FR2601164A1 - METHOD FOR DETERMINING TIME - BASED VARIATION OF SEVERAL SPECTRAL ROUTES OF SIGNAL EVOLUTIONS. - Google Patents

Abstract

A) PROCESS FOR DETERMINING THE VARIATION AS A FUNCTION OF TIME OF SEVERAL SPECTRAL RAYS OF EVOLUTIONS IN SIGNALS. B) THE OBJECT OF THE INVENTION IS TO DETERMINE, USING THE RAPID TRANSFORMATION OF FOURIER THE EVOLUTION AS A FUNCTION OF TIME OF SEVERAL SPECTRAL RAYS OF A FREQUENCY SPECTRUM CONSISTING OF SHORT-TERM SIGNAL SEGMENTS, THE NUMBER OF MEASUREMENT DATA REQUIRED FOR FOURIER TRANSFORMATION TO BE DETERMINED TO AVOID NEGATIVE INFLUENCE ON THE ACCURACY OF THE FREQUENCY POSITION OF THE SPECTRAL RAYS. C) THE INVENTION RELATES TO METHODS FOR DETERMINING THE VARIATION AS A FUNCTION OF TIME OF SEVERAL SPECTRAL RAYS OF SIGNAL EVOLUTIONS.

Description

i. "Method for determining the variation as a function of time

  The invention relates to the measurement of the frequency position of several spectral lines in the spectral representation of signal evolutions, mainly when a variation of the frequency position of the lines takes place. The invention can be applied in technological diagnosis, for example in rotation examinations, in speech analysis and in the fields of medicine, for example, by means of frequency modulation. in the

  rehabilitation of the handicapped of the way or the speech.

  For the determination of the variation as a function of time of several spectral lines, Fourier analysis is known for successive time intervals (for example in the apparatus 2031 of the firm BrUel and Kjaer). The use of the Fourier analysis for successive time intervals has so far been carried out with N measurement data, all the N measurement data possibly being multiplied, before the transformation, by special window functions, for example by a Haning function, to reduce truncation effects. As a result of the N measurement data, 2. in a given scan time tA; the resolution of the frequency is: f = 1 / NtA For the low frequencies K / NtA (K = 1,2 ...) there is consequently a large relative error, which prevents in this zone an exact determination of the variation as a function of time of the frequency position of spectral lines. Despite a coarse frequency resolution af, the accuracy with which the spectral lines are determined could be greater than the resolution of the frequency provided that there is a substantially periodic signal whose base period is fully covered by N data. measured. If the N measurement data cover more or less than a multiple of the base period, the result is known truncation effects, which not only cause amplitude errors but also produce additional spectral lines in the spectral spectrum. Fourier. From the publication of Auth 20 W .; Lacroix A .: "Dreidimensional Darstellung von Sprachgrundfrequenzsynchron berechneten Sprach-Spektrogrammen" (Three-dimensional representation of speech spectrograms computed synchronously with respect to the basic frequency of speech), NTZ, H. (1971) p. 502-507, it is known, therefore, to carry out the Fourier transform with a set of N values which always cover a base period or a multiple of it. In this way, in spite of a coarse resolution of the frequency, the result for short signal segments is a granule of accuracy of the spectral lines determined within the frequency frame. The disadvantage is that the number M must also take continuous values for continuous variations of the base period, and therefore it is not possible to directly apply the fast transformation algorithm. of

26011-64

  3.- Fourier, because this one does not allow a continuous variation

number of points.

  In order to take advantage, for the spectral determination of short-term signal segments, the advantages associated with the rapidity of the fast Fourier transformation, in accordance with the Schafer, R.W., Rabiner L.R publication; "Digital Representation of Speech Signals", Proceedings of the IEEE, Volume 63, No. 4, April 1975, pages 662-677, 10 within the base period, complete with value 0 the number of measuring points to as many points as necessary, until the number N is reached which is necessary for a fast Fourier transformation. However, this has the disadvantage that it leads to a convolution of the window function (eg Hanning function in the Schafer publication with NM zeros added) by the measured values.This convolution "scrambles" and shifts the spectral lines and, in this way, degrades the resolution of the spectral lines again. Frequency and accuracy of the spectral lines

  amplitude and frequency position.

  The object of the invention is to determine the variation as a function of time of the frequency position, so that the frequency modulation is solved in a sufficiently precise manner as a variation of the lines.

spectral as a function of time.

