is the value of the band 'n';

'FBASE' is a base frequency;

'SPX [n]' is the value of the band 'π' said modified spectrum; and

'FXBASE' is a base frequency.

The peaks identified and calculated on each pair of third level spectra are associated with the peaks retained on the second level spectrum whose start of the window corresponds. The peaks of the second and third level analyzes are associated taking into account their frequencies. The peak frequency values deduced from the second level windows will correspond more or less closely to the peak frequency values from the third level windows. However, as the third level windows are normally longer, allowing higher frequency precision to be obtained, these could include peaks not present on the second level spectra, in particular on components which appear on the sample after the last of the second level windows. In this case, the peaks will be rejected.

We thus obtain the respective values of amplitudes and frequencies for each peak on a pair of spectra of second and third levels given. The peaks are classified in ascending order for each spectrum, ie each value of amplitudes and frequencies and, if necessary, the phase of each peak.

Either on a given spectrum 'q' values 'AMP' (amplitudes), 'FRE' (Frequencies), these values are kept on a temporary register which will then be used to determine the progression of the parameters and their associations to registers.

Second and third level windows with 'n3a' points were therefore analyzed. These windows made it possible to deduce the values of amplitudes and frequencies for each of the peaks. These data come from TFRs. However, these algorithms calculate the harmonic elements in two distinct parts, that is to say the real and imaginary part, whose square root of the sum of the squares of these determines each value of spectrum in amplitude and the frequency. If necessary for further processing, the phase angle 'PHA' of each component can be extracted directly from these real / imaginary elements and be associated with each peak. Registers are created to establish a time link between the analysis windows which successively produce amplitude and frequency values on peaks. These registers are created in such a way that the peaks of the successive spectra are continuously associated. Each of these peaks represents, on the basis of the harmonic analysis, as many signal elements in the form of sinusoidal oscillations of frequencies and proper amplitudes.

The index allocation process is intended to ensure that the detected peaks can be put together according to their respective frequency pairing. Thus, on the spectra of successive windows (second and third levels), the peaks which correspond most in frequency and in amplitude are put in priority on the same indices.

In the analysis process on successive windows, the number of peaks per successive spectra varies, which corresponds to the variations of the signal itself. A given analysis window will have little peak for a given time if the signal has poor harmonic content. In other periods of time (gradually or suddenly), the signal may become richer and thus contain more peaks, for example during transitions. Finally, over different periods of time, certain components could vary more or less strongly in frequency, and so on. The allocation of indices must take account of these variations and must ensure that the frequency components are allocated to the same indices if they are reconciled in frequency or in amplitude.

Since the number of peaks is limited, the previous step is advantageous to ensure that the parameterization of an analyzed signal is consistent and can allow the treatment or regeneration of the latter. This amounts to saying that a signal which would have been generated by sinusoidal oscillations could be regenerated by an equivalent number of sinusoidal oscillations. The signals can be reduced into harmonic elements which are as many sinusoidal oscillations. With a selection of these elements during the analysis, a dynamic and continuous regeneration can be performed on the analyzed signals, whatever their properties. In practical cases, we have no prior idea of the content of a signal. However, the allocation of the indices from the peaks is carried out in such a way that the entire analysis process does not have to know this content beforehand so that it can be used on any signals.

The index allocation process can be carried out in several successive stages. An example of the work done will be in order:

• Allocation of registers on the initial spectrum (spectrum No. 0);

• On each following spectrum, the peaks will be assigned to the compatible registers, process 'P1' to 'P4';

• 'P1': Search for peaks compatible in frequency with the previous spectrum on all the peaks;

•, 'P2': Search for peaks compatible in frequency with an already assigned register of a previous spectrum on the peaks not yet assigned;

• 'P3': Allocation of peaks not yet assigned to new registers; and

• 'P4': Search for compatible peaks in amplitude with confirmation of the allocation of the registers, and reassignment of the non-register compatible in amplitude on the closest peaks in frequency whose allocation is not yet confirmed.

The peaks are put in increasing frequency order on the registers. This order is established on the first window, then on the following windows. The new peaks will be added in sequence in ascending order on the new peaks and so on.

The temporary registers containing the information on the frequencies and the amplitudes of the peaks at the passage of the first window (initial spectrum) are copied in the registers of the last peaks' PIC_A and 'PIC_F' respectively for the amplitudes and the frequencies. These last peaks will contain the active peaks on the current window. These data are also copied on the old peaks 'PRE_A' and 'PRE_F', these latter registers will keep the information on registers silenced over a period of time so as to keep the reference and be able to associate new peaks with them of the following windows.

Either on the initial spectrum with 'n0' peaks:

TP_A [0] = first amplitude peak of the initial spectrum; TP_F [0] = first frequency peak of the initial spectrum;

TP_A [nO] = last peak amplitude of the initial spectrum; and TP_F [nO] = last peak frequency of the initial spectrum.

The values of the temporary registers P_A 'and TP_F' are copied to the current registers' PIC_A and 'PIC_F' and the previous value registers' PRE_A 'and' PRE_F '.

PRE_A [0] = PIC_A [0] = TP_A [0] PRE_F [0] = PIC_F [0] = TP_F [0];

PRE_A [nO] = PIC_A [nO] = TP_A [nO]; and PRE_F [nO] = PIC_F [nO] = TP_F [nO]

New non associated peaks will be added to the sequence, whereas if they are associated, they will replace the values of the compatible registers on the given index of 'PIC_A' and 'PIC_F', on the second spectrum comprising a new peak which is not compatible with the previous registers:

TP_A [m] = new amplitude peak compatible with no spectrum register n ° 0;

TP_F [m] = new frequency peak compatible with no spectrum register # 0;

PRE_A [n0 + 1] = PIC_A [n0 + 1] = TP_A [m];

PRE_A [n0 + 1] = PIC_F [n0 + 1] = TP_F [m]; And so on...

The peaks on a spectrum of a given time window are then evaluated in order to associate them with the preceding registers containing the peaks of the preceding windows.

Allocation of spectra compatible registers with spectra previous

Frequency compatibility is established on a variation of frequency value at successive spectra corresponding, for example, to 'nf successive bands of frequency spacing on unmodified windows, by carrying out the search within a margin of one band, then two bands, then three bands, up to 'nf bands.

The amplitude compatibility is established on a variation of amplitude value at the successive spectra corresponding, for example, to amplitude variations between double and half the value of the current spectrum compared to the previous spectrum.

The peaks of the current analysis window in 'TP_A' and TP_F 'are first compared with the registers' PRE_A 'and' PRE_F ', starting on a frequency separation band up to' nf bands d spacing. Compatibility is observed if the difference between the values of register TP_F 'and one or the other of registers' PRE_F' is less than a predetermined threshold. The closest peaks are therefore paired as a priority. The values of the peaks thus paired are then compared on the values of amplitudes. Within a range of amplitude spacing 'na', the peaks are considered compatible and the values TP_A 'and TP_F' are copied to the matched register 'PIC_A' and 'PIC_F' then 'PRE_A' and ' PRE_ F '. Thus, if the peak T is compatible with the register 'j', it is copied there. Is:

PRE_A [j] = PIC_A [j] = TP_A [i]; and PRE_A [j] = PIC_A [j] = TP_A [i].

The peaks on a spectrum of a given time window which are not evaluated as compatible are copied to new registers in order or to empty registers which have already been allocated, but which no longer contain a peak on the previous spectrum.

In a first case, if a peak could not be associated with a register, it is considered free and it is then placed on an empty register. TP_A [k] ', TP_F [k] = peak' which could not be evaluated compatible on all the registers' PRE_A [0] \ 'PRE_F [0]' to 'PRE_A [n] \' PRE_F [n ] \

Comparing with the registers' PIC_A [0] ',' PIC_F [0] 'to' PIC_A [n] ',' PIC_F [n] \ it should be noted that 'PRE_A [p]', 'PRE_F [p]' is a register of old spectrum which is not present on the registers' PIC_A [pj 'and' PlC_F [p] \ which are null. Then, 'PRE_A [p] \' PRE_F [p] 'is considered as re-attributable and can receive the new peak:

PRE_A [p] = PIC_A [p] = TP_A [k]; and PRE_F [p] = PIC_F [p] = TP_F [k].

In a second case, if a peak could not be associated with a register, it is considered free. But if there is no empty register, for example because all the registers 'PIC_A', 'PIC_F' are allocated on all the 'PRE_A', 'PRE_F' created, then it will be placed in a new register.

TP_A [k] ', TP_F [k]' = peak which could not be evaluated compatible across all registers' PRE_A [0] \ 'PRE_F [0]' to 'PRE_A [n] \' PRE_F [n ] \

Comparing with the registers' PIC_A [0] \ 'PIC_F [0]' to 'PIC_A [n]', 'PICJF [n]', it should be noted that all these are associated with all the registers' PRE_A ', 'PRE_F' corresponding. Thus, 'PRE_A [n + 1] \ 'PRE_F [n + 1]' is created like the new peak and can receive it and can receive the new peak:

PRE_A [n + 1] = PIC_A [n + 1] = TP_A [k]; and PRE_F [n + 1] = PIC_F [n + 1] = TP_F [k].

The association of peaks on registers therefore makes it possible to use this information in a useful way for the processing and reconstruction of a signal to apply different processes to it, such as for example:

• transport by transmitting successive 'PIC_A' and 'PIC_F' registers;

• signal storage from successive 'PIC_A' and 'PIC_F' registers; and

• signal processing using the successive 'PIC_A' and 'PIC_F' registers on a time basis.

The registers allow a characterization of the signal on a minimum of data which are, moreover, informative on the signal.

)

Among the data collected on the windows of second level spectra when the observed peaks are close together and of relatively low amplitudes compared to the largest value of amplitude observed on the current spectrum (for example 32 times lower than the maximum) , these peaks can then be grouped on the same composite peak containing several of these ill-defined peaks. This composite peak is then classified apart from the elementary peaks which, as described above, represent the peaks defined on a specific band of spectrum. The elementary peaks recorded as described above represent as many elementary oscillations (sinusoidal oscillations) of natural amplitudes and frequencies (and optionally phase). The composite peaks represent, for their part, a combination of close spectral lines which are manifested in particular as noise, such as for example a violin bow noise, a flute blast, a surrounding noise, etc. The composite peaks in this case represent as many areas of noise delimited by the lower and upper bands. These spectral lines can be put in registers like the elementary peaks, by comprising three parameters, namely the amplitude (PIC_A), the lower frequency will be identified (PIC_FB) of the frequency zone of the spectral lines in question as well as the upper frequency ( PIC_FH) of the frequency zone of the spectral lines. These last two parameters can be treated as frequency values in the subsequent parameter processing. This therefore results in a saving of data by reducing a noise band (peaks not defined) by 'Q' contiguous spectral lines on three parameters of amplitudes and low and high frequencies. In this way, depending on the nature of the signal, the defined, distinct and higher energy (amplitude) elements of the signal will be reduced on elementary peaks, and the undefined elements of the signal will be reduced on composite peaks.

Thus, a composite peak is recorded on registers distinct from the elementary peaks, but the associated data are treated in the same way as for the elementary peaks. Therefore, the subsequent data processing on the peaks implies that these peaks are elementary or composite. Composite peaks are specifically represented as noise generators delimited in frequency bands by as many bandpass filters. A composite peak is characterized by a lower band 'fb' and an upper band 'fh'. The bands are close together and are of average amplitudes 'ab', the value 'ab' characterizing the amplitude of the composite peak ('PIC_A'). The result is a white noise generator with amplitudes established at 'ab', bounded by a bandpass filter whose central frequency at 'fc' hz is the median between 'fb' and 'fh' hz. This value 'fc' characterizes the central frequency of the composite peak and it is deduced from the parameters ('PIC_FB' and 'PIC_FH'). The filter bandwidth is also deduced from the parameters ('P1C_FB' and 'PIC_FH'). So the three parameters describing the composite peak, namely 'P1C_A,' PIC_FB 'and' PIC_FH ', can be reconstituted by the combination of noise generator and bandpass filter.

The three parameters of the composite peaks can be treated in data as for the elementary peaks. However, the registers reserved for the elementary peaks on successive spectra will remain distinct from the composite peaks. In this case, an elementary peak register will never evolve into a composite peak and vice versa.

The data is then collected from the analysis on each successive window to be classified. First, as they are of the absolute type, they lend themselves by their nature to a series of layouts which allow them to be classified and adapted in order to minimize their number.

In a first step, the raw absolute data is adapted to a number of bits as a function of the desired precision.

In a second step, the frequency and amplitude values are converted into relative forms. The successive values determined by the contents of the registers are stored and represent the specific evolution from one value to another. Addresses that are associated with the registers are also added.

The order of the data follows the source of these according to the analysis steps on the three levels, then according to the allocation of the registers which correspond successively to the analysis windows of the sample and the peaks associated with them. Thus, the data can be stored or transmitted step by step, as the sample is analyzed on successive windows.

The data received from the registers follow a specific order which allows classification or routing in a continuous and unlimited manner, in sequence on 'n' spectra, then 'pn' peaks. On each spectrum, the number of peaks can vary depending on the number of these peaks that have been detected.

The data collected on the various previous stages of the analysis are associated with the amplitudes and frequencies of the peaks of the successive spectra. By establishing the frequency limit on a given frequency with an accuracy of 'bf hz, the frequency values can be determined beforehand on a certain number of' rbf bits. They correspond to the values obtained previously on the peaks of the successive spectra, typically using 16 to 24 bits.

The amplitudes on analysis data from samples of 'be' bits, ie the values ('PIC_A'), correspond to the values obtained previously on the peaks of the successive spectra. Amplitude data can be greatly reduced. By assuming a maximum on 'rbe' bits, the values are brought to a lower maximum by dividing by a constant, that is to say the values ('VAL_A'). A value can be encoded on a limited number of bits in the range of amplitudes, typically on 12 to 16 bits according to the desired precision. The data are processed in variations from zero values for the amplitudes and from an absolute initial value for the frequencies. This processing ensures that only the relevant values are retained, in this case the non-zero values and the variable values. However, this transformation implies a break in the continuity of the sequence (ie the spectra (durations)) and inside these, the peaks in succession. It will be necessary to introduce an identification of the registers on the VR_ADR 'data whose address identifies the peak number associated with specific values of amplitudes and frequencies.

The amplitude values are established in relative mode in the form of variations of the values for each peak. The amplitude variations are represented under 'VR_A. By using the variations of amplitudes on the successive registers and as these data vary in time, the data in variations are necessarily less than the absolute data, without loss of precision and by using fewer bits.

For example, if on 'PIC_A of the initial window, the amplitude value is 3,024 and the peak of the same index of the second window the amplitude value is 2,980, then the values on' VR_A 'will be 3,024 respectively and -44.

The frequency values are established absolutely (basic values) for the initial duration (0 ms) and when the frequency value on the previous spectrum is zero. In these cases and only in these cases the values are expressed in absolute terms over a determined number of bits.

Frequency values are established relatively (variation values) for non-initial durations, when the previous value is not zero. In this case, the values are expressed on a smaller number of bits and represent the variation between two values on a cell of duration 'n' given.

Let the calculation of the relative frequency:

or

'n': current duration; 'n-1': previous duration;

'nbas': duration on the last value set in absolute on NR_FBAS'; and

'VAL_F: Frequency values (absolute).

The values of the peaks are then expressed in variation on PICA by VR_A \ and 'PIC_F' by VR_FBAS 'and' VR_FVAR '.

The data received from the registers follow a specific order which allows the classification or the routing in a continuous and unlimited manner in sequence on spectra 'n' and peaks 'pn'. On each spectrum, the number of peaks can vary depending on the number of these peaks that have been detected. The introduction of the addresses makes it possible to classify or convey the values on peaks which do not follow one another. The following table represents this succession where, for example, the following peaks would be absent:

Spectrum # 0, Peak # 1 Spectrum # 1, Peak # 0

The data are weighted according to their respective weights. The different data are formatted in order of magnitude and by order of origin of the data. To ensure optimal classification, the data will be converted specifically according to their nature (addresses, amplitudes, frequencies).

As this data on a relative basis includes the addresses, these make it possible to remove the insignificant elements such as for example the null values and the elements below a threshold.

Addresses:

As described above, the addresses are specified to identify the registers in the sequence of the previous table. There are two nested sequences: the succession of spectra and, inside them, the succession of peaks. The latter is circular (return to the first peak at the start of a given spectrum). Thus, only the address of the first peak must be established in absolute, by specifying which peak it is (normally peak n ° 0, but if it was zero on a given spectrum, it could be spectrum n ° 1 or a following). So the address specifies the initial peak. The following peaks are established relative to the initial peak. For example, if peak # 0 is immediately followed by peak # 2, the absolute address of peak # 0 will be the value (0) and the relative address of the next peak will be (+2). The number of data is thus reduced to define the addresses.

The definition of the addresses takes account of a specific encoding to define firstly whether it is absolute or relative, then the number of bits necessary to contain it. The address is therefore defined in two sections: that of the type of encoding and the value itself. Typically, a maximum of 256 peaks can be considered as the maximum necessary to contain the data of the analysis, that is, in absolute terms, eight bits of value at most.

