WO1994003866A1

WO1994003866A1 - Process for determining spectral components of a sequence of data and device for implementing it

Info

Publication number: WO1994003866A1
Application number: PCT/DE1993/000509
Authority: WO
Inventors: Andreas Wolf; Hans Werner Arweiler
Original assignee: Siemens Aktiengesellschaft
Priority date: 1992-07-29
Filing date: 1993-06-07
Publication date: 1994-02-17
Also published as: DE4225401C1; AU4306693A

Abstract

In order to determine spectral and/or periodic portions in a sequence of data (d(n)) containing binary values (0; 1) at a number (N) of position numbers (n), the data sequence (d(n)) is evaluated by position number at discrete evaluation points (m) with a complex analysis function (f(n, m)). To this end, to form a complex binary analysis function (BA(n, m)) on the complex analysis function (f(n, m)), a comparator function (k) is used in accordance with the prescription: k {f(n, m)} = + 1 for f(n, m) > (S); k {f(n, m)} = - 1 pour f(n, m) < (S); k {f(n, m)} = - 1 or + 1 for f(n, m) = (S); with (S): as the threshold value within the range of values of the analysis function (f(n, m)). The values (0, 1) of the data sequence (d(n)) are then multiplicatively concatenated with the binary values (-1, +1) of the binary analysis function (BA(n, m)) allocated to them and the sum of the results of concatenation (QS) is formed and evaluated for at least one evaluation point (m).

Description

Method for determining spectral components of a data sequence and device for carrying out the method

The invention relates to a method for determining

spectral components of a data sequence that are part of a number

contains binary values from position numbers, and a device for carrying out the method.

The task arises in digital measurement technology

digital signal in the form of a data sequence with a

Numerous binary values with regard to periodic components

or to examine the frequency spectrum. There is one

Application of classic transformation methods, for example the Fourier, Z and Laplace transformation,

conceivable.

The discrete Fourier transform (DFT) of a sequence of numbers d (n) is, for example, for the computational implementation of the known transformations

Regulation /

known; With:

N: field length of the data sequence d (n),

m: discrete evaluation points.

According to equation (1), the data sequence to be examined is

d (n) item number at discrete evaluation points

m evaluated with the complex analysis function e ^-jz = f (n, m) By applying the Euler 's relationship to the complex analysis function one obtains:

as the representation of the discrete Fourier transform (DFT) separated by real and imaginary part.

In the known methods, the

Fourier transformations are carried out as discrete Fourier transformations DFT according to equation (2), with algorithms that reduce computing time, such as e.g. the

Fast Fourier Transform FFT, can be used. The computing time and complexity is discrete

Fourier transform DFT and the Fast Fourier transform FFT essentially by multiplying the multivalued analysis functions f (n, m) by the binary

Number sequence d (n) determined. In spite of algorithms that shorten computing time, the attainable limit frequencies lie

comparatively low with extremely high circuit complexity for real-time implementation.

Real-time analysis using Fast Fourier transformation - e.g. for a data sequence d (n) with a number of

N = 1024 position numbers or binary values - is

currently with conventional successive arithmetic units to a cut-off frequency of approximately 1 MHz or to one

Data rate limited to approximately 1 Mbit / s.

The object of the invention is therefore to create an extremely fast, low-effort method for the reliable determination of spectral components in a binary data sequence.

This problem is solved by a method for determination spectral components of a data sequence that contains binary values for a number of position numbers,

- in which the data sequence corresponds to position number

discrete evaluation points are evaluated with a complex analysis function,

╌ by using a comparator function

Value of the analysis function depending on the size of this value in relation to a threshold value, a binary value according to the rule k {f (n, m)} = + 1 for f (n, m)> (S)

k {f (n, m)} = - 1 for f (n, m) <(S)

k {f (n, m)} = - 1 or + 1 for f (n, m) = (S)

with (S): threshold value within the value range of the analysis function (f (n, m)) is assigned to form a complex binary analysis function and

╌ then the values of the data sequence are multiplicatively linked to the binary value of the binary analysis function assigned to them, and

- where the sum of the link results for

at least one evaluation point is formed and evaluated.

An essential basic idea of the invention is that the analysis is a (preferably bipolar) binary

Data sequence with a binary analysis function provides sufficiently precise analysis results so that an elaborate multiplication of a binary data sequence with a multi-value analysis function can be replaced by a simple link.