  The object of the invention is to determine, by means of the fast Fourier transformation, the evolution as a function of time of several spectral lines of a frequency spectrum consisting of segments of signals this short duration, the number measurement data that is required for the Fourier transform to be determined in order to avoid a negative influence on

  the accuracy of the frequency position of the spectral lines.

  4. A goal is achieved, according to the invention, in a method in which successive signal segments are digitally captured and the signals are subjected to a fast Fourier transformation, characterized in that the set of measured values of each segment of signal which cover the base period, are sequentially repeated in sequence until either a base power 2 (2n) or a suitable number for the rapid transformation of 10 is reached or just exceeded. Fourier, and the succession of signals thus composed is subjected to the rapid Fourier transformation by determining in a first step, in a known manner, the base period T of the first signal segment and putting in memory in a first zone of the M measured values belonging thereto, in that, in a second step, the M measured values are transferred to a second memory area having N memory positions re, the M values measured from the first memory area being first stored on the first M memory positions of the second memory area in the same order as in the first memory area and then the NM positions in the second memory area being occupied in the same order, so that the resulting k A M + I results in the second memory area as a succession of N measurement data are repeated, the number of L data characterizing the truncation when the number of N data is reached, in that, in a third step, the fast Fourier transformation of the N measured values from the second memory area is performed, and in that that, in a fourth stage, the intensities of i. K-th spectral lines are addressed and sent to the output or display, taking the values 1, 2 ... M / 2 and K determining the part of the integer number of the N / M ratio, and that the Process steps are then repeated for 5.

the following signal segments.

  The intensities of the spectral lines thus determined can be carried, as dependent functional values, in the form of a curve as a function of time over a fixed period At or as a function of the base period by means of the sensor of the base period , each spectral line being represented by a band whose lower edge is determined by the frequency position, the height of which is determined by the intensity and whose extension in the abscissa is determined by time. The method is suitable for determining nonstationary signals of short duration spectra, when in a signal segment (time interval) an approximation of a stationary behavior is applied. This means that the evolution of non-stationary signals, which is marked by amplitude and frequency modulation, is broken down into segments in which the amplitude and frequency modulation is still negligible. This is possible for many technological and biological signals, eg

  power of an industrial apparatus, voice or the like.

  Amplitude and frequency modulation is manifest

  then by a variation in time of the spectra of short duration.

  This method has the advantage that the accuracy of the frequency position of the spectral lines from short-lived signal segments in the spectrum, which is formed after the fast Fourier transformation, is

  increased compared to known methods.

  Another possibility is to perform in a first step an analog digital convversion of the signal to be analyzed, with a scanning frequency which is at least higher by the factor L to

  the value which it should have, according to the postulate of the sweeping theorem, for the highest frequency

260 1,164

  6. lysing, to determine, in a known manner, in a second step, the base period of the first signal segment with the M measured values belonging thereto, to select, in a third step, the first M / L measured values, of the M values measured, by capturing in a memory only each L-th value, until a maximum number of data is reached or exceeded for the fast Fourier transformation, for example an entire base-two power (2n ), to perform, in a fourth step, the fast Fourier transformation, to determine in a known manner, in a fifth step, the intensities of the spectral lines, and to send them to the output or the display, and then to repeat the stages of

  process for the following signal segments.

  Thanks to the scanning frequency, increased by the factor L, the M / L measuring points to be transformed are distributed in the base period of the measurement window, so that the truncation effect is more only if it were determined by the number that would be given on the basis of the sweep theorem. The present invention is illustrated by the following nonlimiting and descriptive examples and with the aid of the accompanying drawings, in which: FIG. 1 represents: a) the power spectrum of the "0" speech signal, at a scanning frequency of 26713 Hz, a measurement window of 9 ms (240 measurement points) and with a zero inclusion subsequent to 4 Y. b) the power spectrum of the speech signal "0" at a scanning frequency of 26713 Hz, and at a measuring window of 150 ms (4000 measurement points), - Figure 2 represents: a) the power spectrum according to figure 35 lb, 7. b) the power spectrum of the speech signal "0" at a scanning frequency of 26713 Hz and with implementation of the method according to the invention, -3 shows an assembly for the implementation of the method. Comparing the spectra of FIGS. 1a and 1b, there is clearly "scrambling" and peak shift, when the inclusion of zeros has been carried out by known methods (inclusion of zeros after determination of the base period, until to reach an N number which is eligible for a fast

Fourier trarnsformation).