For example, it is possible to define this type of encoding for each 'initial peak' (on a spectrum sequence) and for each peak following the initial peak:

The address data are identified (VPB_ADC) for the encoding of the addresses and fVPB_ADV) for the address values themselves.

Amplitudes:

The amplitude variation values are weighted according to their order of magnitude. As mentioned in the previous step, these values are established on 'ma' signed bits, ie for values between - (2 ^Λ ma) and + (2 ^Λ rna). The values are then divided into two sections, the code and the mantissa. It is possible to define the mantissa values on a reduced number of bits. The distribution of values over their orders of magnitude requires 'bca' code bits.

The following distribution could for example be defined for the encoding of the amplitudes:

The amplitude values are identified VPB_AX 'for the encoding and VPB_AM' for the value of the mantissa.

Frequencies: The frequency values are weighted according to their order of magnitude. As described in the previous step, these values are set to 'nf or' rnf signed bits, either for values between - (2 ^Λ rnf) and + (2 ^Λ mf) for relative values or between 0 and (2 ^Λ nf) for negative values. The values are divided into two sections, the code and the mantissa. It is possible to define mantissa values on 'nmf bits for absolute values. The distribution of the values according to their order of magnitude requires' bcf code bits.

The following distribution could for example be defined for the encoding of the frequencies:

The frequency value data are identified VPB_FX 'for the encoding and' VPB_FM 'for the value of the mantissa.

The initial steps made it possible to obtain the parameters with maximum precision by using a combination of different analysis windows in succession. The following steps made it possible to record continuously on registers the values obtained on the windows. successive in a coherent order and sequence. Finally, the data could be classified, routed or transmitted. The data thus accessible are of a useful nature for signal processing of any kind. They are reduced and the concepts of suitable data reduction are lossless.

Other characteristics and advantages of the signal analysis and data representation method according to the present invention will become more apparent on reading the description which follows of an example of application of the method.

Or a short sample of 10,224 points sampled at 48 kHz, this sample comprises the sum of four sinusoidal oscillations of varying amplitudes and frequencies.

The origin of this sample will now be described first in order to better highlight the analysis process later.

The sample results from four sinusoidal oscillations constructed from envelopes of specific amplitudes and frequencies and respective zero phases. The duration of the envelopes is 213 ms (10,224 points over 48 kHz of sampling). The temporal resolution of the envelopes is chosen at 5.32 ms, that is to say defined on 40 successive values which change every 5.32 ms.

The respective envelopes for generating the sample are shown graphically in Figures 2, 4, 6, and 8 and numerically below. The amplitude values are arbitrary values on a maximum of 2047, the frequency values are in Hertz. Oscillation # 1 (Envelope graphics: Figure 2):

Amplitude envelope values

2039, 2039, 2039, 2039, 2039, 2039, 2039, 1975,

1895, 1815, 1727, 1647, 1567, 1479, 1399, 1319,

1231, 1151, 1071, 991, 903, 823, 743, 655,

575, 495, 407, 327, 247, 167, 79, 31,

0, 0, 0, 0, 0, 0, 0, 0

Frequency envelope values (Hertz) 440.00, 450.32, 460.63, 470.52, 478.68, 485.56, 490.72, 493.72, 494.58, 493.72, 490.72, 485.56, 478.68, 470.52, 460.63, 450.32, 440.00, 429.61, 409.37, 419.37 , 394.44, 389.28, 386.28, 385.42, 386.28, 389.28, 394.44, 401.32, 409.48, 419.37, 429.68, 440.00, 440.00, 440.00, 440.00, 440.00, 440.00, 440.00, 440.00 The sine wave n ° 1 generated from these envelopes produces the sample of 8,192 points shown in Figures 3A and 3B (points 8,193 to 10,224 not shown are zero).

Oscillation # 2 (Envelope graphics: Figure 4):

Amplitude envelope values

393, 450, 508, 566, 623, 681, 733, 791,

849, 906, 964, 1021, 1074, 1098, 1098, 964,

853, 738, 623, 513, 398, 283, 172, 57,

33, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0 Frequency envelope values (Hertz)

1478.98, 1504.77, 1530.55, 1556.33, 1582.1 1, 1610.47,

1636.25, 1662.03, 1687.81, 1713.59, 1739.38, 1765.16,

1793.52, 1819.30, 1845.08, 1870.86, 1896.64, 1922.42, 1948.20, 1973.98, 2002.34, 2028.13, 2053.91, 2074.53,

1760.00, 1760.00, 1760.00, 1760.00, 1760.00, 1760.00,

1760.00, 1760.00, 1760.00, 1760.00, 1760.00, 1760.00, 1760.00, 1760.00, 1760.00. 1760.00

The sinusoidal oscillation No. 2 generated from these envelopes produces the sample of 8,192 points represented in FIGS. 5A and 5B (the points 8,193 to 10,224 not shown are of zero values).

Oscillation # 3 (Envelope graphics: Figure 6):

Amplitude envelope values

0, 0, 0, 0, 0, 814, 814, 814,

814, 814, 814, 814, 0, 0, 0, 0, 0, 0, 0, 0, 814, 814, 814, 814,

814, 814, 814, 814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Frequency envelope values (Hertz)

7686.25, 7672.50, 7658.75, 7645.00, 7631.25, 7617.50,

7603.75, 7590.00, 7577.97, 7564.22, 7550.47, 7536.72,

7522.97, 7509.22, 7495.47, 7481.72, 7467.97, 7454.22,

7440.47, 7426.72, 7412.97, 7399.22, 7385.47, 7371.72,

7359.69, 7345.94, 7332.19, 7318.44, 7304.69, 7290.94,

7277.19, 7263.44, 7480.00, 7480.00, 7480.00, 7480.00, 7480.00, 7480.00, 7480.00, 7480.00

The sinusoidal oscillation n ° 3 generated from these envelopes produces the sample of 8,192 points represented in Figures 7A and 7B (the points 8,193 to 10,224 not shown are of zero values).

Oscillation # 4 (Envelope graphics: Figure 8):

Amplitude envelope values

544, 522, 498, 476, 454, 430, 408, 384,

362, 338, 316, 274, 274, 274, 274, 274,

274, 274, 250, 206, 162, 118, 72, 28,

10, 6, 6, 6, 6, 6, 6, 6,

0, 0, 0, 0, 0, 0, 0, 0

Frequency envelope values (Hertz)

14105.78, 14104.06, 14102.34, 14100.63, 14098.91,

14097.19, 14095.47, 14093.75, 14092.03, 14090.53,

14088.81, 14087.09, 14085.37, 14083.65, 14081.93,

14080.21, 14078.50, 14076.78, 14075.27, 14073.55,

14071.84, 14070.12, 14068.40, 14066.68, 14064.96,

14063.24, 14061.52, 14060.02, 14058.30, 14056.58,

14054.86, 14080.00, 14080.00, 14080.00, 14080.00,

14080.00, 14080.00, 14080.00, 14080.00, 14080.00

The sinusoidal oscillation n ° 4 generated from these envelopes produces the sample of 8,192 points represented in Figures 9A and 9B (the points 8,193 to 10,224 not shown are of zero values).

The sum of oscillations n ° 1 to n ° 4 produces the sample represented in Figures 10A and 10B which constitutes the sample to be analyzed in this example (the points 8 193 to 10 224 not shown are of zero values). Corresponding values are either integer or floating point depending on preferences. In the example, the data is expressed in 16-bit signed. The first 256 values in Figure 10A are given below. They correspond to the values of the first level 1 window out of 256 values:

0, 5005, 682, 1380, 8562, 7032, 3553, 9602, 12136, 6758, 8890, 14533, 10450, 7860, 13921, 13546, 7830, 11305, 15012, 9340, 8525, 14470, 11940, 7357, 12482, 14509, 8653, 10322, 15902, 11932, 9325, 15567, 15627, 10159, 13788, 17854, 12397, 11457, 17313, 14653, 9509, 13894, 15231, 8357, 8674, 12984, 7659, 3355, 7946, 6542, -573, 1395, 4162, -2500, -4693, 291, -2884, -8550, -4437, -2882, -9440, -8759, -3659, -7983, -1 1409, -5750, -5828, -11804, -8814, -4828, -10412, -11876, -6134, -8575, -13918, - 9652, -7858, -14456, -14116, -9230, -13787, -17733 , -12507, -12771, -19057, -16364, -12282, -17642, -18927, -12640, -14188, -18676, -13368, -10106, - 15205, -13418, -6771, -9455, - 1 1770, -4860, -3300, -8068, -4106, 1319, - 2935, -3571, 3290, 2224, -2258, 2814, 5883, 288, 1242, 7158, 3726, 364, 6298, 7131, 1514, 4614, 9554, 4934, 3850, 10581, 9696, 5305, 10580, 14211, 9146, 10488, 17022, 14253, 11236, 17484, 18715, 13146, 15990, 20719, 15649, 13656, 19410, 17500, 11660, 15294, 17406, 10618, 9989, 14750, 10314, 5443, 10007, 9919, 3022, 4614, 8554, 2909, 327, 5860, 4103, -1626, 2248, 4987, -1174, -1311, 4176, 537, -3841, 1190, 1684, -4941, -3355, 670, -5058, -8122, -3072, -5267, -11761, -8759, -6668, -13567, -14598, -9716, - 13750, -18624 , -13196, -19604, -17702, -12883, -17588, -19660, - 13291, -13826, -18754, -14137, -10120, -15166, -14576, -7939, -10226, - 13745, - 7750, -5818, -11328, -8883, -3490, -7821, -9959, -3700, -4312, -9653, -5584, -1901, -7367, -7374, -1069, -3488, -7267, -1353, 889, -4309, -1535, 4581, 1125, -271, 6937, 7511, 3151, 8118, 12892, 8341, 8899, 15793, 13875, 10125, 15862, 17923, 12142, 13949, 19117, 14537, 1 1595, 17239, 16338, 10228, 13358, 16578, 10466; 9348, 14888, 11890, 6992, 11796, 13362, 7132, 8522

For the rest of the analysis, the different windows are chosen as follows: lengths defined for the first level of short windows typically close to 256 points in succession, for the second level of short windows of variable spacings typically of lengths 1024 points and for the third level of the long windows coordinated with the windows of second level typically of lengths of 2048 points. To simplify, the windows of the three levels are therefore of fixed lengths. The signal shown in Figures 10A and 10B is divided into windows of lengths indicated above. A classic TFR algorithm will be applied to each of the levels.

Beforehand, the windows of selected lengths are weighted as is usually done on TFRs. This weighting removes the discontinuities at the start and end of a window.

Figure 11A represents the first level 1 window including points 0 to 255 of the sample and Figure 11 B represents a weighting window where 'Fpnd' is a typical weighting curve of length equivalent to that of the window, therefore 256 points. The two curves are multiplied point by point to give the final window 'Fech', illustrated in Figure 1 1 C. This weighting process is carried out for each window and it is therefore implicit.

In the example of Figure 11B, a Blackmann-Harris type window (in three terms on 61 db attenuation at the edges of windows) is used. This corresponds to the following equation for 'np' points (256 in Figures 11 A-11 C and in the other first level windows, 1024 points in the second level windows and 2048 in the third windows level):

BH (n) = A - B (cos (2 / 7n / np)) + C (cos (4τrn / np)) or np = 256: Number of points in the window

A = 0.44959: ^1st term constant

B = 0.49364: Constant ^2nd term

C = 0.05677: Constant ^3rd term

This equation gives the following 256 values which correspond to those of a 256-point window as it is represented graphically under 'Fpnd' in Figure 11C, i.e. the following values:

0.0127, 0.0128, 0.0130, 0.0134, 0.0140, 0.0147 0.0156,

0.0167 0.0179 0.0193, 0.0208, 0.0225, 0.0244, 0.0265 0.0287 0.0311,

0.0337 0.0364 0.0425, 0.0458, 0.0493, 0.0529 0.0568 0.0609,

0.0651 0.0696 0.0791, 0.0841, 0.0894, 0.0949 0.1005 0.1064,

0.1 125 0.1188 0.1321, 0.1390, 0.1462, 0.1536 0.1612 0.1690,

0.1771 0.1854 0.2025, 0.2114, 0.2205, 0.2299 0.2394 0.2491,

0.2591 0.2692 0.2901, 0.3008, 0.3117, 0.3228 0.3341 0.3455,

0.3571 0.3689 0.3928, 0.4050, 0.4173, 0.4297 0.4423 0.4549,

0.4677 0.4805 0.5064, 0.5195, 0.5326, 0.5457 0.5588 0.5720,

0.5852 0.5984 0.6246, 0.6377, 0.6508, 0.6637 0.6766 0.6894,

0.7021 0.7147 0.7395, 0.7517, 0.7637, 0.7755 0.7872 0.7986,

0.8099 0.8209 0.8423, 0.8525, 0.8626, 0.8723 0.8818 0.8909,

0.8998 0.9083 0.9243, 0.9318, 0.9390, 0.9458 0.9522 0.9583,

0.9639 0.9692 0.9785, 0.9826, 0.9862, 0.9894 0.9922 0.9946,

0.9965 0.9980 0.9998, 1.0000, 0.9998, 0.9991 0.9980 0.9965,

0.9946 0.9922 0.9862, 0.9826, 0.9785, 0.9740 0.9692 0.9639,

0.9583 0.9522 0.9390, 0.9318, 0.9243, 0.9165 0.9083 0.8998,

0.8909 0.8818 0.8626, 0.8525, 0.8423, 0.8317 0.8209 0.8099,

0.7986 0.7872 0.7637, 0.7517, 0.7395, 0.7272 0.7147 0.7021,

0.6894 0.6766 0.6508, 0.6377, 0.6246, 0.6115 0.5984 0.5852,

0.5720 0.5588 0.5326, 0.5195, 0.5064, 0.4934 0.4805 0.4677,

0.4549 0.4423 0.4173, 0.4050, 0.3928, 0.3808 0.3689 0.3571,

0.3455 0.3341 0.3117, 0.3008, 0.2901, 0.2796 0.2692 0.2591,

0.2491 0.2394 0.2205, 0.21 14, 0.2025, 0.1938 0.1853 0.1771,

0.1690 0.1612 0.1462, 0.1390, 0.1321, 0.1254 0.1188 0.1 125, 0.1064, 0.1005, 0.0949, 0.0894, 0.0841, 0.0791, 0.0742, 0.0696, 0.0651, 0.0609, 0.0568, 0.0529, 0.0493, 0.0458, 0.0425, 0.0394, 0.0364, 0.0337, 0.0311, 0.0287, 0.0265, 0.0244, 0.0225, 0.0208, 0.019 0.0179, 0.0167, 0.0156, 0.0147, 0.0140, 0.0134, 0.0130, 0.0128

The values in each window of the sample are multiplied by the corresponding length weighting window; thus the first 256 points of the sample which correspond to the first short window of first level will be converted as it is graphically represented under 'Fech' in Figure 1 1 C by the following values:

0, 64, 9, 19, 120, 104, 55, 160, 217, 130, 185, 327, 255, 208, 399, 421, 264, 412, 591, 397, 390, 713, 632, 418, 760, 945, 602, 766, 1257, 1004, 834, 1477, 1571, 1081, 1551, 2122, 1554, 1513, 2407, 2143, 1461, 2240, 2575, 1480, 1608, 2517, 1551, 709, 1752, 1504, -137, 348, 1078, -673, -1312, 84, -868, -2665, -1432, -963, -3262, -3128, -1350, -3040, -4482, -2329, -2432, -5073 , -3898, -2196, -4870, -5707, -3027, -4343, -7230, -5140, -4288, -8079, -8074, -5401, -8250, -10844, -7812, -8144, - 12401, -10861, -8310, - 12163, -13289, -9034, -10317, -13811, -10048, -7718, -11792, -10563, -5408, -7658, -9662, -4042, -2779, -6878, -3542, 1151, -2588, -3181, 2960, 2020, - 2069, 601, 5482, 270, 1175, 6816, 3570, 351, 6104, 6946, 1481, 4534, 9422, 4882, 3820, 10524 , 9662, 5295, 10571, 14208, 9146, 10486, 17007, 14225, 11197, 17389, 18569, 13007, 15769, 20358, 15313, 13302, 18812, 16868, 11173, 14563, 16463, 9970, 9308, 13634, 9453 , 4944, 9004, 8837, 2665, 4025, 7378, 2480, 275, 4874, 3368, -1317, 1795, 3926, -910, -1001, 3139, 397, -2793, 851, 1182, -3406, -2270, 445, -3291, -5180, -1919, -3221, -7037, - 5126, -3814, -7582, -7966, -5174, -7143, -9432, -6838, -6341, -9169, -8053, -5698, -7558, -8204, -5383, -5431, -7141, -5215, -3614, -5240, -4870, -2563, -3188, -4135, -2248, -1627, -3050, -2302, -870, -1872, -2289, -816, -912, - 1955, -1082, -352, -1305, -1247, -172 , -536, -1063, -188, 117, -540, -182, 515, 120, -27, 658, 671, 265, 642, 957, 580, 580, 961, 788, 536, 781, 820, 516 , 549, 696, 489, 361, 495, 432, 250, 301, 345, 202, 167, 248, 186, 103, 165, 180, 93, 109.

