WO2001053981A1

WO2001053981A1 - A method and a device for signal processing

Info

Publication number: WO2001053981A1
Application number: PCT/SE2000/002627
Authority: WO
Inventors: Anders Sundberg
Original assignee: Saab Ab
Priority date: 2000-01-19
Filing date: 2000-12-21
Publication date: 2001-07-26
Also published as: SE515642C2; SE0000146D0; SE0000146L; EP1248994A1; AU2001228937A1

Abstract

Through a method for signal processing a number of samples are taken from a signal in digital state and Discrete Fourier Transformations having a restricted word length are applied on the samples, a mean value of the results of these transformations is calculated, the calculated mean value is compared with a known ideal value for a result of a said transformation of said signal without any systematical error emanation from a restricted word length, and in connection with subsequent Discrete Fourier Transformations having a restricted word length of signals a correction is made depending upon the deviation between said mean value and the ideal value established by said comparison.

Description

A method and a device for signal processing

FIELD OF THE I NVENTION AND PRIOR ART

The present invention relates to a method for signal processing, in which a Discrete Fourier Transformation (DFT) having a restricted word length is applied on a signal in digital state and a device for such signal processing.

It may be a question of all types of signals, for which it is desired to analyse a content primarily by carrying out a frequency analysis. The signals may be of any type and being deliberately transmitted by a transmitter or resulting from any physical phenomena of an arbitrary object, such as vibrations caused by electromagnetical or other influences by any object.

For exemplifying but accordingly not in any way restricting the invention a component moveable in for example an industrial process may be mentioned, said component transmitting a sig- nal having a frequency varying to a component being stationary in the space and receiving the signal reflected by the stationary object through a receiver for finding its position in the space by means of a frequency analysis in the form of a Discrete Fourier Transformation of a signal obtained by forming a difference be- tween the transmitted and received signal with respect to the frequency composition thereof.

Such a signal processing in the form of a Discrete Fourier

Transformation having a restricted word length often results in the introduction of systematical errors and a degraded dynamic of the result of the transformation results in the form of a higher noise level with respect to the level of the signal on which the signal processing is applied, which in certain cases means that the information desired to be obtained from the signal may not at all be extracted therefrom but will completely drown in the noise. A reason for the choice to carry out a said Discrete Fourier Transformation having a restricted word length in spite of that is that it is mostly in the practise not possible to make the analysis at a full word length, since this would take far too long time. Thus, truncating errors are by that generated, i.e. errors being a consequence of the use of too few bit at the Discrete Fourier Transformation , for example 8-12 bit instead of 16 , having the problems mentioned above as a consequence.

SUMMARY OF THE I NVENTION

The object of the present invention is to provide a method and a device making it possible to solving the problems mentioned above of such methods and devices already known to a large extent.

This object is according to the invention obtained by providing a method of the type defined in the introduction, in which a) a plurality of samples are taken from a signal in digital state and said Discrete Fourier Transformations are applied on these samples, b) a mean value of the results of these transformations is calculated , c) the calculated mean value is compared with a known ideal value for a result of a said transformation of said signal without any systematical errors emanating from a restricted word length, and after that in connection with subsequent Dis- crete Fourier Transformations having a restricted word length of signals a correction is made depending upon the deviation between said mean value and the ideal value established by said comparison.

Through said subsequent Discrete Fourier Transformations of a signal it is in this way possible to arrive at a signal being error corrected in a substantial degree while suppressing the systematical errors and the degraded dynamic obtained at such a transformation without any preceding error correction . Thus, the level of different types of noises and disturbances may be low- ered with respect to the actual signal at the same time as systematical errors obtained as a consequence of the restricted word length of the transformation may be substantially removed. An important advantage of carrying out an error correction in this way is the fact that it is not necessary to have any knowl- edge of the type of the error. The only information to be known is the ideal signal transform for the signal for which the mean value has been formed , i.e. the ideal value for a result of a said transformation. Furthermore, this signal , which is used for determining how the error correction of subsequent signals is to take place, should be linear. However, it is not any requirement that the signal used for arriving to the deviation in question for a later correction has to be the same signal as the signal intended to be processed and analysed through said Discrete Fourier Transformation having a restricted word length later on. A long sequence of a random noise signal of the type of coloured noise having a representative distribution or white Gauss noise could for example instead be selected as such a signal. Neither is it necessary that the expected ideal value for a said transformation, i.e. the value which had been obtained if a full word length had been used , is zero, so that for example a part of the value obtained at the mean value formation will be later on subtracted in connection with the Discrete Fourier Transformation of a signal, but would this ideal result be zero, would exactly the result obtained by the mean value formation be subtracted.