  Figure 2 demonstrates the improvement that is obtained with the method according to the invention. With respect to the spectrum according to FIG. 1a, or respectively 2a, no offset is observed for frequency lines. The rays

  have virtually no "scrambling".

  From a signal curve starting at time t = to, n values of a signal segment are determined in a known manner and stored in a first memory area. From these n values, according to the known method according to the application DDR WPG 01 L / 259 175 3, the base period T is determined and, consequently, the

number M of the measured values.

  For the fast Fourier transformation, there is a second memory area having the capacity NI. The measured values M are placed in succession after each other, and stored in a repeating sequence, in K blocks (K = N / M) in the memory zone 30 having the capacity N, then subjected to the rapid transformation of Fourier. The last block in the second memory area has, before the fast Fourier transform, the number D = N - K. M of measured values and therefore has a truncation in the length of the base period. This truncation is all the less sensible, as a subsequent error after the rapid Fourier transformation, that the ratio K = N / M is

higher.

  The analog-to-digital translator (ADO) in the measurement amplifier 1-translates at a higher scanning frequency than would be necessary, according to the scanning theorem, for example at 833 kHz for recording speech signals at limited band, at a

  upper limit frequency of 4 kHz.

  A real-time base frequency indicator 2 determines the base period of the measured values translated by the ADC, for example 11 ms, ie M = 9163 measurement points. The number M is transmitted to a signal processing unit 3. It is necessary to give

  the order that eight frequency bands are to be determined.

  After the identical part, the first frequency must be identical to the base frequency, that is to say, rise for example to 90.909 Hz. The following sequences must be determined as harmonics with n. 90.909 Hz (m = 2.3.6). The function of the signal processing unit 3 is then to determine; from the number M = 9163 and from the order M / L = 16, the value L = 573, and from submitting, among the M = 9163 measured values stored, only each 573 th to a fast Fourier transformation . This results in truncation of 5 measuring points. Compared to 9163 measurement points per period, this means a truncation error of less than

  1> 4, relative to the length of the base period.

  This low truncation error is only the result of small line position errors, less than 1% o, by

  compared to the base frequency, although the resolution of the frequency is identical to the base frequency.

  Data is output or displayed on a device

  display, using a computer 4.

26.01164

9.

Claims (2)

CLAIMS N E N T I O N T I 0 N S   1. A method for determining the variation as a function of time of several spectral lines of signal evolutions, in which successive signal segments are digitally captured and the signals are subjected to a rapid transformation of Pourier, characterized in that that the set of measured values of each signal segment which cover the base period are sequentially sequenced to one another until a base power 2 (2n) is reached or just exceeded. or a suitable number for the fast Fourier transformation, and in that the succession of signals thus composed is subjected to the fast Fourier transformation by determining in a first step, in a known manner, the basic period T of the first segment. signal and storing in a first memory area the M measured values belonging thereto, in that, in a second step, the M measured values are nsféiés in a second memory area having N memory positions, the M measured values from the first memory area being first stored on the first M memory positions of the second memory area in the same order as in the first memory area and then the next NM memory locations in the second memory area being occupied in the same order, thereby resulting in the k's. M + X given in the second memory area as a succession of N repeating measurement data, the number of L data characterizing the truncation when the number of N data is reached, in that, in a third step, the fast Fourier transformation of the N measured values from the second memory area, and in a fourth step the intensities of the i. K spectral lines are addressed and sent to the output or the display, taking the values 1, 2 ... M / 2 and K determining the part of the integer of the N / M ratio and that the process steps are then repeated   for the following signal segments.   2. A method for determining the variation as a function of time of several spectral lines of signal evolutions, in which successive signal segments are digitally captured and the signals are subjected to a fast Fourier transformation, which is characterized in that in a first step, an analog-to-digital conversion of the signal to be analyzed is performed, with a scanning frequency which is at least greater by the factor L than the value it should have, according to the postulate of the scanning theorem, for the highest frequency to be analyzed, in that the base period of the first signal segment is determined in a known manner in a second step with the M values belonging thereto, in that one selects in a third step, the first / 1> measured values, among the M measured values, by capturing in a memory only each L-th value, until it is reached or exceeded u n number of data admissible for the fast Fourier transformation, for example an entire power base two (2n), in that it is effec25 killed, in a fourth step, the rapid Fourier transformation, in that one determines, in a known manner, in a fifth step, the intensities of the spectral lines and sends them to the output or the display, and   in that the process steps are then repeated for the following signal segments.