Alternatively, other types of weighting window can be used, such as Hamming and Blackmann.

Then, each weighted window is transformed into frequency domain by a general Fourier transform on the 'np' points of the sample 'ECH'. This results in a 'Spec' spectrum of 'nf points (128) where:

nf = np / 2, and

SPEC [0..nf-1] = TFR (FECH [0..np-1]).

Since the top level windows in the example are 256 points, this results in 'Spec' spectra of 128 values. The second level windows in the example are 1024 points and thus give 'Spec' spectra of 512 values. Finally, the third level spectra in the example are 2048 points and they therefore give 'Spec' spectra of 1024 values. In the present example, considering the respective window lengths, there are four first level windows for a second and third level window. The analysis sequence comprises different stages which are carried out in order on the basis of 1024 point windows comprising four first level windows. The sequence of steps which follow is therefore carried out entirely on the steps for a given window, then the following as the sample is read:

• Analysis on four windows (4 x 256 points) of first level and calculations of transitions, positioning of windows of second and third levels;

• Analysis on second level windows (in the example 1024 points) and calculations of the amplitudes and (temporary) frequencies of the peaks;

• Analysis on a third level window (in the example 2048 points) and calculations of the frequency values of the peaks;

• Allocation of registers for peaks so as to take account of the preceding passages by assigning compatible peaks to the same registers as in the passage from the previous window; and

• Data processing by converting them from absolute values to variation values, extraction of relevant data and sequencing and weighting of data on their binary weights.

Analysis on Windows of first level:

An analysis on first level windows is therefore firstly carried out in order to detect transients of the signal to be analyzed. These transients will then be used to position the windows of higher level (s). The weighted analysis windows are shown for the successive first level windows in Figures 12A to 12D on the curves 'Fech n ° 0' to 'Fech n ° 31'.

The first level analysis is performed on successive and contiguous short windows (in the example 256 points). A TFR will be performed on each of these to then deduce the second and third level windows.

Thus the sample, of which the 8,192 non-zero points are represented graphically in FIGS. 10A to 10D, is divided into 32 windows of 256 points, each window being weighted as described above.

The 'Fech' curves of Figures 12A to 12D show the 32 windows identified from 'n ° 0' to 'n ° 31', the figure on the left of each curve gives the index of the start point of the window and the one on the right gives the index of the window end point. For example, the window 'Fech n ° 6' in Figure 12A starts and ends respectively at the sample points (1536) and (1791). Since the second level windows were chosen to be 1024 points long in the example, four first level windows will be required to determine the starting point of each second level window. In particular the first level windows n ° 0 to n ° 3 will determine the starting point of the second level window n ° 0, the first level windows n ° 4 to n ° 7 will determine the starting point of the second window level # 1, and so on. A TFR function is applied to each first level window, according to the following function:

SPEC [0..127] = TFR (FECH [0..255])

For example, the first weighted window of first level whose 256 values are displayed previously and corresponding to the curve 'Fech n ° 0' of Figure 12A will give 128 values which correspond to the curve 'Spec n ° 0' of Figure 12A ; the values are these:

440, 5824, 16690, 13923, 3071, 20, 303, 2173, 3422, 1644, 137, 12, 11, 9, 9, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 122, 1908, 4673, 3400, 613, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 6, 4.2, 1,1,1,1, 2,2,2,2,2, 2,2,1,2,2,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1, 1, 1.1

On the curve 'Spec n ° 0' in Figure 12A, each value corresponds to the amplitude of the harmonic content of a given frequency band. As in the example, the sample rate of the sample is 48,000 Hz, the maximum frequency is 24,000 Hz. Since the window is 256 points and the spectrum is distributed linearly in 128 values, the last band, one hundred and twenty-eighth, is 24000 Hz. Each band is 187.5 Hz or 1 ^st band of 0 Hz to 187.5 Hz, the second from 375 Hz to 187.5 Hz, the third from 375 Hz to 562.5 Hz, etc. In FIG. 12A and the preceding values, three peaks are observed on the spectrum, that is to say on the third band at the value 16690 (375 - 562.5 Hz), the ninth band at the value 3422 (1500-1688 Hz), the seventy-sixth strip to the value 4673 (14 062.5 - 14 250 Hz). At the frequency envelopes which determined the sample, the values of the spectrum correspond approximately to the first points of the envelopes of the four oscillations which produced the analyzed signal, i.e. according to the values indicated above:

Signal Signal Spectrum Spectrum Frequency

Amplitude Frequency Amplitude

1 2 039 440.00 Hz 16 690 375-562.5 Hz

2,393 1,478.98 Hz 3,422 1,500-1688 Hz

30

4 544 14 105.78 Hz 4 673 14 062.5-14 250 Hz

On the first level analysis windows, the data collected is used to observe the changes on the successive spectra, in this case the transitions so that the second and third level analysis windows are aligned with the start of the first level with the largest variations. Therefore, according to the window lengths of the example, that is to say 256 points (first level) and 1024 points (second level), the start of each second level analysis window is chosen from the four first level windows of which sample points match. For example, the start of the first second level window is aligned at points 0 or 256 or 512 or 768, as the first four first level windows are at points (0..255), (256..511), ( 512..767), (768..1023) respectively.

To determine the nature of the transitions on the successive first level spectra, the respective amplitudes of the 128 frequency bands are compared individually on the successive spectra. A given spectrum is thus compared with the previous one, the amplitude of each band is subtracted from the corresponding band of the previous spectrum. On a given spectrum, the results are put in absolute and added on a register named 'sdif. In order to weight the results, the amplitude values of a given spectrum are also added to a second register called 'tspc'. The calculation of the two registers corresponds to these two equations. The result of a spectrum of transitions' tdif on a given spectrum consists of the division of sdif by tspc. In the example, the values' tdif are arbitrarily multiplied by a constant, that is 16 384. In the case of the initial spectrum (n ° 0), as there is no previous spectrum, 'sdif is equal to' tspc ', since the previous values are necessarily zero. The calculation of transitions therefore follows these three equations:

127 sdif = \ SPEC [s, n] - SPEC [s - 1, n]; n = 0

127 tspc ≈ ∑SPEC [s, n];

11 = 0

vtrn = sdif * 16384 / tspc;

For the first level spectra the respective values of 'vtrn' are

n ° 0: 16 384, n ° 1: 1299, n ° 2: 1107, n ° 3: 1174 n ° 4: 1063, n ° 5: 4160, n ° 6: 975, n ° 7: 1102, n ° 8: 1217, n ° 9: 1262, n ° 10: 1321, n ° 11: 1377, n ° 2, 6 008, n ° 13: 1424, n ° 14: 1523, n ° 15: 1819, n ° 6 1765, n ° 17: 1996, n ° 18: 2 402, n ° 19: 2 698, n ° 20. 7830, n ° 21: 2 442, n ° 22: 2 768, n ° 23: 3 310, n ° 2 2485, n ° 25: 2 254, n ° 26: 1978, n ° 27: 1923, n ° 28, 58 285, n ° 29: 8 141, n ° 30: 16 739, n ° 31: 21 074 These values are also shown to the right of the 'Spec' curves in Figures 12A to 12D. The values which determine the starting points of the second level windows are in the example every four first level spectra and they are framed in Figures 12A to 12D. Thus the first level spectra numbered respectively 0, 5, 9, 12, 19, 20, 24 and 28 comprising the higher values of 'vtrn' in the sections of four spectra will determine the starting points of the second level windows.

Analysis on second level windows:

As will become evident on reading this section concerning the analysis of the signal on second level windows, this analysis will be used for the calculation of the amplitudes and for the summary calculation of the frequencies of the components of the signal to be analyzed.

In the present example, the size of the second level analysis windows is 1024 sample points. As for the first level windows, the second level analysis is carried out on successive windows, but the positions of these, determined by their respective starting point, are determined by the results of the first level analyzes, in the occurrence by choosing, as a starting point, the same as for the first level window which has the maximum of transitions (the value 'vtrn' higher) among four contiguous windows whose points cover 1024 points. In the present example, eight second level windows will therefore be chosen. The following table summarizes the positions of the second level windows according to the values obtained previously: Windows Window Starting point Windows

First Level Selected Second Level

0-3 0 0 0

4-7 5 1,280 1

8-11 9 2 304 2

12-15 12 3,072 3

16-19 19 4 864 4

20-23 20 5 120 5

24-27 24 6 144 6

28-31 28 7 168 7

The second level windows are weighted in the same way as the first level windows, but on a BH (n) function of 1024 points:

Is :

np = 1024: Number of points in the window

A = 0.44959: ^1st term constant

B = 0.49364: Constant ^2nd term

C = 0.05677: Constant ^3rd term

BH (n) = A - B (cos (21fn / np)) + C (cos (4Hn / np)).

Figures 13A to 13D represent on the curves identified 'Fech n ° 0' to 'Fech n ° 7', the eight second level windows. The relative sample points are indicated on the left-right border of the 'Fech' curves (see for example on 'Fech n ° 0', points 0 to 1023).

Then each weighted window is transformed into frequency domain by a general Fourier transform either on 'np' points (1024) of a 'FECH' sample giving a 'Spec' spectrum of 'nf points (512) where: SPEC [0..511] = TFR (FECH [0..1023])

The spectra relating to the eight second level windows are represented in FIGS. 13A to 13D on the curves identified 'Spec n ° 0' to 'Spec n ° 7'. The 512 specific values on the spectrum of window n ° 0 or 'Spec n ° 0' are in particular:

8170, 8170, 8170, 9754, 6949, 30550, 40054, 47105, 752714, 3449255, 4314478, 1627141, 123139, 34911, 38661, 13029, 8618, 15263, 10179, 4478, 7395, 9401, 7297, 2060, 6963, 6148, 5243, 1119, 4344, 3831, 51973, 365762, 964172, 857105, 269424, 51957, 37692, 34159, 8374, 6560, 15501, 11249, 2596, 41 12, 8839, 6130, 1139, 3103, 5720, 3889 , 655, 2480, 3858, 2572, 656, 2114, 2698, 1734, 758, 1829, 1868, 1194, 787, 1674, 1353, 968, 736, 1546, 1015, 917, 625, 1495, 852, 919, 518 , 1393, 746, 903, 433, 1300, 703, 845, 365, 1180, 675, 735, 344, 1042, 632, 640, 353, 888, 584, 584, 353, 716, 515, 518, 349, 565 , 463, 534, 360, 436, 420, 552, 377, 338, 420, 554, 400, 295, 460, 540, 422, 279, 528, 499, 424, 244, 573, 460, 443, 245, 639 , 404, 464, 225, 651, 337, 438, 194, 636, 273, 422, 176, 617, 221, 392, 167, 594, 193, 368, 188, 575, 180, 372, 180, 579, 176 , 379, 196, 603, 189, 394, 176, 620, 202, 428, 142, 622, 222, 454, 117, 624, 235, 471, 88, 614, 250, 478, 63, 562, 235, 459 , 46, 513, 237, 4 45, 70, 492, 261, 459, 78, 488, 282, 464, 78, 478, 308, 473, 71, 477, 344, 489, 77, 506, 415, 506, 77, 512, 432, 499, 100, 485, 460, 483, 123, 478, 496, 465, 121, 483, 500, 430, 124, 482, 524, 428, 106, 497, 543, 410, 108, 497, 558, 430, 105, 519, 575, 455, 109, 530, 589, 456, 147, 537, 631, 471, 175, 541, 650, 486, 182, 542, 690, 484, 208, 549, 722, 494, 207, 559, 766, 520, 198, 592, 833, 549, 222, 622, 892, 561, 225, 678, 990, 644, 254, 747, 1094, 705, 268, 850, 1242, 764, 309, 967, 1441, 863, 368, 1151, 1694, 980, 399, 1375, 2040, 1133, 513, 1792, 2635, 1437, 660, 2555, 3780, 2008, 1061, 4315, 6829, 2896, 111315, 739100, 1146112, 534791, 46672, 6803, 9815, 4943, 914, 3241, 4308, 2385, 507, 2114,2725, 1583,357,1580, 1982, 1183,271, 1287,1571,947,201, 1069, 1291, 806, 183, 959, 1104, 690, 154, 857, 959, 619, 138, 787, 842, 556, 94, 686, 721, 506, 88, 627, 614, 448, 65, 538, 507, 395, 51, 443, 393, 303, 25, 322, 285, 233, 35, 235, 196, 174, 20, 166, 131, 125, 27, 132, 97, 103, 24, 108, 76, 89, 36, 68, 45, 60, 39, 57, 37, 49, 48, 49, 44, 62, 29, 51, 34, 49, 35, 51, 33, 50, 34, 53, 28, 60, 23, 54, 37, 49, 38, 45, 36, 47, 40, 43, 47, 37, 43, 46, 33, 53, 33, 48, 41, 37, 54, 34, 41, 50, 38, 46, 35, 51, 36, 47, 37, 45, 40, 47, 40, 50, 32, 55, 36, 48, 37, 47, 42, 38, 51, 40, 52, 32, 55, 37, 43, 47, 39, 47, 42, 45, 47, 37, 52, 44, 42, 49, 41, 40, 53, 35, 46, 46, 44, 47, 45,

40, 50, 41, 48, 41, 44, 48, 45, 38, 40, 55, 40, 51, 37, 47, 51, 35, 52, 40, 44, 40, 50, 39, 47, 46, 44, 42, 45, 47, 43, 38, 58, 31, 54, 45, 42, 45, 44, 40, 55, 36, 52

On 512 frequency bands, the second level spectra have a resolution of 46.875 Hz (24,000 Hz / 512). Each value of the spectrum is associated with a specific band. On each spectrum, the maximums are observed and on a given spectrum are retained the values beyond a threshold which is proportional to the maximum peak of the spectrum in question. For example, for spectrum No. 0, the maximum is detected on the eleventh band, ie the value 4314478. The value of the peak detection threshold may vary, depending on the desired resolution. In the example, the threshold is chosen so that only the values greater than 64 times less than the value of the maximum peak are retained, i.e. values beyond 67,414 (4,314,478 / 64). In the spectrum in question, three peaks meet this criterion, either on the eleventh band at the value 4 314 478 (469 - 516 hz), at the thirty-third band at the value 964 171 (1500-1547 hz), and at the three hundred and second strip at the value 1 146 112 (14 109-14 156 Hz). At the frequency envelopes which determined the sample, the values of the initial spectrum of 1024 points (21 ms duration) correspond to the means of the first four points (4 x 5.32 ms) of the envelopes of the four oscillations which produced the analyzed signal.

The first four points of the frequency envelopes of the oscillations which produced the sample are respectively:

Oscillation 1: average 455 Hz (440.00, 450.32, 460.63,

470.52) Oscillation 2: average 1518 hz (1478.98, 1504.77,

1530.55, 1556.33) Oscillation 3: Zero amplitude on the first four points Oscillation 4: average 14 103 hz (14 105.78, 14 104.06,

14 102.34, 14 100.63)

Signal Signal Spectrum Spectrum Frequency Amplitude Frequency Amplitude

1 2 039 455 Hz 4 314 478 469-516 Hz 2 393 1518 Hz 964 171 1500-1547 Hz 3 0

4,544 14,103hz 1,146,112 14,109 -14,156 hz

The values of the amplitudes and frequencies (temporary, the final calculation being made on the level 3 spectra) which will be associated with the peaks of the set of second level spectra will be calculated by interpolations on the respective spectra so as to obtain an accuracy higher level.

Let the calculation of the amplitude and frequency values on the peaks of the second level spectra for each peak: npic: band number of the peak n: index

SPEC [n]: amplitude value on the FBASE peak: band frequency 48.875 Hz (sampling 48 kHz / Points 1024)

npic + \

AMP = ∑SPEC [n] 13; n = npic-

npic + 2

SPEC [n]

FRE = n≈npic — 2 npic + 2

∑SPEC [n] ιι = npic — 2

The calculation of the first peak for example will give these values determined from the values around the ninth band as it is displayed previously for the spectrum of window 0 on 512 values from the first to the five hundred and twelfth band:

AMP = ((SPEC [9] + SPEC [10] + SPEC [1 1]) / 3 AMP = (3449 255 + 4 314 478) + (1 627 141) / 3 AMP = 1 310 291

FRE = ((8) SPEC [8] + (9) SPEC [9d + (10) SPEC [10] + (11) SPEC [11] + 12) SPEC [12]) * FBASE / (SPEC [8] + SPEC [9] + SPEC [10] + SPEC [11] + SPEC [12])

FRE = ((8 * 752 714) + (9 * 3 449 255) + (10 * 4 314 478) + (11 * 1 627 141) + (12 * 123 139)) * (12 * 123 139)) * (12 * 123 139)) * 48.875 / (752 714 + 3 449 255 + 4 314 478 + 1 627 141 + 123 139) FRE = 454.68 Hz

We thus obtain the respective values of amplitudes and frequencies for the spectrum n ° 0 of the windows of second level in comparison with the average values of the envelopes.