According to a preferred embodiment of the invention the systematical error resulting from a given Discrete Fourier Transformation having a restricted word length is determined by carrying out the steps a)-c) one single time, and after that said correction is carried out at subsequent Discrete Fourier Transformations having a restricted word length of signals without any repetition of the steps a)-c). This way to proceed is very advantageous, since the same systematical errors result and the same error correction is asked for all the time when using the same Discrete Fourier Transformation, so that there would mostly make no sense to repeat the error correction calculation.

According to another preferred embodiment of the invention the steps a)-c) are carried out for a signal of another type than the signal on which the correction is applied later on. This may be advantageous for example when a later signal, on which said Discrete Fourier Transformation having a restricted word length is intended to be applied, is not available that easy, but another signal having the known characteristics is easily available.

According to another preferred embodiment of the invention said correction is made in connection with said subsequent transformation of signals after applying said subsequent Discrete Fourier Transformation on the signal in question. This is a possible way to proceed for obtaining an error corrected signal, and it may easily be realised through suitable means. However, it would also be possible, which is a subject of a method according to another preferred embodiment of the invention, to carry out the correction in connection with said subsequent transformation of signals on the signal in question before said subse- quent Discrete Fourier Transformations with a restricted word length is applied on the signal in question by forming an inverse transform for the Fourier Transformation being error corrected depending upon the result of step c) and applying this on signals on which said Fourier Transformation is to be applied. A calculation of such an error corrected inverse transform may for sure require some resources, but the result of the subsequent Discrete Fourier Transformation of a signal will in return be directly error corrected.

According to another preferred embodiment of the invention said signals are formed before said Discrete Fourier Transformation by applying analog/digital-conversion on analog signals, which most often will be necessary, since the signals to be processed are most often present in analog form.

According to another preferred embodiment of the invention a Discrete Fourier Transformation having a restricted word length is carried out according to the Cooley-Turkey-algorithm , which has done well for Discrete Fourier Transformation having a restricted word length .

According to another preferred embodiment of the invention said plurality of samples in step a) is higher than 200, preferably higher than 400. Such a high number of samples makes said mean value formation give a reliable result for obtaining an op- timum error correction.

According to another preferred embodiment of the invention said subsequent Fourier Transformation is made for applying a frequency analysis on the signal and it is carried out for a signal obtained by transmitting a signal having a frequency varying over time from a moving object and receiving it after it has been reflected from a stationary object and then using it for forming said frequency signal having a frequency being equal to the frequency difference between a signal transmitted and received at a given moment and by that a measure of the instantaneous distance between the object moving and said stationary object. The invention has turned out to be particularly well applicable to exactly this type of signal processing and enables a reliable determination of the distance in question within a considerably larger measuring range than without such error correction.

The object of the invention is also obtained by providing a device according to the appended independent device claim , and the function and the advantages thereof and of the preferred embodiments defined in the dependent device claims appear as clearly as desired from the discussion above of the method according to the invention and the embodiments thereof.

Further advantages as well as advantageous features of the in- vention appear from the following description and the other dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

With reference to the appended drawings, below follows a description of preferred embodiments of the invention cited as examples.