By using the comparator function on the Complex analysis function becomes a first or second value of the complex analysis function according to the predetermined threshold value in an easily realizable manner

Binary value assigned. It can be used without limitation

The method defines whether, if a value of the complex analysis function is equal to the threshold value, this value of the analysis function is assigned the first or the second binary value. The multiplicative linkage to be carried out in the method according to the invention is thereby advantageously reduced to the width of only one place in each case. This results in further advantages of the method according to the invention in the extraordinarily high process speed and the very low circuit complexity for carrying out the method. The method according to the invention can be implemented entirely in digital technology using simple logic modules. The analysis function can be formed, for example, by periodic rectangular functions or sawtooth functions; A particularly advantageous embodiment of the method according to the invention is, however, that trigonometric functions are used as the complex analysis function and that the threshold value has the value zero. at

Using trigonometric analysis functions and a threshold value of zero, a particularly high convergence of the results achievable with the method according to the invention can be achieved in comparison with results achievable with the Fast Fourier transformation. In this embodiment of the method, the comparator function k can, for example, according to the regulation k {f (n, m)} = + 1 for f (n, m) ≥ 0 (3) k {f (n, m)} = - 1 for f (n, m) <0 on the complex analysis function f (n, m) are applied, so that there is a total of a Fourier transform BFT according to the equation

with a binary analysis function BA (n, m). With the substitutions cs (n, m) = k {cos (2πnm / N)} and (5) sn (n, m) = k {sin (2 nm / N)} (6) one obtains from equation (4 / b)

In order to implement real-time processing for the highest possible frequencies, methods for determining spectral components in a data sequence generally offer hardware implementations that work in parallel. Table 1, which compares the processing of a data sequence d (n) with a length N = 1024 with the known Fast Fourier Transformation (FFT) in a parallel processing process on the one hand and the method (BFT) according to the invention on the other hand, for comparison purposes, go the advantages of the invention already mentioned Process particularly clear in terms of processing speed and implementation costs

out.

It can be seen from Table 1 that the cut-off frequencies for real-time implementation in the known method (FFT) for parallel real-time implementation are 31 MHz and in the inventive method in the range of 430 MHz. The method according to the invention is characterized by a comparatively small number of necessary gates. In contrast, a parallel FFT circuit would not be economical due to the large number of 322560 gates.

An embodiment of the method according to the invention which is advantageous with regard to the implementation of the method consists in that the complex binary analysis function is formed and stored in advance for a large number of position numbers and evaluation points.

The accuracy and reliability of detection

According to an advantageous embodiment of the method according to the invention, periodic components can be increased in that the positions of the data sequence are scanned several times and corresponding to the number of scans several times with the position number-specific one Value of the binary analysis function can be linked.

Contains a preferred device for carrying out the method according to the invention

a device which assigns the binary values of the complex binary analysis function to unipolar binary values,

a linkage stage which multiplies the unipolar binary values of the data sequence by the position number-specific unipolar binary values of the complex binary analysis function assigned to the respective evaluation point, and

- A summing device which forms the cross sum for the real and imaginary part of the result of the combination. If the data sequence is in the form of bipolar binary values, these are previously converted into unipolar binary values

Values converted.

The device according to the invention is relatively simple and can be constructed using purely digital technology; she

delivers through the simple linking steps in

Results that can be evaluated in the shortest possible time.

To increase the reliability and accuracy of results, an advantageous embodiment of the device according to the invention contains

a multiple scanner which samples each value of the data sequence several times, preferably twice, and

a device that assigns each binary value of the complex binary analysis function unipolar binary values in a number corresponding to the number of samples.

The device according to the invention is advantageously independent of external data feed devices and signal propagation times through a memory in which the complex binary analysis function or the unipolar binary values assigned to their values for those of interest

Evaluation points are saved. A particularly preferred embodiment of the logic level in terms of circuitry is that the logic level is formed by EXCLUSIVE-OR logic elements with a subsequent inverting level. The invention is explained in more detail below using exemplary embodiments with the aid of a drawing; show it:

Figure 1 differences between a known complex

Analysis function and a binary analysis function used in the method according to the invention,

Figure 2 shows an example calculation for the determination of

Real and imaginary parts of a binary analysis function,

Figure 3 is a graphical representation of results of the inventive method and

Figures 4 and 5 devices for performing the method according to the invention.

FIG. 1 illustrates positions and number of pointers of a complex analysis function in a discrete Fourier transformation DFT according to equation (1) and a binary analysis function BA (n, m) used in the method according to the invention for an example with a field length N = 8 of a data sequence d (n) and for evaluation points m = 1 and m = 2. Due to the comparator function k, the binary analysis function

BA (n, m) four possible pointer positions z1 to z4 regardless of the discrete evaluation point m selected in each case (FIGS. 1A and 1C). In contrast, the known discrete Fourier transform results for the Analysis function f (n, m) depending on the evaluation point m different possible pointer positions zl to z8 each with the unit length (FIG. 1B) and zl to z4 (FIG. 1D).