Signal Signal Spectrum Spectrum Fréc Amplitude Frequency Amplitude

1 2,039,455 Hz 3,130,291,454.68 Hz 2,393 1,518 Hz 729,012 1,517.31 Hz 3 0

4 544 14 103 Hz 806 667 14 103.31 Hz

The peaks are listed in order for each spectrum. Thus for the eight second level spectra, we obtain the following values of amplitudes and frequencies (in hertz):

Peak

1 P / cn ° 2 Pic n ° 3 Pic n ° 4

Spectrum n ° 0 Amp. 3,130,291,729,012,806,667

Freq. 454.68 1,517.31 14,103.31 Spectrum n ° 1 Amp. 2,966,943 1,191,627 1,292,901,613,798

Freq. 491.52 1648.42 7596.90 1 409 4.83 Spectrum no. 2 Amp. 2,542,991 1,512,754 1,282,781,446,193

Freq. 488.13 1,750.96 7,542.26 14,089, 17 Spectrum # 3 Amp. 2,282,733 1,727,397 415,120

Freq. 467.53 1,831.89 14,082.60 Spectrum no. 4 Amp. 1 297 155 540 594 1 288 219 223 889

Freq. 399.95 2,011.09 7,407.29 14,070.80 Specter # 5

Amp. 1,196,053,355,556 1,266,767 155,037

Freq. 392.47 2,031.72 7,392.64 14,069.34

Specter # 6

Amp. 724 616 1 235314

Freq. 386.15 7339.66

Specter # 7

Amp. 202 874

Freq. 411.06

Analysis on Third Level Windows:

The analysis of the signal on third level windows will be used to calculate the frequencies of the components of the signal to be analyzed.

The size of the third level analysis windows is fixed in this example at 2048 sample points. Like the windows of first and second levels, they are carried out on successive windows and their positions, i.e. their respective starting points are the same as on the equivalent windows of the second level analyzes. Thus, each second level analysis window corresponds to a third level analysis window. In this example, we can therefore choose eight third level analysis windows next to the eight second level analysis windows.

The third level windows are weighted in the same way as the first and second level windows but on a BH (n) function of 2048 points.

Is

np = 2,048: Number of points in the window A = Constant 0.44959 ¹ 0.49364 term B = Constant ^2nd term C = 0.05677 Constant ^3rd term

BH (n) = A - B (cos (21Jn / np)) + C (cos (41Jn / np))

The frequencies are calculated in the same way as on the second level analysis results, ie by interpolation of values around the peaks. On 2,048 points, the frequency resolution is 23.4375 Hz (24,000 / 1,024) on the spectra which will be obtained. As the frequency distribution of the spectrum is linear, this frequency resolution is insufficient in the low frequencies. On the other hand, a window of more than 2048 points will be too long and the detection of variations in components in amplitude or in frequency would then be weak. To overcome this problem of precision on the components of low frequencies, without lengthening the window, two separate analyzes will be carried out on each window of third level, either a first analysis (standard) to determine the elements of high frequencies and a second analysis ( range) to determine the elements of low frequencies.

Figures 14A to 14H show on the curves identified 'Fech n ° 0' to 'Fech n ° 7' the eight third level windows. The relative sample points are indicated at the left-right border of the 'Fech' curves, as for example on 'Fech n ° 0' points 0 to 2047. FIG. 14A in particular corresponds to the first window of third level. The 'Fech' windows constitute the inputs to the first standard type analyzes, the results of which will be indicated on the 'Spec' curves in Figures 14A to 14H. The third level 'Fech' windows are modified to eliminate high frequency elements. In the example, we choose to consider the high-low frequency limit at 6,000 Hz, which is a quarter of the bandwidth of the standard spectrum, which is 24,000 Hz in the example. This process takes place in two stages.

The first step is to filter each 'Fech' window by a Low Pass, the cutoff frequency (FC) of which is set at 6000 Hz, for example a fourth-order IIR type filter (n = 4), that is:

FFLT [θ..204l] = IIR (FECH [Q..2047_)

The second step consists in compressing the 'Fech' window from 2,048 to 512 points, or a quarter according to the ratio of the bandwidth used, and adding zeros before and after the compressed window to bring it back to 2,048 points, or 768 zeros before and after.

The 'Fxe' curves in Figures 14A to 14H represent the 'Fech' windows thus modified, either on 'n' and 'm' at 2048 points:

0 \ n: 0..161

FXE [n] = FFLT [m 14] | n: 768 + (m 14) over m: 0..2047;

0 l ”: 1280..2047

Each weighted 'Fech' window is transformed into frequency domain by a general Fourier transform on 'np' points (2048) of a 'Fech' sample giving a 'Spec' spectrum of 'nf points (1024) or :

SPEC [0..1023] = TFR (FECH [0..2047])

Each modified 'Fxe' window is transformed into a frequency domain by a general Fourier transform on 'np' points (2048) of a 'Fxe' sample, resulting in a 'SP of' nf points (1024) spectrum where:

SPX [0..1023] = TFR (FXE [0..2047])

The spectra relating to the eight third level windows are represented in FIGS. 14A to 14H on the curves identified 'Spec n ° 0' to 'Spec n ° 7'. The 1024 specific values on the spectrum of window n ° 0, namely 'Spec n ° 0', are in particular:

7314, 7314, 7314, 17577, 30677, 22546, 9269, 6210, 6098, 4795, 4866, 32583, 71452, 52691, 18430, 9998, 21923, 172619, 1004029, 4368138, 8557792, 6218562, 1841 102, 251450, 18918 , 2831, 21545, 29647, 54632, 42273, 21326, 5292, 6588, 1800, 12100, 14470, 5762, 7904, 9490, 4634, 7573, 2316, 9780, 14907, 6941, 1563, 6927, 4690, 8121, 4176 , 6846, 12978, 10023, 5550, 6507, 4620, 5856, 10926, 8755, 1171 1, 6798, 21817, 49088, 147299, 423530, 950401, 1553248, 1870421, 1679155, 1127268, 568087, 236240, 81746, 60037, 57131, 70564, 60158, 40983, 18478, 19968, 5905, 14128, 25633, 24700, 22081, 15312, 8620, 12883, 7286, 8946, 16464, 16447, 14529, 10641, 6953, 10573, 8032, 6953, 12463, 13524, 12400, 9508, 6181, 9119, 8370, 6340, 10164, 11955, 11643, 9356, 5855, 8076, 8524, 6343, 8691, 10887, 11372, 9654, 6049, 7332, 8521, 6692, 7811, 9970, 11064, 9946, 6496, 6924, 8486, 7143, 7502, 9234, 10622, 101 10, 7087, 6816, 8397, 7484, 7537, 8767, 10143, 10158, 7579, 6851, 8340, 7714, 7728, 8585, 9735, 10098, 7992, 6954, 8293, 7876, 7972, 8601, 9379, 9969, 8302, 7076, 8263, 7947, 8143, 8747, 9196, 9916, 8670, 7248, 8289, 8067, 8292, 8949, 9195, 9986, 9102, 7519, 8352, 8235, 8497, 9160, 9247, 10103, 9606, 7947, 8517, 8474, 8792, 9436, 9389, 10264, 10110, 8506, 8826, 8800, 9133, 9752, 9602, 10478, 10662, 9222, 9338, 9201, 9596, 10237, 9927, 10730, 11168, 9976, 10008, 9716, 10117, 10842, 10389, 11055, 11629, 10710, 10814, 10373, 10686, 11533, 11029, 11561, 12159, 11456, 11714, 11152, 11306, 12339, 11900, 12314, 12840, 12263, 12741, 12140, 12037, 13190, 12896, 13252, 13704, 13189, 13865, 13340, 13006, 14195, 14017, 14437, 14873, 14339, 15206, 14809, 14228, 15435, 15419, 15914, 16380, 15827, 16824, 16584, 15847, 16996, 17111, 17768, 18327, 17753, 18827, 18765, 17982, 19108, 19282, 20055, 20741, 20210, 21466, 21593, 20829, 22006, 22257, 23200, 24057, 23571, 25039, 25364, 24672, 26040, 26397, 27602, 28697, 28245, 30046, 30655, 30154, 31982, 32611, 34242, 35786, 35414, 37791, 38942, 38850, 41591, 42865, 45433, 47891, 47802, 51394, 53727, 54714, 59741, 63005, 68027, 729 52, 74415, 81615, 87815, 93346, 107346, 121429, 138527, 155242, 173480, 206068, 250229, 389452, 637410, 843218, 879464, 742075, 540594, 383167, 284461, 223049, 182695, 147443, 125713, 1139 102832, 96223, 87625, 80209, 75647, 67823, 63097, 60274, 56113, 54589, 51376, 48608, 47545, 43966, 41983, 40733, 38288, 37807, 36051, 34680, 34540, 32392, 31361, 30690, 28963 28775, 27603, 26882, 27052, 25516, 24899, 24497, 23198, 23136, 22235, 21881, 22213, 21032, 20613, 20342, 19304, 19275, 18503, 18373, 18824, 17852, 17559, 17353, 16499, 16489, 15786, 15807, 16337, 15483, 15281, 15104, 14368, 14392, 13704, 13855, 14462, 13645, 13493, 13368, 12738, 12739, 12044, 12275, 12932, 12185, 12080, 11989, 11407, 11409, 10714, 10955, 11688, 10983, 10914, 10873, 10356, 10362, 9636, 9883, 10674, 9979, 9902, 9908, 9494, 9488, 8708, 8962, 9820, 9181, 9064, 9060, 8733, 8764, 7944, 8167, 9069, 8491, 8386, 8342, 8065, 8136, 7289, 7511, 8476, 7942, 7809, 7716, 7477, 7596, 6741, 6929, 7909, 7430, 7345, 7182, 6927 , 7100, 6249, 6440, 7424, 6978, 6952, 6747, 6478, 6674, 5801, 5971, 6980, 6579, 6601, 6382, 6062, 6274, 5382, 5540, 6592, 6204, 6279, 6066, 5721, 5930, 5022, 5184, 6231, 5813, 5916, 5720, 5403, 5618, 4654, 4804, 5920, 5498, 5605, 5420, 5116, 5340, 4325, 4459, 5630, 5236, 5373, 5145, 4834, 5049, 3977, 4140, 5393, 4991, 5152, 4895, 4615, 4832, 3639, 3822, 5189, 4763, 4944, 4679, 4401, 4619, 3309, 3468, 4960, 4558, 4777, 4476, 4213, 4427, 2959, 3170, 4808, 4332, 4623, 4317, 4041, 4253, 2591, 2796, 4616, 4114, 4473, 4128, 3876, 4118, 2203, 2400, 4498, 3949, 4336, 3944, 3699, 3986, 1812, 1899, 4338, 3733, 4215, 3757, 3501, 3863, 1435, 1347, 4220, 3540, 4150, 3558, 3329, 3814, 1377, 621, 4096, 3317, 4150, 3381, 3092, 3774, 1979, 844, 4076, 3005, 4234, 3178, 2857, 3853, 3863, 2879, 4296, 2437, 4426, 2972, 2563, 4110, 8895, 8211, 4976, 1897, 3148, 3809, 11820, 419483, 1709959, 1917647, 637492, 38064, 6365, 3764, 4339, 3991, 19064, 20063, 8424, 4819, 2343, 3915, 3939, 2596, 10286, 10739, 5240, 4237, 2564, 3514, 3503, 2517, 7497, 7932, 4322, 39 25, 2667, 3284, 3252, 2459, 6091, 6559, 3888, 3666, 2668, 3095, 3059, 2385, 5234, 5732, 3605, 3495, 2726, 3026, 2928, 2335, 4658, 5178, 3416, 3343, 2722, 2945, 2887, 2321, 4210, 4773, 3279, 3217, 2698, 2846, 2815, 2312, 3853, 4461, 3180, 3116, 2692, 2786, 2781, 2301, 3565, 4192, 3069, 3010, 2679, 2720, 2708, 2306, 3307, 3930, 2947, 2852, 2602, 2562, 2574, 2238, 3001, 3620, 2790, 2677, 2477, 2322, 2300, 2064, 2565, 3139, 2449, 2300, 2196, 1981, 1963, 1797, 2059, 2543, 1997, 1807, 1814, 1592, 1542, 1456, 1564, 1969, 1573, 1357, 1403, 1180, 1157, 1132, 1098, 1420, 1167, 982, 1097, 875, 823, 858, 773, 1016, 845, 664, 811, 634, 595, 640, 528, 742, 637, 451, 608, 450, 418, 493, 353, 532, 467, 303, 467, 329, 289, 390, 261, 384, 363, 194, 354, 257, 222, 312, 176, 290, 284, 105, 266, 218, 182, 230, 101, 207, 223, 74, 243, 139, 110, 201, 76, 157, 183, 26, 182, 128, 88, 174, 57, 133, 144, 16, 144, 90, 60, 148, 62, 119, 122, 30, 143, 77, 72, 128, 64, 101, 119, 34, 117, 81, 53, 118, 56, 86, 114, 45 , 104, 80, 65, 102, 63, 80, 102, 50, 94, 81, 61, 92, 76, 72, 91.51, 99, 68, 71, 86, 71, 64, 87, 68, 69 , 91.61, 82, 68, 69, 84, 73, 75, 67, 81, 78, 67, 75, 67, 79, 74, 61, 77, 76, 70, 73, 79, 67, 71, 74, 59, 86, 60, 76, 69, 60, 90, 54, 78, 66, 75, 69, 67, 69, 71, 68, 75, 59, 80, 60, 73, 67, 68, 70, 69, 67, 67,

69, 77, 62, 70, 61, 85, 54, 67, 73, 69, 66, 64, 65, 69, 70, 63, 69, 64, 78, 52, 70, 76, 54, 74, 66, 65, 77, 51, 72, 66, 72, 58, 69, 62, 72, 56, 76, 61, 63, 70, 61, 73,

70, 53, 71, 62, 74, 58, 64, 74, 73, 55, 75, 56, 72, 53, 81, 63, 62, 58, 73, 61, 74, 59, 60, 74, 58, 65, 70, 52, 76, 61, 67, 54, 69, 78, 48, 69, 68, 64, 67, 61, 66, 61, 65, 68, 53, 80, 49, 75, 50, 80, 56, 62, 69, 58, 62, 74, 54, 73, 55, 68, 58, 69, 60,

65, 64, 67, 66, 56, 70, 63, 70, 70, 48, 68, 66, 71, 46, 78, 55, 68, 61, 67, 62, 62,

66, 60, 74, 57, 65, 59, 66, 76

The spectra relating to the eight third level windows modified for the low frequencies are represented in FIGS. 14A to 14H on the curves identified 'Spx n ° 0' to 'Spx n ° 7'. The 1024 specific values on the spectrum of window n ° 0, i.e. 'Spx n ° 0', are in particular:

7323, 7323, 7323, 7323, 7323, 7323, 7323, 7323, 7323, 4942, 9232, 13458, 17956, 22787, 26453, 28673, 30856, 33183, 33420, 29761, 22996, 15842, 10289, 6992, 9337 14344, 16371, 13290, 6278, 2849, 7318, 7884, 6354, 6956, 7020, 2923, 4850, 12483, 15986, 13038, 5054, 8863, 19158, 26930, 32961, 39893, 49391, 60934, 72028, 78863, 78020, 68642, 53399, 37361, 25349, 19528, 18551, 18302, 15156, 10026, 10058, 12394, 9846, 9698, 21940, 40514, 69416, 112745, 173558, 265921, 417448, 656262, 1010049, 1520235, 2241113, 3208532, 4399399, 5712660, 6981898, 8012892, 8632993, 8736606, 8312340, 7443430, 6282146, 5007588, 3781386, 2715564, 1861436, 1219623, 762002, 451936, 254185, 136489, 70532, 35543, 1899 2951, 7623, 13034, 17676, 21492, 24935, 27306, 28072, 29527, 35102, 43707, 51270, 55125, 54906, 51710, 47076, 42302, 37911, 33397, 27953, 21670, 15782, 11405, 8077, 5122, 4487, 6244, 7183, 6841, 6245, 5648, 4120, 1867, 3420, 6443, 9075, 11952, 15140, 17382, 17331, 14658, 10225, 5760, 41 10, 5877, 7662, 8345, 7999, 7707, 8624 ,. 10028, 10520, 9683, 8078, 6493, 5221, 4441, 4796, 6030, 7171, 7810, 7876, 7119, 5204, 2181, 1425, 4718, 7357, 9561, 1 1747, 13786, 15070, 15132, 13960, 11883 , 9337, 6771, 4610, 3016, 1735, 1652, 3515, 5489, 6762, 7081, 6622, 5792, 4974, 4496, 4698, 5663, 7047, 8340, 9002, 8565, 6827, 4000, 671, 2452, 4892 , 6666, 8228, 9956, 11729, 13081, 13590, 13086, 1 1706, 9844, 8012, 6647, 5913, 5668, 5695, 5898, 6258, 6631, 6711, 6266, 5356, 4348, 3724, 3803, 4615, 5963, 7539, 9052, 10238, 10828, 10653, 9871, 9031, 8719, 9110, 10045, 11127, 11613, 10757, 8458, 5906, 6581, 11232, 17048, 21516, 21666, 15193, 8084, 25177, 48590, 70791, 90758, 112967, 144625, 189992, 249719, 324411, 415720, 524473, 649190, 786684, 933428, 1085920, 1239848, 1389303, 15271 15, 1646123, 1740434, 1805909, 1839949, 1651, 1941, 459288 1538280, 1405297, 1260877, 1110864, 960946, 816535, 682004, 559938, 451697, 359280, 285999, 233120, 194798, 160004, 121387, 80772, 50325, 46632, 56026, 59037, 53849, 47163, 47593, 55662, 64763, 70332, 71364, 69086, 65561, 62445, 60292, 58641, 56494, 52860, 47318, 40351, 33132, 26794, 21796, 18179, 16323, 16577, 18075, 19222, 18785 16198, 11599, 5927, 3101, 7193, 11060, 13908, 16392, 19117, 22061, 24677, 26332, 26656, 25740, 24120, 22520, 21492, 21165, 21217, 21023, 19969, 17839, 15017, 12294, 10305, 9101, 8530, 8725, 9720, 11090, 12253, 12690, 1 1994, 10027, 7153, 4610, 4703, 6758, 8805, 10536, 12188, 13917, 15585, 16845, 17356, 17011, 16031, 14881, 14030, 13703 , 13749, 13731, 13197, 11977, 10334, 8812, 7792, 7216, 6963, 7175, 7925, 8963, 9934, 10520, 10426, 9476, 7816, 6067, 5244, 5758, 6859, 7994, 9127, 10355, 11643 , 12769, 13456, 13547, 13123, 12474, 11932, 11674, 1 1628, 11534, 1 1 104, 10225, 9059, 7942, 7099, 6506, 6147, 6200, 6756, 7608, 8464, 9093, 9284, 8886, 7950, 6823, 6031, 5882, 6213, 6753, 7433, 8290, 9300, 10305, 11077, 11455, 1 1449, 11233, 11014, 10897, 10836, 10688, 10302, 9620, 8741, 7849, 7050, 6330, 5747 , 5547 , 5898, 6625, 7433, 8108, 8484, 8434, 7962, 7266, 6646, 6291, 6192, 6280, 6565, 7095, 7852, 8711, 9480, 10008, 10273, 10377, 10440, 10501, 10508, 10378, 10043, 9496, 8809, 8084, 7359, 6607, 5878, 5409, 5455, 5970, 6678, 7340, 7799, 7949, 7780, 7407, 6999, 6661, 6400, 6227, 6213, 6448, 6945, 7611, 8286, 8837, 9233, 9532, 9797, 10018, 10125, 10058, 9800, 9383, 8865, 8295, 7668, 6942, 6158, 5529, 5335, 5637, 6216, 6825, 7299, 7546, 7551, 7392, 7174, 6944, 6693, 6432, 6249, 6257, 6512, 6960, 7478, 7949, 8339, 8690, 9042, 9359, 9556, 9572, 9410, 9116, 8744, 8321, 7827, 7219, 6521, 5887, 5549, 5617, 5980, 6437, 6841, 7108, 7219, 7212, 7138, 7009, 6804, 6537, 6295, 6188, 6287, 6567, 6939, 7307, 7642, 7976, 8335, 8673, 8899, 8955, 8855, 8661, 8428, 8163, 7820, 7338, 6724, 6103, 5688, 5616, 5830, 6163, 6482, 6718, 6851, 6903, 6904, 6854, 6730, 6536, 6333, 6208, 6226, 6384, 6621, 6871, 7115, 7383, 7696, 8009, 8228, 8292, 8218, 8072, 7917, 7758, 7539, 7188, 6691, 6140, 5714, 5549, 5629, 5829, 6038, 6208, 6332, 6425, 6498, 6528, 6478, 6339, 6156, 6010, 5965, 6035, 6182, 6353, 6527, 6724, 6967, 7224, 7415, 7479, 7421, 7305, 7191, 7095, 6967, 6734, 6361, 5903, 5499, 5278, 5258, 5355, 5483, 5601, 5706, 5804, 5893, 5949, 5942, 5860, 5737, 5626, 5576, 5600, 5679, 5781, 5890, 6025, 6202, 6396, 6540, 6579, 6517, 6412, 6327, 6281, 6230, 6101, 5842, 5477, 5109, 4848, 4734, 4722, 4752, 4801, 4874, 4975, 5089, 5183, 5217, 5174, 5077, 4974, 4907, 4896, 4938, 5014, 5110, 5225, 5365, 5507, 5600, 5602, 5521, 5405, 5316, 5276, 5255, 5185, 5011, 4736, 4433, 4194, 4052, 3973, 3915, 3875, 3880, 3950, 4073, 4206, 4291, 4291, 4211, 4092, 3982, 3912, 3895, 3925, 3991, 4085, 4202, 4322, 4404, 4403, 4308, 4150, 3986, 3857, 3767, 3677, 3536, 3321, 3062, 2824, 2640, 2485, 2308, 2096, 1872, 1671, 1505, 1360, 1215, 1086, 1052, 1210, 1571, 2099, 2752, 3465, 4151, 4739, 5207, 5577, 5886, 6150, 6365, 6523, 6626, 6677, 6664, 6563, 6349, 6022, 5613, 5178, 4777, 4451, 4220, 4089, 4048, 4071, 4125, 4172, 4184, 4148, 4069, 3965, 386 1, 3783, 3747, 3757, 3802, 3865, 3927, 3969, 3972, 3926, 3840, 3742, 3674, 3662, 3708, 3781, 3834 3827, 3748, 3610, 3435, 3248, 3075 2948,2891, 2912,2988 3078, 3141 3154, 3115, 3043, 2958, 2881, 2832 2825, 2859, 2924, 3002 3070, 3100 3071, 2983, 2868, 2774 , 2744, 2793 2896, 3004, 3065, 3052 2967, 2831 2670, 2510, 2382, 2314, 2321, 2386 2476, 2552, 2582, 2558 2489, 2394 2300, 2233, 2216, 2250, 2318, 2394 2454, 2478, 2454, 2382 2283, 2194 2155, 2187, 2280, 2391, 2471, 2490 2444, 2346, 2217, 2080 1964, 1899 1901, 1959, 2042, 2117, 2156, 2143 2079, 1980, 1873, 1795 1774, 1819 1908, 2005, 2076, 2102, 2073, 1992 1878, 1766, 1697, 1702 1781, 1899 2008, 2066, 2056, 1984, 1870, 1741 1630, 1572, 1582, 1645 1725, 1788 1818, 1809, 1758, 1670, 1563, 1470 1432, 1465, 1556, 1667 1756, 1793 1767, 1687, 1575, 1466, 1397, 1397 1469, 1582, 1693, 1768 1787, 1745 1649, 1523, 1402, 1330, 1332, 1395 1481, 1551, 1584, 1573 1518, 1429 1322, 1231, 1192, 1224, 1314, 1422 1510, 1549, 1527, 1452 1349, 1250 1188, 1193, 1264, 1366, 1458, 1514 1526, 1494, 1420, 1315 1209, 1147 1156, 1228, 1328 , 1415, 1459, 1 446 1380, 1279, 1173, 1094 1074, 1122 1215, 1313, 1383, 1408, 1381, 1304 1193, 1083, 1014, 1020 1101, 1222 1338, 1414, 1431, 1385, 1289, 1172 1072, 1031, 1072, 1176 1296, 1383 1409, 1367, 1271, 1148, 1028,944,928,987, 1092, 1200, 1282 1323, 1313 1251, 1148, 1038,967.972, 1051, 1171, 1289, 1368, 1386, 1339 1241, 1121 1018

The third level spectra on modified windows, namely 'Spx n ° ^* 0' to 'Spx n ° 7', will make it possible to calculate the frequencies of the peaks of low frequency bands by choosing, in the example, the frequencies from 0 to 3000 Hz. On 1024 frequency bands, the third level spectra 'Spx n ° 0' to 'Spx n ° 7' have a resolution of 5.859375 hz (6000 hz / 1024). Each value of the spectrum is associated with a specific band. Only the bands from the first to the five hundred and twelfth will be retained, in order to cover the bands from 0 to 3000 hz. The third level spectra on unmodified windows, ie 'Spec n ° 0' to 'Spec n ° 7', will allow to calculate the frequencies of the peaks of high frequency bands (frequencies from 3,000 to 24,000 Hz in the present example). On 1024 frequency bands, the third level spectra 'Spec n ° 0' to 'Spec n ° 7' have a resolution of 23.4375 hz (24 000 hz / 1024). Each value of the spectrum is associated with a specific band. However, like the low frequency bands, i.e. 6000 hz and less, are calculated from the third level spectra on the modified windows, ie 'Spx n ° 0' to 'Spx n ° 7', and lower bands of the third level spectra on the unmodified windows either 'Spec n ° 0' to 'Spec n ° 7', only the one hundred and twenty-eighth to the thousand and twenty-fourth of the bands of these last spectra will be used.

As for the second level analyzes, the maximums are observed on each spectrum, and on a given spectrum, the values beyond a threshold which is proportional to the maximum peak of the spectrum in question are retained, first of all on the spectrum of modified windows, ie 'Spx n ° 0' to 'Spx n ° 7', and then on the spectrum of unmodified windows, ie 'Spec n ° 0' to 'Spec n ° 7'.

Starting from the spectrum of modified windows 'Spx', for example for 'Spx n ° 0', a maximum is detected on the eighty-second band, ie the value 8 736 606. Each band is 5.859375 wide hz as previously calculated. Peaks are collected up to 3000 Hz. The peak detection threshold value is chosen according to the desired resolution. In the example, only values greater than 64 times less than the value of the maximum peak will be retained, i.e. values above 136,509 (8,736,606 / 64). In the spectrum in question, two peaks meet this criterion, either on the eighty-second band at the value 8 736 606 (475-480 hz) and either the two hundred and seventieth band at the value 1 841 146 (1576-1582 hz).

According to the spectrum of the unmodified windows 'Spec', for example for 'Spec n ° 0', following the established threshold (136 509 in the example) where each band is 23.4375 Hz wide as it was calculated previously, the peaks on frequencies beyond 3000 Hz are collected from the one hundred and twenty-eighth band on the unmodified window spectrum. On the spectrum 'Spec n ° 0', two peaks meet this criterion, either on the three hundred and twenty-sixth band at the value 879 463 (7 617-7 641 hz) and the six hundred and third band at 1 917 647 ( 14 133-14 156 Hz).

To the frequency envelopes which determined the sample, the values of the two complementary spectra (Spx n ° 0 and Spec n ° 0) of 2048 points, for a duration of 43 ms, correspond the means of the first eight points (8 x 5.32 ms) of the envelopes of the four oscillations which produced the analyzed signal.

The first eight points of the frequency envelopes of the oscillations which produced the sample are respectively:

Oscillation 1 average 471 Hz (440.00, 450.32, 460.63, 470.52, 478.68, 485.56, 490.72, 493.72)

Oscillation 2 average 1570 Hz (1478.98, 1504.77, 1530.55, 1556.33, 1582.11, 1610.47, 1636.25, 1662.03)

Oscillation 3: average 7638 hz (7686.25, 7672.50, 7658.75, 7645.00, 7631.25, 7617.50, 7603.75, 7590.00) Oscillation 4: average 14 100 hz (14105.78, 14104.06, 14102.34, 14100.63, 14098.91, 14097.19, 14095.47, 14093.75)

Signal Signal Spectrum Spectrum Frequency

Amplitude Frequency Amplitude

1 2 039 471 Hz 8 736 606 475 - 480 Hz

2,393 1,570 Hz 1,841 146 1,576 - 1,582 Hz

3 0 7 638 Hz 879 463 7 617 - 7 641 Hz

4,544 14,103 hz 1,917,647 14,133 - 14,156 hz

The peaks identified on each pair of third level spectra will be associated with the peaks retained on the second level spectrum to which the start of the window corresponds. For example, on the second level spectrum 'Spec n ° 0', the following peak values were obtained:

Pic n ° 1 Pic n ° 2 Pic n ° 3

Amp 3 130 291 729 012 806 667

Freq 454.68 1517.31 14103.31

The peaks of the second and third level analyzes are associated taking into account their frequencies, namely:

Level 2 Level 3 n ° 1 454.68 hz n ° 1 475 - 480 hz n ° 2 1517.31 hz n ° 2 1576 - 1582 hz n ° 3 14 103.31 hz n ° 4 14 133 - 14 156 hz

Note that peak # 3 detected on the third level analysis and whose frequency is 7,617-7,641 Hz does not correspond to any peak in the second level analysis. The reason is that this frequency component appears after the end of the initial window of the analysis of second level, either after the thousand and twenty-fourth point and before the end of the third level analysis window, or before the two thousand and forty-eighth point of the sample. This is confirmed by observing the amplitude envelope of oscillator No. 3 from which the sample is taken. The first five values of the amplitude envelope are zero. Thus, the component of oscillator n ° 3 only appears after 26.6 ms (sixth envelope point), that is to say after 1276 sample points. In the specific case where a peak is detected in the third level analysis and does not correspond to a peak in the second level analysis, it is rejected, since the third level analysis is only used to calculate the values fines of the frequency components.

The frequency values on the peaks of the third level spectra are calculated analogously to the process performed on the peaks of the second level spectra. The peak values detected on the spectra (Spx) of modified windows are calculated on these same windows, just as the peak values detected on the spectra (Spec) of unmodified windows are calculated on these same windows.

The following frequency calculation will be performed for each peak identified on the spectrum of modified windows (Spx):

npic + NFAC

∑ (n) * SPX [n] n≈npic-nfac

ERE npic + nfac FXBASE

∑SPX [n] n = npic-nfac or npic: band number of the peak; nfac: Compression rate of the modified window (four in the example); n: index;

SPX [n]: value of amplitudes on the peak; and FXBASE: Band frequency 5.859375 Hz (Maximum band 6 kHz / Number of bands 1024).

The following frequency calculation will be performed for each peak identified on the spectrum of unmodified windows (Spx):

or npic: band number of the peak; n: index;

SPΕC [n]: value of amplitudes on the peak; and FBASΕ: band frequency 23.4375 Hz (maximum band 24 kHz / number of bands 1024).

For example, the calculation of the first peak of the modified window spectrum (SPX) gives the following values, determined from the values around the eighty-second band as it is displayed previously for the spectrum of window no. 0 modified on 1024 values from the first to the thousand and twenty-fourth band ('npic': = 81): FRE = ((74) SPX [74] + (75) SPX [75] + (76) SPX [76] + (77) SPX [77] + (78) SPX [78] + (79) SPX [79] + (80) SPX [80] + (81) SPX [81] + (82) SPX [82] + (83) SPX [83] + (84) SPX [84] + (85) SPX [85] + ( 86) SPX [86] + (87) SPX [87d + (88) SPX [88]) FBASE / (SPX [74] + SPX [75] + SPX [76] + SPX [77] + SPX [78] + SPX [79] + SPX [80] + SPX [81] + SPX [82] + SPX [83] + SPX [84] + SPX [85] + SPX [86] + SPX [87] + SPX [88d)

FRE = ((74) 2241113 + (75) 3208532 + (76) 4399399 + (77) 5712660 + (78) 6981898 + (79) 8012892 + (80) 8632993 + (81) 8736606 + (82) 8312340 + (83 ) 7443430 + (84) 6282146 + (85) 5007588 + (86) 3781386 + (87) 2715564 + (88) 1861436) ^* FBASE / (2241113 + 3208532 + 4399399 + 5712660 + 6981898 + 8012892 + 8632993 +8736606 + 8312340 + 7443430 + 6282146 + 5007588 + 3781386 + 2715564 +)

FRE = 473.55 Hz

For example, the calculation of the first retained peak of the unmodified window spectrum (SPEC) gives the following values, determined from the values around the six hundred third band as it is displayed previously for the spectrum of window n ° 0 no modified on 1024 values from the first to the thousand and twenty-fourth band (npic: = 602):

FRE = ((600) SPEC [600] + (601) SPEC [601] + (602) SPEC [602] + (603) SPEC [603]

+ (604) SPEC [604]) * FBASE / (SPEC [600] +

SPEC [601] + SPEC [602] + SPEC [603] + SPEC [604])

FRE = ((600) 419483 + (601) 1709959 + (602) 1917647 + (603) 637492 + (604) 38064) * FBASE / (419483 + 1709959 + 1917647 + 637492 + 38064)

FRE = 14,100.27 Hz

The peaks are classified in order in a temporary register during the analysis on a given spectrum. Thus, for the eight third level spectra, we obtain these frequency values (in hertz). The amplitude values are those which were calculated on the second level analysis.