The sequence of the method according to the invention is described in detail below with reference to FIGS. 2 and 3. To choose from an example

unipolar binary data sequence d '(n), the number N = 8 of position numbers n unipolar binary values 0.1 according to equation (8) d' (n) = (1,0,0,0,1,0,0 , 0) (8), the data sequence d '(n) is evaluated position by number at discrete evaluation points m = 0 to m = 7 with a complex trigonometric analysis function f (n, m) (equation (2)). For this purpose, according to equation (3), using the comparator function k, a first value of the analysis function f (n, m) lies below a threshold value S = 0

Binary value -1 assigned. A second binary value +1 is assigned to each value of the analysis function f (n, m) that lies above the threshold value S or is equal to the threshold value S. A complex binary analysis function BA (n, m) is thus formed with a real and imaginary part according to equations (5) and (6), to which unipolar binary values 0; 1 are then assigned. Line B of FIG. 2 shows the relationship between the respective discrete evaluation point m = 0 to 7 (line A in FIG. 2) and the respective form of equations (6) and (5)

Row C column-shaped unipolar binary values for the imaginary part sn '(n, m) and the real part cs' (n, m) result from inserting n, m into the equations (6) and (5) by position number. The on complex binary analysis function formed in this way

(BA (n, m) for different position numbers n and

Evaluation points m can preferably be formed and stored in advance.

The respective values 0.1 of the data sequence d '(n) are then multiplicatively linked with the respective unipolar binary value 0.1 of the binary analysis function BA (n, m) assigned to them. In terms of circuitry, the multiplicative combination is carried out in a simple manner by means of an EXCLUSIVE-OR combination and subsequent inversion. In line D of FIG. 2, the EXCLUSIVE-OR combination of the respective parts sn '(n, m) and cs' (n, m) of the binary analysis function with the data sequence d' (shown on the far left in line D) is accordingly first (n) shown. Because of the negative

The sign of the imaginary part is only to be inverted due to the multiplicative link (the imaginary part remains unchanged due to the double inversion due to the multiplicative link on the one hand and the negative sign according to equation (7) on the other). In the columns of FIG. 2 assigned to the respective evaluation points m, the values of the imaginary part are each in the first sub-column, while the values of the real part are each in the third sub-column under the symbol INV.

In lines E and F of FIG. 2, the cross-sums QSI and QSR for the real-Re and imaginary part Im are separated. Line G contains the amount QS of the linking results for the evaluation points m = 0 to m = 7, determined from the cross-sums QSI and QSR. Deviating from the relationship known from the DFT, the value QS represents m = 0 does not represent the mean of the data sequence d (n).

In the case of a single sampling of each value of the data sequence d '(n), the DFT or BFT basically gives the double spectrum over the value N. In the present

For example, only the first 4 evaluation points m = 0 to m = 3 are considered.

A maximum of 5.6 of the total QS occurs at the evaluation point m = 2. The period of the trigonometric functions on which the analysis functions sn (n, m) and cs (n, m) are based is "4" at the evaluation point m = 2. The maximum at m = 2 thus indicates a periodic portion with the period 4 (value 1 in the first and fifth position of the data sequence d '(n)). The small field length N chosen only for better explanation leads to comparatively little characteristic results.

As can also be seen from FIG. 3 below, as is generally known from the field of Fourier transformations, significantly longer field lengths N are required in order to arrive at meaningful results.

FIG. 3 shows a simulation BFT1, BFT2 according to equation (7) for a data sequence dl (n) = (0.1.0.0.0.0.0.0.0.1.0.0.0.0, 0, ...) (9) with the striking period of 8 in the spectral range and a number N = 128 of position numbers n. FIG. 3 illustrates that the method according to the invention is particularly useful for double scanning (simulation) BFT2, which then supplies 256 evaluation points m , only marginally from an analysis result with a discrete Fourier Transformation DFT1 deviates with a sample value (corresponding striking spectral line MSP).

FIG. 4 shows a device for carrying out the method according to the invention, the data sequence d '(n) according to equation (8), for example, to be evaluated by position number by way of example at the discrete evaluation point m = 2. The device contains a device 10 and 11 which assigns the unipolar binary values 0 and 1 to the binary values -1 and +1 of the complex binary analysis function. This assignment takes place separately according to the real and imaginary part, so that the imaginary part by

Expression sn '(n, m) and the real part is represented by the expression cs' (n, m). That way

modified values of the binary analysis function BA (n, m) are written into memories 12 and 13, from which the values can be read out which the

are assigned to the respective evaluation point m and the position numbers n. In the present example, the values for the real and imaginary parts sn '(n, 2) and cs' (n, 2) are read out of the memories 12 and 13 with regard to the selected discrete evaluation point m = 2.