. Or the classification of the peaks on the successive spectra:

Pic n ° 1 Pic n ° 2 Pic n ° 3 Pic n ° 4

Spectrum # 0

Amplitude 3 130 291 729 012 806 667

Frequency 473.55 1,575.39 14 100.27

Specter # 1

Amplitude 2 966 943 1 191 627 1 292 901 613 798

Frequency 493.39 1,704.81 7,570.80 14,091.49

Specter # 2

Amplitude 2,542,991 1,512,754 1,282,781,446,193

Frequency 475.73 1,805.41 7,545.29 14,084.50

Specter # 3

Amplitude 2,282,733 1,727,397 415,120

Frequency 446.59 1,875.64 14,079.31

Specter # 4

Amplitude 1 297 155 540 594 1 288 219 223 889

84

'<£ »$. &&? 5 "** '" P Pic n ° 1 Pic n ° 2 Pic n ° 3 Pic n ° 4

Frequency 390.26 2,034.65 7,379.44 14,068.39 Spectrum 5

Amplitude 1,196,053 355,556 1,266,767 155,037

Frequency 386.83 2,046.56 7,364, 11 14,067.14 Spectrum # 6

Amplitude 724 616 1 235 314

Frequency 393.61 7331.07 Spectrum 7

Amplitude 202 874

Frequency 416.50

Either the temporary registers identified TP_A 'and TP_F' which respectively contain the values of amplitudes and frequency of peaks at the passage of each spectrum, for example, at the passage of the initial window (Spectrum n ° 0), the values of peaks n ° 1 to n ° 3 will be transmitted to the following registers:

TP_A [0] = 3 130 291 TP_F [0] = 473.55 TP_A [1] = 729 012 TP_F [1] = 1575.39

TP_A [2] = 806 667 TP_F [2] = 14 100.27

Allocation of peak registers

The index allocation process is intended to ensure that the detected peaks can be put together according to their respective frequency pairing. Thus, on the spectra of successive windows, in this case eight in number in the present example, the peaks which correspond most in frequency and in amplitude are given priority over the same indices. In the example, where the sample was created by the addition of four sinusoidal ^{oscillations'} idales frequency and variable amplitudes, means to attribute four different clues that will identify where successive peaks will be placed. In the example, the number of peaks per successive spectra varies, which corresponds to the variations of the signal itself. Indeed, spectrum n ° 0 has three peaks and spectrum n ° 1 has four, because the component of 7,570.8 of spectrum n ° 1 is absent from spectrum n ° 0. This component is also present in the spectrum n ° 2, disappears on spectrum n ° 3, to reappear on spectra n ° 4 and n ° 5. The attribution of the indices takes into account these variations and makes so that the frequency components are allotted to the same indices.

This process is advantageous as the number of peaks is limited and to ensure that the parameterization of an analyzed signal is consistent and can allow the processing or regeneration of the latter. This amounts to saying in the case of the present example that four indices will be assigned and will correspond to the four sinusoidal oscillations. Thus one could regenerate the signal with four sinusoidal oscillations.

In practical cases, we have no prior idea of the content of a signal. However, the allocation of the indices from the peaks is carried out in such a way that the entire analysis process does not have to know this content beforehand so that it can be used on any signals.

The following steps summarize the process for allocating indices • Allocation of registers on the initial spectrum (spectrum no.

0);

• On each spectrum following the peaks will be assigned to the compatible registers, process P1 to P4; • P1: Search for peaks compatible in frequency with the previous spectrum on all the peaks;

• P2: Search for peaks compatible in frequency with an already assigned register of a previous spectrum on the peaks not yet assigned;

• P3: Allocation of peaks not yet assigned to new registers; and

• P4: Search for peaks compatible in amplitude with confirmation of the allocation of the registers, and reassignment of the registers which are not compatible in amplitude on the peaks closest in frequency whose allocation is not yet confirmed.

Allocation of registers on spectrum 0:

The temporary registers at the passage of the first window (Spectrum n ° 0) are copied into the registers of the last peaks, namely PIC_A and PIC_F respectively for the amplitudes and the frequencies. These data are also copied on the old peaks is PRE_A and PRE_F.

PIC_A [0] = TP_A [0] = 3 130 291 PIC_F [0] = TP_F [0] = 473.55 PIC_A [1] = TP_A [1] = 729 012 PIC_F [1] = TP_F [1] = 1575, 39

PIC_A [2] = TP_A [2] = 806 667 PIC_F [2] = TP_F [2] = 14 100.27

PRE_A [0] = PIC_A [0] = 3 130 291 PRE_F [0] = PIC_F [0] = 473.55 PRE_A [1] = PIC_A [1] = 729 012 PRE_F [1] = PIC_F [1] = 1575, 39 PRE_A [2] = PIC_A [2] = 806 667 PRE_F [2] = PIC_F [2] = 14 100.27

Allocation of compatible registers: Frequency compatibility is established on a variation of frequency values at successive spectra corresponding for example to six successive bands of frequency spacing (ie for example 180 Hz = 6 * 30 Hz) on the unmodified windows, by searching for inside a margin of one band, then two bands, then three bands.

Amplitude compatibility is established on a variation of amplitude values at successive spectra corresponding for example to amplitude variations between double and half the value of the current spectrum compared to the previous spectrum.

Specter n ° 1:

Minimum frequency variations on Indices

Frequency compatibility of spectrum n ° 1 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed margin on six bands in selection, steps P1, P2:

1 2 3

Origin 30 60 90

PIC F1 (0) 493.39 493.39 493.39 PIC A1 (0) 2 966 943 2 966 943 2 966 943

PIC F1 (1) PIC A1 (1) PIC_F1 (2)

PIC_A1 (2)

PIC_F1 (3)

PIC_A1 (3)

TP_F1 (0)

TP_A1 (0)

TP_F1 (1)

TP_A1 (1)

TP_F1 (2)

TP_A1 (2)

TP_F1 (3)

TP_A1 (3)

4 5 6

Origin 120 150 180

PIC_F1 (0)

PIC_A1 (0)

PIC_F1 (1)

PIC_A1 (1)

PIC_F1 (2)

PIC_A1 (2)

PIC_F1 (3)

PIC_A1 (3)

TP_F1 (0

TP_A1 (0

TP_F1 (1

TP_A1 (1

TP_F1 (2

TP_A1 (2

TP_F1 (3

TP_A1 (3

evaluated as compatible on spectrum n ° 1 compared to spectrum n ° 0 (PIC_F0 (n)). The peak TP_F1 (3) of spectrum n ° 1 does not correspond to a previous peak, therefore a new index is assigned to it by the process (P3). The frequency-compatible peaks are copied to the PIC_F and PIC_A registers in the order: Frequency compatible Not frequency compatible

PIC_F1 (0) PIC_A1 (0) PIC_F1 (1) PIC_A1 (1) PIC_F1 (2) PIC_A1 (2) PIC_F1 (3) PIC_A1 (3)

Is:

Functions

The compatibility of the amplitudes of the peaks of spectrum No. 1 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 1 and the previous one are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the preceding spectra (PIC_A ( n)) whose variation is increasing (positive in the following table) or half the value of amplitudes of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

Amplitude Values

PRE_A0 (0) 3 130 291 PRE_A0 (1) 729 012

What gives these variations

Variation Limit Amplitude Variation

Amplitude Compatible

PIC_A1 (0) -163 348 1,565 145.5

Compatible Amplitude PIC_A1 (1) 462 615 595813,5

Amplitude Compatible PIC_A1 (2) -192 869 403 333.5

Not Compatible Ampl. PIC_A1 (3) 1 292 901 646 450.5 Reassigned

Only the peak n ° 3 of the spectrum n ° 1 is not compatible in amplitude. As there is no other peak of the spectrum n ° 1 which is associated with the peak PRE_A0 (3), the peak n ° 3 is assigned to it by the process (P4). The non-zero PIC_F and PIC_A registers are copied to the respective PRE_F and PRE_A registers.

Spectrum 2:

Minimum frequency variations on Indices

Frequency compatibility of spectrum # 2 with spectra precedents on six bands and allocation on compatible indices when the frequency variation is within the prescribed margin on six bands in selection, process P1, P2:

1 2 3

Origin 30 60 90

4 5 6

Origin 120 150 180

Therefore, all the peaks (TP_F2 (0) to TP_F2 (3)) were evaluated as compatible on the spectrum n ° 2 compared to the spectrum n ° 1. The peaks compatible in frequency are copied on the registers PIC__F and PIC_A in l 'order:

Frequency compatible Not frequency compatible

PIC_F2 (0) 475.73 TP_F2 (0) PIC_A2 (0) 2542991 TP_A2 (0) PIC_F2 (1) 1805.41 TP_F2 (1) PIC_A2 (1) 1512754 TP_A2 (1) • PIC_F2 (2) 14084.50 TP_F2 ( 2) PIC_A2 (2) 446193 TP_A2 (2) PIC_F2 (3) 7,545.29 TP_F2 (3) PIC_A2 (3) 1,282,781 TP_A2 (3)

Is:

The compatibility of the amplitudes of the peaks of spectrum No. 2 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 2 and the previous one are established on amplitude variation limits correspond to half the amplitude value of each last peak of the preceding spectra (PIC_A ( n)) whose variation is increasing (positive in the following table), or half the amplitude value of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

Amplitude

PRE_A1 (0) 2 966 943 PRE_A1 (1) 1 191 627 PRE_A1 (2) 613 798 PRE_A1 (3) 1 292 901

What gives these variations

Variation Limit Amplitude Variation

Amplitude Compatible

PIC_A2 (0) -423 952 1 483471, 5

Amplitude Compatible PIC_A2 (1) 321 127 756377

Amplitude Compatible PIC_A2 (2) -167 605 306 899

Compatible Amplitude PIC_A2 (3) -10 120 646 450.5

All the peaks of spectrum n ° 2 are compatible in amplitude. The non-zero PIC_F and PIC_A registers are copied to the respective PRE_F and PRE_A registers.

Specter # 3

Minimum frequency variations on Indices

Freq. hz Min. Var.min.

PRE_F2 (0) 475.73 TP_F3 (0) 446.59 29.14 0 PRE_F2 (1) 1805.41 TP_F3 (1) 1875.64 70.23 1 PRE_F2 (2) 14084.5 TP_F3 (2) 14 079, 31 5.19 2 PRE_F2 (3) 7545.29 TP_F3 (3) 0.00 9999.00 0

Frequency compatibility of spectrum no. 3 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed margin on six bands in selection, steps P1, P2. The calculation is of the same order as on spectra n ° 1 and n ° 2. The peaks (TP_F3 (0) to TP_F3 (2)) were evaluated as compatible on the spectrum n ° 3 compared to the previous spectra, TP_F3 ( 3) is zero, the compatible non-zero frequency peaks are copied to the PIC_F and PIC A registers in the order:

Frequency compatible Not frequency compatible

Is

The compatibility of the amplitudes of the peaks of spectrum No. 3 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 3 and the previous ones are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the previous spectra (PIC_A ( n)) whose variation is increasing (positive in the following table) or half the value of amplitudes of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

Amplitude

PRE_A2 (0) 2,542,991 PRE_A2 (1) 1,512,754 PRE_A2 (2) 446 193 PRE_A2 (3) 1,282,781

What gives these variations

Variation Limit Amplitude Variation

Amplitude Compatible

PlC_A3 (0) -260 258 1 271 495.5

Amplitude Compatible PIC_A3 (1) 214 643 863 698.5

Amplitude Compatible PlC_A3 (2) -31 073 223 096.5

Not Compatible Ampl. PlC_A3 (3) -1 282 781 641 390.5 Reallocated

All the peaks of spectrum No. 3 are compatible in amplitude. However, peak No. 3 is of zero amplitude. The last amplitude values and corresponding frequencies are stored in the corresponding PRE_F and PRE_A registers, the non-zero PIC_F and PIC_A are copied to the respective PRE_F and PRE_A registers.

Specter # 4

Minimum frequency variations on Indices

Frequency compatibility of spectrum no. 4 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed margin on six bands in selection, steps P1, P2. The calculation is of the same order as on spectra n ° 1 and n ° 2. The peaks (TP_F4 (0) to TP_F4 (3)) were evaluated as compatible on the spectrum n ° 4 compared to the previous spectra, the peaks compatible in frequency are copied to the registers PIC_F and PIC_A in the order:

Frequency compatible Not frequency compatible

PIC_F4 (0) 390.26 TP_F4 (0) PIC_A4 (0) 1 297 155 TP_A4 (0) PIC_F4 (1) 2 034.65 TP_F4 (1) PIC_A4 (1) 540 594 TP_A4 (1) PIC_F4 (2) 14 068 , 39 TP_F4 (2) PIC_A4 (2) 223 889 TP_A4 (2) PIC_F4 (3) 7 379.44 TP_F4 (3) PIC_A4 (3) 1 288 219 TP_A4 (3)

Is

The compatibility of the amplitudes of the peaks of spectrum No. 4 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 4 and the previous ones are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the preceding spectra (PlC_A ( n)) whose variation is increasing (positive in the following table) or half the value of amplitudes of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

What gives these variations

Variation Limit Amplitude Variation

Amplitude Compatible

PIC_A4 (0) -985 578 1,141,366.5 Not Compatible Ampl.

PIC_A4 (1) -1 186 803 863 698.5 Reassigned

Amplitude Compatible

PIC__A4 (2) -191 231 207 560

Not Compatible Ampl.

PIC_A4 (3) 1 288 219 644 109.5 Reassigned

The peaks PIC_F4 (0) and PIC_F4 (2) of the spectrum n ° 4 are compatible in amplitude. However, peaks 1 and 3 are not.

However, as there are no other peaks detected on the current spectrum which are in the same frequency zones, they are reassigned to the same peaks as compatible by the process (P4). All registers

PIC_F and PIC_A non zero are copied on the respective registers PRE_F and PRE_A.

Specter # 5

Minimum frequency variations on Indices:

Frequency compatibility of spectrum no. 5 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed margin on six bands in selection, steps P1, P2. The calculation is of the same order as on spectra n ° 1 and n ° 2. The peaks (TP_F5 (0) to TP_F5 (3)) were evaluated as compatible on the spectrum n ° 5 compared to the previous spectra, the peaks compatible in frequency are copied to the registers PIC_F and PIC_A in the order: Frequency compatible Not frequency compatible

PIC_F5 (0) PIC_A5 (0) PIC_F5 (1) PIC_A5 (1) PIC_F5 (2) PIC_A5 (2) PIC_F5 (3) PIC_A5 (3)

Is :

Functions

The compatibility of the amplitudes of the peaks of spectrum No. 5 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 5 and the previous ones are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the previous spectra (PIC_A ( n)) whose variation is increasing (positive in the following table) or half the amplitude value of the last peak of a previous spectrum (PRE _A (n)) for a decreasing variation (-) in the following table :

Amplitude

PRE_A4 (0) 1,297,155 PRE_A4 (1) 540,594

Amplitude

PRE_A4 (2) 223 889 PRE_A4 (3) 1 288 219

What gives these variations

Variation Limit Amplitude Variation

Amplitude Compatible

PIC_A5 (0) -101 102 648 577.5

Amplitude Compatible PIC_A5 (1) -185 038 270 297

Amplitude Compatible PIC_A5 (2) -68 852 111 944.5

Amplitude Compatible PIC_A5 (3) -21 452 644 109.5

The peaks PIC_F5 (0) to PIC_F5 (3) of spectrum No. 5 are compatible in amplitude. All the non-zero PlC_F and PIC_A registers are copied to the respective PRE_F and PRE_A registers.

Specter n ° 6:

Minimum frequency variations on Indices:

Frequency compatibility of spectrum no. 6 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed range on six bands in selection, steps P1, P2. The calculation is of the same order as on spectra n ° 1 and n ° 2. The peaks TP_F6 (0) and TP_F6 (3) were evaluated as compatible on the spectrum n ° 6 compared to the previous spectra, TP_F6 (1) and TP_F6 (2) are zero, the non-zero compatible peaks in frequency are copied to the registers PIC_F and PIC_A in the order:

Frequency compatible Not frequency compatible

PlC_F6 (0) PIC_A6 (0) PIC_F6 (1) PIC_A6 (1) PIC_F6 (2) PIC_A6 (2) PIC_F6 (3) PIC_A6 (3)

Is

The compatibility of the amplitudes of the peaks of spectrum No. 6 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 6 and the previous ones are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the preceding spectra (PIC_A ( n)) of which the variation is increasing (positive in the following table) or half the amplitude value of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

Amplitude

PRE_A5 (0) 1,196,053 PRE_A5 (1) 355,556 PRE_A5 (2) 155,037 PRE_A5 (3) 1,266,767

What gives these variations

Variation Limit Amplitude Variation

PIC_F6 (0) Amplitude Compatible PIC_A6 (0) -471 437 598 026.5 PIC_F6 (1) Not Ampl Ampl. PIC_A6 (1) -355 556 177 778 Reassigned PIC_F6 (2) Not Compatible Ampl. PIC_A6 (2) -155 037 77 518.5 Reallocated PIC_F6 (3) Amplitude Compatible PIC_A6 (3) -31 453 633 383.5

The peaks PIC_F6 (0) and PIC_F6 (3) of the spectrum n ° 6 are compatible in amplitude. Peaks 1 and 2 are zero. The last values of amplitudes and frequencies which correspond to them are preserved in the corresponding registers PRE_F and PRE_A. All non-zero PIC_F and PIC_A registers are copied to the respective PRE_F and PRE_A registers.

Specter n ° 7: Minimum frequency variations on Indices

Frequency compatibility of spectrum n ° 7 with the previous spectra on six bands and allocation to compatible indices when the frequency variation is within the prescribed margin on six bands in selection, steps P1, P2. The calculation is of the same order as on spectra no. 1 and no. 2. The peak TP_F7 (0) was evaluated as compatible on spectrum no. 7 compared to the previous spectra. TP_F7 (1) to TP_F7 (3) are zero. The compatible peaks that are not zero in frequency are copied to the PIC_F and PIC A registers in the order:

Frequency compatible Not frequency compatible

Is

The compatibility of the amplitudes of the peaks of spectrum No. 7 is then checked. The amplitude variation margins for evaluating the compatibility between spectrum No. 7 and the previous ones are established on amplitude variation limits corresponding to half the amplitude value of each last peak of the preceding spectra (PIC_A ( n)) whose variation is increasing (positive in the following table) or half the value of amplitudes of the last peak of a previous spectrum (PRE_A (n)) for a decreasing variation (-) in the following table:

What gives these variations

Variation Limit

The peak PIC_F7 (0) is not compatible in amplitude but since there are no other peaks detected on the current spectrum which is in the same frequency zone, it is reassigned to the same peak as compatible by the process (P4). The PIC_F7 (1) to PIC_F7 (3) of spectrum n ° 7 are zero. The last values of amplitudes and frequencies which correspond to them are preserved in the corresponding registers PRE_F and PRE_A. All the non-zero PlC_F and PIC_A registers are copied to the respective PRE_F and PRE_A registers.

This completes the allocation of the registers for spectra n ° 0 to n ° 7. In order, the values of the registers therefore follow this progression on peaks 0 to 3:

Spectra n ° 0 to n ° 3:

n ° 0 n ° 1 n ° 2 N ° 3

PIC_F (0) PIC_A (0) PIC_F (1) PIC_A (1) PIC_F (2)

PIC_A (2) PIC_F (3) PIC_A (3)

Spectra n ° 4 to n ° 7

n ° 4 n ° 5 n ° 6 n ° 7

PIC_F (0) PIC_A (0) PIC_F (1) PIC_A (1) PIC_F (2) PIC_A (2) PIC_F (3) PIC_A (3)

Thus each register corresponds to an oscillator which was used for the construction of the analyzed signal, whereas beforehand, the analysis process has no way of knowing the harmonic content of the analyzed signal. This will therefore allow this information to be used in a useful way for the processing and reconstruction of a signal, for applying different processes to it, for signal transport or storage, etc .; all with a minimum of signal data which is moreover informative.

If we graphically represent the four registers of amplitude-frequency pairs, we will obtain the envelopes of Figures 15A (Pic O), 15B (Pic 1), 15C (Pic 2), 15D (Pic 3), which correspond to the envelopes having used to construct the original signal as illustrated respectively in Figures 2, 4, 6, 8; in the following order with the average frequency values:

440.00 Hz

1760.00 Hz

14 080.00 Hz

7 480.00 Hz 8

The inversion of Figures 15C and 15D is due to the fact that the components which appear first are assigned to the registers in order of appearance. However, the peak register No. 2 (average frequency 7,438 Hz) includes non-zero values from spectrum No. 1 and the envelope of oscillator No. 3 (median frequency 7,480 Hz) of the original signal had thus been drawn, i.e. with the first zero amplitude values.

The comparison of the initial envelopes with the envelopes obtained using the signal analysis method according to the present invention shows us a difference in the resolution of the envelopes. The initial envelopes are 40 values for a resolution of 5.32 ms, while the analysis registers converted into envelopes are eight values for a resolution of 21.33 ms.

However, the selection of window dimensions or their spacing is possible. For example, one could use windows of the same dimensions (second level of 1024 points, third level of 2048 points), but instead of having an average spacing of 1024 points between the successive windows, this could be reduced. However, this implies a larger number of spectra. The resolution chosen in the example is however sufficient for signal processing and regeneration. For example, during regeneration, the values received to regenerate on the basis of the registers can easily be interpolated between the values received. Classification, ordering and reduction of parameters: The data collected from the analysis are of the absolute type. By their nature, they lend themselves to a series of layouts that allow them to be classified and adapted in order to minimize their number. An example of this type of conversion is explained in the following lines.

In a first step, the raw absolute data is converted to a number of bits according to the desired precision.

In a second step, the frequency and amplitude values are converted into relative forms since the data are associated with registers whose content evolves over time, i.e. that the successive values determined by the content of the registers are stored so as to represent their specific evolution from one value to another, by adding addresses which are associated with the registers.

In a third step, the relative data are weighted according to their respective dimensions.

The following successive spectra (8) correspond to the level of successive windows of 1024 at a sampling rate of 48,000 Hz as in the example, with a spacing between the spectra of 21.33 ms:

Spectrum n ° 0 - »0 ms Spectrum n ° 4 ^ 85.33 ms

Spectrum # 1 ^ 21, 33 ms Spectrum # 5 ^ 106.67 ms

Spectrum # 2 - 42.67 ms Spectrum # 6 ^ 128.00 ms

Spectrum # 3 - 64.00 ms Spectrum # 7 -> 149.33 ms

The order of the data firstly follows the origin of these from the analysis program on the three levels, then the allocation of the registers which successively correspond to the analysis windows of the sample and the peaks associated with them. Thus, the data can be stored or transmitted step by step as the sample is analyzed on successive windows.

The data received from the registers follow a specific order which allows their classification or their routing in a continuous and unlimited manner, either in sequence on 'n' spectra and 'pn' peaks. On each spectrum, the number of peaks can vary depending on the number of these peaks that have been detected. The spectrum n ° 0 corresponds to the duration 0 ms, the spectrum n ° 1 to the duration 21, 33 ms and so on:

n Spectra No. Peaks Parameters pn Amplitude Frequency

First step - Precision:

The data collected on the various previous stages of the analysis are associated with the amplitudes and frequencies of the peaks of the successive spectra. By establishing the frequency limit, for example at 16,777 Hz with an accuracy of 0.001 Hz, the frequency values can be determined beforehand on 24 bits (Table following column PIC_F). They correspond to the values obtained previously on the peaks of the successive spectra. The values in the table are multiplied by 1000 to be converted into whole data (i.e. a maximum of 16,777,000, the maximum of the 24-bit data is 16,777,215). The results are found in the following table in column (VAL_F). For example on PIC n ° 0 to 0 ms the frequency 473.55 Hz (PIC_F) is encoded 473 550 (VAL_F).

The amplitudes on analysis data from 16-bit samples as in the example will give results on a maximum of 24 bits (16,777,215), ie the values (PIC_A) in the table. They correspond to the values obtained previously on the peaks of the successive spectra. The amplitude data can be greatly reduced, assuming a maximum on 14 bits, the values are brought back for a maximum of 16,383 either divided by the value 1024, or the values (VAL_A). For example, on PIC n ° 0 to 0 ms the amplitude of 3 130 291 (PIC_A) is encoded 3 057 (VAL_A).

So we get the following values on the set registers obtained on the successive spectra, that is to say the values in duration 0.00 first for the peaks n ° 0 to n ° 3, 21, 33 ms later new values for the peaks n ° 0 to n ° 3, and and so on. The peaks n ° 0 to n ° 3 are represented and on each, the values over the respective durations:

Duration Ms

Total Bits

Total Bytes

Reduction 64,108

As calculated, the number of data in bytes is 152 (56 amplitudes, 96 frequencies), a reduction rate of 108 compared to the sample which, as seen previously, has 8 192 points of 16 bits, that is 16384 bytes.

Second step - Variations:

From the previous table, the data are treated as variations from zero values for the amplitudes and from an absolute initial value for the frequencies. This processing ensures that only the relevant values are retained, in this case the non-zero values and the variable values. However, this transformation implies a break in the continuity of the sequence which proceeds, in order, with the spectra (durations) and inside them, the peaks in succession. It is advantageous to introduce an identification of the registers on the data, namely (VR_ADR) whose address identifies the peak number associated with specific values of amplitudes and frequencies; for example on Pic n ° 0 at 0 ms, address 0 identifies the register associated with Pic n ° 0 over successive periods.

The amplitude values are established in relative mode, either the variation of the values for each peak, or, for example at duration 0, the amplitude variation value of this peak starting from zero, then at the following duration ( 21, 33 ms), the variation of the amplitude value compared to the duration 0, and so on for each peak. Amplitude variations are represented in the tables under (VR_A). For example, for peak n ° 0, the first two absolute values of amplitudes (VAL_A) are 3 057, then 2 897. These values put in variation become respectively (VR_A) '3 057' (3 057 - 0) then '-160' (2 897 - 3 057). These values are derived from 12-bit absolute values. In relative, they are therefore established on 13 bits to add the sign. The zero variations are not retained (example on peak n ° 1 at 149.33 ms).

The frequency values are established absolutely (basic values) for the initial duration (0 ms), and, when the previous frequency value was zero (for example on peak n ° 3 at 21, 33 ms), the values are expressed in this case always on 24 bits. When they are expressed in absolute, the values are represented in the table under (VR_BAS). For example, on peak n ° 1 at duration 0, the frequency value (VAL_F) is 1,575,390. It thus remains on (VR_FBAS) on the peak and the corresponding duration. Another example is, on peak # 3 at duration 21, 33 ms. The frequency value (VAL_F) is 7,570,800 there. As the peak n ° 3 at the previous duration (0) was of zero frequency, the value remains 7,570,800 (VR_FBAS).

Frequency values are established relatively (variation values) for non-initial durations when the previous value is non-zero. In this case, the values are expressed in 13 bits and represent the variation between two values.

Either on a given space of duration 'n':

n: current duration; n-1: previous duration; nbas: duration on the last value set as absolute on

VR_FBAS;

VAL_F: Frequency values (absolute)

where the argument in parentheses is the relative frequency in decimals (FREL) and where 4,095 is a constant which allows encoding of the values on 13 signed bits.

For example, on peak n ° 0, the absolute frequency values (VAL_F) are respectively on the durations 0 ms to 42.67 ms of 473 550 (0 ms), 493 390 (21, 33 ms) and 475 730 ( 42.67 ms).

As described above, the value at 0 ms (initial duration) is established in absolute value, so 'nbas' is associated with (0 ms) either: VAL_F [nbas] = VAL_F [0ms] = 473550

Over the duration 21, 33 ms:

VAL_F [n] = VAL_F [21, 33ms] = 493 390

VAL_F [n-1] = VAL_F [0ms] = 473 550

VAL_F [nbas] = VAL_F [0ms] = 473550 (last absolute value).

The relative frequency expresses the variation compared to the basic frequency and is the argument in parenthesis, that is: FREL [21, 33ms] = (VAL_F [21, 33ms] - VAL_F [0ms]) / VAL_F [0ms]

FREL [21, 33ms] = (493 390 - 473 550) / 473 550 FREL [21, 33ms] = 0.0490,

that is to say a variation of the order of 0.490 times the absolute value of frequencies.

This value is encoded on 13 bits (sign + 12 bits):

VR_FVAR [21, 33ms] = 4,095 * (VAL_F [21, 33ms] - VAL_F [0ms]) / VAL_F [0ms]

VR_FVAR [21, 33ms] = 4095 ^* FREL [21, 33ms] VR_FVAR [21, 33ms] = 4095 * 0.0490 VR_FVAR [21, 33ms] = 172

Over the 42.67 ms duration:

VAL_F [n] = VAL_F [42.67 ms] = 475,730

VAL_F [n-1] = VAL_F [21, 33ms] = 493 390

VAL_F [nbas] = VAL_F [0] = 473550 (last absolute value).

The relative frequency expresses the variation compared to the basic frequency and it is the argument between brackets, that is to say:

FREL [42.67ms] = (VAL_F [42.67ms] - VAL_F [21, 33ms]) / VAL_F [0ms]

FREL [42.67 ms] = (475,730 - 493,390) / 473,550 FREL [42.67 ms] = -0.3730,

a variation of the order of 0.490 times the absolute frequency value.

This value is encoded on 13 bits (sign + 12 bits):

VR_FVAR [42.67ms] = 4,095 * (VAL_F [42.67ms] - VAL_F [21, 33ms]) / VAL_F [0ms]

VR_FVAR [42.67ms] = 4,095 * FREL [42.67ms] VR_FVAR [42.67ms] = 4,095 * (-0.3730) VR_FVAR [42.67ms] = -153

The values thus calculated on the addresses, that is to say the amplitudes and the frequencies are represented in the following table for the peaks n ° 0 to n ° 3 on the successive durations, the empty boxes on VR_A, VR_FBAS, VR_FVAR correspond to zero values or not applicable:

VR_ADR VR_A VR_FBAS VR FVAR

Duration Amp. Rel Fré. Abs. Fre. Rel. ms 13-bit address 24-bit 13-bit

VR_ADR VR_A VR_FBAS VR_FVAR

Duration Amp. Rel Fré. Abs. Fre. Rel. ms 13-bit address 24-bit 13-bit

149.33

PIC n ° 2 0.00 21, 33 42.67 64.00 85.33 106.67 128.00 149.33

PIC n ° 3 0.00 21, 33 42.67 64.00 85.33 106.67 128.00 149.33

Total Bits 290 377 120 247 Total Bytes 36 47 15 31 129

Discount 127

As calculated, the number of data in bytes is 129 (36 addresses, 47 amplitude variations, 15 absolute frequencies and 31 frequency variations), a reduction rate of 127 compared to the sample initial which included 8,192 16-bit dots, or 16,384 bytes, and compared to the previous step which included a reduction rate of 108 (152 bytes).

The data received from the registers follow a specific order which allows their classification or their routing in a continuous and unlimited manner, either in sequence on 'n' spectra and 'pn' peaks. On each spectrum, the number of peaks can vary depending on the number of these peaks which have been detected. The spectrum n ° 0 corresponds to the duration 0 ms, the spectrum n ° 1 to the duration 21, 33 ms and so on. The introduction of the addresses makes it possible to classify or to convey the values on peaks which do not follow one another. The following table represents this succession where, for example, the following peaks would be absent:

Spectrum # 0, Peak # 1 Spectrum # 1, Peak # 0

Third step - Weightings:

From the previous table, the different data are formatted according to their respective orders of magnitude and the order of origin of the data. As indicated above, the table does not give the order of data succession, but indicates a classification on each peak for successive spectra (duration). To ensure optimal classification, the data are therefore converted specifically according to their nature (addresses, amplitudes, frequencies).

Addresses:

We have seen previously that the addresses are specified to identify the registers. Following the sequence in the previous table, there are two nested sequences, namely the succession of spectra and, inside these, the succession of peaks. The latter is circular (return to the first peak at the start of a given spectrum). Thus, only the address of the first peak must be established in absolute by specifying which peak it is (normally peak n ° 0, but if it was zero on a given spectrum it could be n ° 1 or a next). So the address specifies the initial peak. The following peaks can be established relative to this initial peak. For example, if peak # 0 is immediately followed by peak # 2, the absolute address of the peak n ° 0 will be the value (0) and the relative address of the peak following n ° 2 will be (+2). We thus reduce the number of data to define the addresses.

The definition of addresses takes into account a specific encoding to define whether it is absolute or relative, then the number of bits necessary to contain it. The address will therefore be defined in 2 sections: that of the type of encoding and the value itself. Typically, a maximum of 256 peaks can be considered as the maximum necessary to contain the data of the analysis, therefore in absolute terms eight bits of maximum value. For example, we could define this type of encoding for each 'Initial Peak' (on a spectrum sequence) and each peak following the initial peak:

The address data are identified (VPB_ADC) for the encoding of the addresses and (VPB_ADV) for the address values proper.

Amplitudes:

The amplitude variation values are weighted according to their order of magnitude. It was shown in the previous step that these values, according to the example, are established on 13 signed bits, i.e. for values between -4,095 and +4,095. The values are divided into two sections, the code and the mantissa. The mantissa values are defined, for example, on nine bits (nine bits + sign) by dividing by 16 the values greater than the magnitude of 255, on nine bits (eight bits + sign) for the values greater than the magnitude of 15 and on five bits (four bits + sign) for values less than the magnitude of 16. The distribution of the values according to their orders of magnitude then requires two code bits.

The following distribution could, for example, be defined for encoding amplitudes:

The amplitude value data are identified (VPB_AX) for encoding and (VPB_AM) for the value of the mantissa.