A logic level V multiplies the binary values 0 and 1 of the data sequence d '(n) by those of the considered

Evaluation point m = 2 assigned position number-specific unipolar binary values 0 and 1 of the complex binary

Analysis function BA (n, m). A summing device 15 forms the cross sum QSI and QSR for the real part Re (2) and the imaginary part Im (2) of the combination result. In a subsequent amount-forming step 16, the amount of the total linking result is determined by squaring and subsequent square rooting. The respective unipolar binary values for the real or The imaginary part of the binary analysis function sn '(n, 2) and cs' (n, 2) have previously been provided in the manner explained in connection with FIG. 2 (cf. line C under m = 4). Linkage level V consists of

EXCLUSIVE-OR logic elements EXOR1 and EXOR2, the logic element EXOR2 being followed by an inversion stage INVT. An inversion level to be added to the logic element EXOR1 for the multiplication is omitted due to the negative sign of the imaginary part.

FIG. 5 shows a section of the device according to FIG. 4, which has been modified with regard to the sampling frequency of the data sequence d '(n) and the linkage. The data sequence d '(n) is scanned twice by a multiple scanning device 20, so that a modified data sequence d' '(n) results, in which each position is duplicated with the corresponding value compared to the original data sequence d' (n) is. A duplicator 21 and 22 orders the binary values -1 and +1 of the complex ones

Binary analysis function unipolar binary values 0 and 1 in a number (here: two) corresponding to the number of samples (here: twice) of the multiple scanning device 20. This results in the proportions sn '' (m, 2) and cs '' (n, 2) for the binary analysis function of BA (n, m) for the imaginary and real part of the evaluated evaluation point m = 2.

As already explained in connection with FIG. 3, multiple scanning with a comparatively small increase in effort enables a further increased correspondence between that determined according to the inventive method and the inventive apparatus

Analysis results compared to the results of a discrete Fourier transform.

Claims

1. Method for determining spectral components of a

Data sequence (d (n)) which contains binary values (0; 1) on a number (N) of position numbers (n),

in which the data sequence (d (n)) is evaluated by discrete evaluation points (m) with a complex analysis function (f (n, m)),

- By using a comparator function (k) each value of the analysis function (f (n, m)) depending on the size of this value with respect to a threshold value (S) a binary value (-1; +1) according to the regulation k {f (n, m)} = + 1 for f (n, m)> (S)

k {f (n, m)} = - 1 for f (n, m) <(S)

k {f (n, m)} = - 1 or + 1 for f (n, m) = (S)

with (S): threshold within the value range of the analysis function (f (n, m)) to form a complex binary analysis function

(BA (n, m)) is assigned and

- The values (0; 1) of the data sequence (d (n)) are then multiplicatively linked to the binary value (-1; +1) of the binary analysis function (BA (n, m) assigned to them, and

- In which the sum (QS) of the linking results is formed and evaluated for at least one evaluation point (m).

2. The method according to claim 1,

characterized in that trigonometric functions are used as the complex analysis function (f (n, m)) and in that the threshold value (S) has the value zero.

3. The method according to claim 1 or 2,

d a d u r c h g e k e n n z e i c h n e t that the complex binary analysis function (BA (n, m)) is created and saved in advance for a large number of position numbers (n) and evaluation points (m).

4. The method according to any one of the preceding claims,

d a d u r c h g e k e n n z e i c h n e t that the positions of the data sequence (d (n)) are scanned several times and the number of scans is linked several times with the position number-specific value (-1; +1) of the binary analysis function (BA (n, m)).

5. Device for performing the method according to one of claims 1 to 4

marked by

a device (10, 11) which assigns the binary values (-1; +1) of the complex binary analysis function (BA (n, m)) to unipolar binary values (0; 1),

- A logic level (V), which combines the unipolar binary values (0; 1) of the data sequence (d '(n)) with the position number-specific unipolar binary values (0,1) of the complex binary: analysis function (BA (n, m)) multiplied, and

- A summing device (15) for the real (Re (m) and imaginary part (Im (m)) of the linking result

forms the cross sum (QSR, QSI).

6. The device according to claim 5,

marked by

- A multiple scanning device (20) which scans each value (0; 1) of the data sequence (d '(n)) several times, preferably twice, and

- A device (21,22) that each binary value (-1; +1) assigns the complex binary analysis function (BA (n, m)) in a number corresponding to the number of samples in each case unipolar binary values (0; 1).

7. The device according to claim 4, 5 or 6

marked by

a memory (12, 13) in which the complex binary analysis function (BA (n, m)) or the unipolar binary values (0; 1) associated with their values (-1; +1) are stored for each evaluation point (m) of interest .

8. Device according to one of claims 4 to 7,

That is, the logic stage (V) is formed by EXCLUSIVE-OR logic elements (EXOR1, EXOR2) with a subsequent inversion stage (INVT).