Frequencies:

The frequency values are weighted according to their order of magnitude. As described in the previous step, these values are established, in this example, on 13 or 24 signed bits, either for values between -4,095 and +4,095 (relative) or between 0 and 16,777 216. The values are divided in two sections: the code and the mantissa. Mantissa values are defined, for example, on 24 bits for absolute values. As for the relative values, which are initially on 13 bits, the mantissa values are defined, for example, on 13 bits (12 bits + sign) for the values higher than the magnitude of 255, on nine bits (eight bits + sign) for values greater than the magnitude of 15 and less than 256, finally on five bits (four bits + sign) for values less than the magnitude of 16. The distribution of the values according to their orders of magnitude will require two code bits.

The following distribution is, for example, defined for frequency encoding:

The frequency value data are identified (VPB_FX) for the encoding and (VPB_FM) for the value of the mantissa.

This way of encoding addresses and values gives the following tables for the present example:

Either for the addresses and the amplitudes: Addresses Amplitudes VPB_ADC VPB_ADV VPB_AX VPB_AM

Duration Code Value Code Value

Total Bits 46 36 58 200 Total Bytes 25 Either for frequencies

Frequency VPB_FX VPB_FM

Duration Code Value

Total Bits 58,283 Total Bytes 35 As calculated, the number of data in bytes is 85 (six and five bytes for codes and address values, seven and 25 for codes and amplitude values, seven and 35 for codes and frequency values), i.e. a reduction rate of 192 compared to the initial sample which included 8,192 16-bit dots, i.e. 16,384 bytes, and compared to the previous step (variations) which included a rate reduction of 127 (129 bytes).

This concludes the example of analyzing a sample and processing the data to classify or route it continuously while reducing the size of the data by a factor of around 200. The initial steps made it possible to obtain the parameters with maximum precision using a combination of different analysis windows in succession. The following steps made it possible to record continuously on registers the values obtained on the successive windows in an order and a sequence both coherent. Finally, the data could be classified or routed or transmitted. The data thus accessible are of a useful nature for signal processing of any kind. They are reduced, but the concept of suitable data reduction is lossless.

The frequency analysis on the different windows has been described using TFR, this type of transform giving the maximum precision for the present method. However, other frequency transforms can also be used, such as for example comb filters where the number of bands must however be as high as the number of TFR spectra.

A signal analysis method according to the present invention makes it possible to obtain certain information at different levels of analysis: level 1 - transitions, level 2 - amplitudes, level 3 - frequencies. Although the previous example has been described with reference to three levels of analysis, level 3 can in certain applications be omitted, the second level of analysis giving very valid frequency values.

In addition, although equations for calculating amplitudes and frequencies have been given, other equations can also be used.

Although the present signal analysis method makes it possible to analyze any type of signal having a temporal variation, the method is however less effective on white noise of short duration (of less length than a level 2 window for example) . However, even in this case, level 1 can detect its nature. It is then possible to shorten the second level window if necessary to correctly perceive the rapid transitions. The result will also be worse on white noise, at the limit on perfect white noise where the spectral lines are strictly equal. Peaks cannot be detected. In such a case, the method will only be able to detect elements which are closely spaced lines and encoded in a similar manner to low energy peaks over wide bands. The decoding can follow this characterization by generating broadband white noise.

The signal analysis method according to the present invention can, of course, be implemented in a system in the form of a computer program. The program also allows adjustments and validation to be made on specific and distinct needs, such as the analysis of broadband or narrowband voice, music, sound in high or medium resolution. Once the different validations performed (windows, parameterization, etc.), the method can also be integrated on a circuit for implantation by parallel processes, for example.

Although the present invention has been described according to a preferred embodiment, it can be modified without however modifying the nature and the spirit of the invention, as defined by the appended claims.

Claims

1. A method of analyzing a signal comprising a time variation, the method comprising: a) sampling the signal at a total number of predefined sampling points; b) split the signal into successive first level analysis windows; said successive first level analysis windows being characterized by a first number of points among said total number of points; c) applying a frequency transform on each of said successive first level windows in order to obtain a frequency spectrum on each of said successive first level windows; d) using said frequency spectra of said first level windows to identify transitions in each of said first level windows; e) define successive second level analysis windows; the start of each second level analysis window corresponding to the start of a first level analysis window having the maximum of transitions among a predetermined number of successive first level analysis windows; said second level analysis windows being characterized by a second number of points among said total number of points; f) applying a frequency transform to each of said successive second level windows in order to obtain a frequency spectrum on each of said second level windows; said spectrum on each of said second level windows comprising peaks; and g) calculating amplitude and frequency values corresponding to said peaks on said frequency spectra obtained over each of said second level windows.

2. Analysis method as described in claim 1, characterized in that in b) said first number of points is weighted on each of said first level analysis windows.

3. Method of analysis as described in claim 2, characterized in that the weighting is carried out using a weighting window of a type chosen from the following types: Hamming, Blackmann and Blackmann -Harris.

4. Analysis method as described in claim 1, characterized in that in c) the frequency transform is a fast Fourier transform (TFR.

5. Analysis method as described in claim 1, characterized in that in d) said transitions in each of said first level windows are determined by comparing the amplitude of each of the frequency bands of the frequency spectrum of said first level window, to the corresponding frequency band of the frequency spectrum of the first level window preceding said first level window.

6. Analysis method as described in claim 5, characterized in that a variable 'vtrn' is calculated on each of said first level windows, where: nbfrèq

∑ \ SPEC [s, n] - SPEC [s -l, n] vtrn = C- ^ nbfrèq

SPEC [s, n]

"O =

C being an arbitrary constant;

SPEC [s, n] being the amplitude of the band 'n' of the frequency spectrum corresponding to the first level window 's'; and nbfrèq being the number of frequency bands in a first level window; the value of 'vtrn' ûu frequency spectrum of the first window of the first level being fixed at the value 'C; and the maximum of transitions corresponding to the maximum value of 'vtrn'.

7. Analysis method as described in claim 1, characterized in that in e) said second number of points is weighted on each of said second level analysis windows.

8. Analysis method as described in claim 7, characterized in that the weighting is carried out using a weighting window of a type chosen from the following types: Hamming, Blackmann and Blackmann -Harris.

9. Analysis method as described in claim 1, characterized in that said second number of points is an integer multiple of said first number of points.

10. Analysis method as described in claim 1, characterized in that in f) the frequency transform is a fast Fourier transform (TFR.

1 1. Analysis method as described in claim 1, characterized in that in g) each of said AMP amplitudes are obtained using the following relation:

np + nba

∑SPEC [n] i AMP • - ^p - ^{nba •}

(2 * nba) + l where np is the position of a peak; nba is a predetermined number of spectral points used to evaluate said amplitude; and

SPEC [n] is the value of the band 'n'.

12. Analysis method as described in claim 1, characterized in that in g) each of said FRE frequencies are obtained using the following relation:

np + nbf

∑ () * SPEC [n] n≈np — nbf

ERE = np + nbf * FBASE;

∑SPEC [n] n≈np-nbf or np is the position of a peak; nbf is a predetermined number of spectral points used to evaluate said frequency;

SPEC [n] is the value of the band 'n'; FBASE is a base frequency.

13. Analysis method as described in claim 1, characterized in that in g) phase values corresponding to said peaks are also calculated.

14. Analysis method as described in claim 1, further comprising: h) storing in separate indexed registers each of said amplitudes and said frequencies corresponding to the first spectrum of said second level spectra; the amplitudes and frequencies associated with the same peak sharing the same index; and for each of the spectra following 's' said first spectrum among said successive second level spectra: i) verifying the frequency compatibility of each of the peaks of the spectrum 's' with each of the peaks of the preceding spectrum; j) store in separate indexed registers each of said frequencies corresponding to peaks of the spectrum 's'; the peaks compatible in frequency with one of said peaks of the previous spectrum sharing the same index as said one of said peaks; new indices not yet assigned so far being assigned to the frequencies corresponding to the peaks which are not frequency compatible; k) check the amplitude compatibility of each of the peaks of the 's' spectrum with each of the peaks of the preceding spectrum; and

I) store in separate indexed registers each of said amplitudes corresponding to each of the peaks of the spectrum 's'; the peaks compatible in amplitude and in frequency with one of said peaks of the previous spectrum sharing the same index as said one of said peaks; new indices not yet assigned so far being assigned to the pairs of amplitude and frequency values corresponding to the non peaks. compatible in amplitude and frequency.

15. Analysis method as described in claim 14, characterized in that in i) the frequency compatibility is established on the basis of variation of frequency value of each of the peaks of the spectrum 's' with each of the peaks in the previous spectrum within a predetermined range.

16. Analysis method as described in claim 14, characterized in that in k) the amplitude compatibility is established on the basis of variation of the amplitude value of each of the peaks of the spectrum 's' with each of the peaks in the previous spectrum within a predetermined range.

17. Analysis method as described in claim 14, further comprising: m) truncating said frequency and amplitude values in said subscript registers to a predetermined number of bits.

18. Analysis method as described in claim 14, further comprising: m) expressing each of said frequency values of a spectrum in said indexed registers in terms of values relating to the frequency value corresponding to the peak previous in said spectrum; the frequency value of said spectrum corresponding to the first peak remaining unchanged.

19. Analysis method as described in claim 1, further comprising: h) defining successive third analysis windows level; the start of each third level analysis window corresponding to the start of a first level analysis window having the maximum of transitions from a predetermined number of successive first level analysis windows; said third level analysis windows being characterized by a third number of points among said total number of points; said third number of points being greater than said second number of points; i) applying a frequency transform on each of said successive third level windows in order to obtain a frequency spectrum on each of said third level windows; said spectrum on each of said third level windows including peaks; and j) calculating amplitude and frequency values, corresponding to said peaks, on said frequency spectra obtained on each of said third level windows.

20. Analysis method as described in claim 19, characterized in that said third number of points is an integer multiple of said second number of points.

21. Analysis method as described in claim 19, characterized in that in h) the third number of points is weighted on each of said third level analysis windows.

22. Analysis method as described in claim 21, characterized in that the weighting is carried out using a weighting window of a type chosen from the following types: Hamming, Blackmann and Blackmann -Harris.

23. Analysis method as described in claim 19, characterized in that in j) each of said AMP amplitudes are obtained using the following relation: np + nba

ΣSPEC [n]

_{AMp =} n ₌ n _El nba

(2 * nba) + 1 where np is the position of a peak; nba is a predetermined number of spectral points used to evaluate said amplitude; and

SPEC [n] is the value of the band 'n'.

24. Analysis method as described in claim 19, characterized in that in j) each of said FRE frequencies are obtained using the following relation: np + nbf

∑ (n) * SPEC [n] n = np-nbf

ERE = np + nbf * FBASE

∑SPEC [n] n = np-nbf where np is the position of a peak; nbf is a predetermined number of spectral points used to evaluate said frequency;

SPEC [n] is the value of the band 'n'; FBASE is a base frequency.

25. Analysis method as described in claim 19, further comprising: k) storing in separate indexed registers each of said amplitudes corresponding to the first spectrum of said second level spectra and of said frequencies corresponding to the first spectrum of said spectra third level; the amplitudes and frequencies associated with the same peak sharing the same index; and for each of the spectra 's' according to said first spectrum among said successive second level spectra:

I) check the frequency compatibility of each of the peaks of the 's' spectrum with each of the peaks of the second level spectrum; m) storing in separate indexed registers each of said frequencies corresponding to the spectrum 's'; the peaks compatible in frequency with one of said peaks of the second level spectrum sharing the same index as said one of said peaks; new indices not yet assigned so far being assigned to the frequencies corresponding to the peaks which are not frequency compatible; n) check the amplitude compatibility of each of the peaks of the 's' spectrum with each of the peaks of the second second level spectrum; and o) storing in separate index registers each of said amplitudes corresponding to the spectrum 's'; the peaks compatible in amplitude and in frequency with one of said peaks of the previous spectrum sharing the same index as said one of said peaks; new indices not yet assigned so far being assigned to the pairs of amplitude and frequency values corresponding to the peaks which are not compatible in amplitude and frequency.

26. The analysis method as described in claim 25, further comprising: p) truncating said frequency and amplitude values in said subscript registers to a predetermined number of bits.

27. Analysis method as described in claim 25, further comprising: p) expressing each of said frequency values of a spectrum in said indexed registers in terms of values relating to the frequency value corresponding to the peak previous in said spectrum; the frequency value of said spectrum corresponding to the first peak remaining unchanged.

28. Analysis method as described in claim 19, further comprising: k) filtering each of said successive third level windows using a low-pass filter having a predetermined cut-off frequency providing a certain bandwidth, resulting from the corresponding third level windows filtered;

I) compressing said corresponding third level windows filtered according to the ratio of the band to the total spectrum of the sampled signal; m) adding null terms before and after said compressed third level windows so that there results in said compressed third level windows a number of points equal to the third number of points; n) applying a frequency transform to each of said successive third level compressed windows in order to obtain a modified frequency spectrum on each of said compressed third level windows; and o) calculating amplitude and frequency values on said frequency spectra obtained on each of said compressed third level windows; where the frequencies calculated on said frequency spectra obtained on each of said third level windows correspond to high frequencies, and where the frequencies calculated on said frequency spectra obtained on each of said compressed third level windows correspond to low frequencies.

29. Analysis method as described in claim 28, characterized in that said low-pass filter is a type IIR filter.

30. Analysis method as described in claim 28, characterized in that in o) each of said amplitudes AMP are obtained using the following relation:

np + nba

ΣSPX [n]

_{AMp =} n ₌ np-nba

(2 * nba) + l where np is the position of a crest; nba is a predetermined number of points in the modified spectrum used to evaluate said amplitude; and

SPX [n] is the value of the band 'n' of said modified spectrum.

31. Method of analysis as described in claim 28, characterized in that in o) each of said FRE frequencies are obtained using the following relation:

np + nbf

Σ (n) * SPX [n]

FRE = n≈np-nbf np + nbf * FXBASE;

∑SPX [n] n≈np-nbf or np is the position of a peak; nbf is a predetermined number of spectral points used to evaluate said frequency;

SPX [n] is the value of the band 'n said modified spectrum; FXBASE is a base frequency.

32. Analysis method as described in claim 28, further comprising: p) storing in separate indexed registers each of said amplitudes corresponding to the first spectrum of said second level spectra and of said frequencies corresponding to the first spectrum of said spectra third level; the amplitudes and frequencies associated with the same peak sharing the same index; and for each of the spectra 's' following said first spectrum among said successive third level spectra: q) verifying the frequency compatibility of each of the peaks of the spectrum 's' with each of the peaks of the second level spectrum; r) store in separate indexed registers each of said frequencies corresponding to the spectrum 's'; the peaks compatible in frequency with one of said peaks of the second level spectrum sharing the same index as said one of said peaks; new clues not yet assigned so far being assigned to frequencies corresponding to peaks which are not frequency compatible; s) check the amplitude compatibility of each of the peaks of the 's' spectrum with each of the peaks of the previous spectrum; and t) store in separate index registers each of said amplitudes corresponding to the spectrum 's'; the peaks compatible in amplitude and in frequency with one of said peaks of the second level spectrum sharing the same index as said one of said peaks; new indices not yet assigned so far being assigned to the pairs of amplitude and frequency values corresponding to the peaks which are not compatible in amplitude and in frequency.

33. Analysis method as described in claim 32, characterized in that in q) frequency compatibility is established on the basis of variations in frequency values of each of the peaks of the spectrum 's' with each of the peaks in the previous spectrum within a predetermined range.

34. Analysis method as described in claim 32, characterized in that in s) the amplitude compatibility is established on the basis of variations in amplitude values of each of the peaks of the spectrum 's' with each of the peaks in the previous spectrum within a predetermined range.

35. Method of analysis as described in claim 1, characterized in that said second number of points is variable from one second level window to another; said second number of points being chosen so that it is relatively short when said transitions are higher than a predetermined threshold among said predetermined number of successive windows of first level analysis, and relatively long when said transitions are less higher than a predetermined threshold among said predetermined number of successive windows of first level analysis.

36. A system for analyzing a signal comprising a time variation, the system comprising: a) means for sampling the signal at a total number of predefined sampling points; b) means for cutting the signal into successive first level analysis windows; said successive first level analysis windows being characterized by a first number of points among said total number of points; c) means for applying a frequency transform to each of said successive first level windows in order to obtain a frequency spectrum on each of said successive first level windows; d) means for using said frequency spectra of said first level windows to identify transitions in each of said first level windows; e) means for defining successive second level analysis windows; the start of each second level analysis window corresponding to the start of a first level analysis window having the maximum of transitions from a predetermined number of successive first level analysis windows; said second level analysis windows being characterized by a second number of points among said total number of points; f) means for applying a frequency transform to each of said successive second level windows in order to obtain a frequency spectrum on each of said second level windows; said spectrum on each of said second level windows comprising peaks; and g) means for calculating amplitude and frequency values corresponding to said peaks on said frequency spectra obtained on each of said second level windows.