In the drawings:

Fig 1 is a block diagram illustrating how the signal processing through a device according to a preferred embodiment of the invention is carried out,

Fig 2 and 3 are two very simplified block diagrams illustrating the function of devices according to two different preferred embodiments of the invention,

Fig 4 and 5 are graphs illustrating the differences of the results of a Discrete Fourier Transformation having a restricted word length without and with an error correction according to the invention, respectively, and an ideal result of a Fourier Transformation of the signal in question,

Fig 6 illustrates schematically a conceivable application of the method and the device according to the invention,

Fig 7 illustrates how the frequency develops over the time for transmitted and received signal of the device according to fig 6, and Fig 8 and 9 illustrate the signal strength with respect to the frequency of signals upon which Discrete Fourier Transformation having a restricted word length is applied in the application according to fig 6 with error correction with respect to a not error corrected signal.

DETAI LED DESCRIPTION OF PREFERRED EMBODIMENTS OF TH E I NVENTION

It is schematically illustrated in fig 1 how a signal processing in the form of a Discrete Fourier Transformation having a restricted word length is carried out and how a correction of errors occurring as a consequence of the restricted word length is carried out according to the invention in connection therewith. An analogue signal having different frequency components intended to be exerted to a frequency analysis arrives to an analog/digital- converter 1 where it is converted into a 8 bit digital signal. This arrives then to a so called 8 bit Hanning-window 2, where a digital filtering takes place, which in principal means a multiplication of the signal by given weight factors. The signal is then sent further and 64 samples are taken at 3, on which then in a unit 4 a Discrete Fourier Transformation having a restricted word length is applied, for example according to the Cooley- Turkey-algorithm with the base 4 and 8-10 bit. This is to be compared with a full word length of 16 bit. The signal coming out from the unit 4 is the result of a Discrete Fourier Transformation having a restricted word length of a digital signal having an inherent truncating error depending upon said restricted word length .

The DFT (Discrete Fourier Transformation)-transform is calculated in the unit 4 according to the principal:

N - 1 i .₂._π.U.„ V ^N

X( )= _, ^{x( n) ' e} n = 0 There k is a given frequency component, n is the sampling value in question, N is 64 in this case.

Different frequency components may in this way be obtained. Error coefficients are first of all calculated in such a way that a number (higher than 400) sequences of Gauss noise DFT is calculated and added to each other phase correctly. These error coefficients are thereafter subtracted at 5, in which the out sig- nal from 5 is a corrected DFT. Subsequent signal processing consists in this case of an additional Hanning window 7 and an ideal DFT 6.

The function of a device of this type is schematically illustrated in fig 2, where the box 8 is a summary for 1 -4 in fig 1 . A calculation of a mean value of the results of the Discrete Fourier Transformations carried out for many samples of signals is made at 5 and the mean value calculated is compared with a known ideal value for a result of a said transformation of the signal without making any systematical errors emanating from the restricted word length. Once the comparison has been made it is determined in 5 how future results of subsequent Discrete Fourier Transformations having a restricted word length of signals in the box 8 are to be error corrected, and this error cor- rection is introduced after the very Fourier Transformation has taken place in the box 8 at 9. Thus, the connection 10 between the signal output and the registration and error correction calculating unit 5 is in the practice switched off once the error correction asked for has been determined.

It is illustrated in fig 3 how in the unit 5 the inverse transform may instead be introduced at 1 1 , so that the error corrected inverse transform for the Fourier Transformation is applied at 12 on the signal on which said Fourier Transformation is to be ap- plied in the box 8, which is designed in the way already mentioned. An error corrected signal is by this obtained at 13. It is illustrated in fig 4 and 5 how a signal sxy(t) has been exerted to Discrete Fourier Transformation according to the invention and compared with ideal results of such a transformation. The following signal has then been analysed:

10.1 sxy(t) := amplssiirnJl 2. -t + 2-π-

Nx-ΔTx My-ΔTy

The strength of different frequency components is illustrated in fig 4, in which 14 shows the signal to which the Discrete Fourier Transformation having a restricted word length is applied and 1 5 is a power spectrum related to an ideal DFT. This is to be compared with fig 5, where the signal 15 is also drawn up, but where the signal 16 has been obtained by carrying out the signal processing with error correction according to the invention in connection with the Discrete Fourier Transformation. It appears that at lower frequency components a considerable rapprochement of the error corrected curve 16 to the ideal curve 15 was possible, which means that the signal dynamic has become larger.

A conceivable application of a device according to a preferred embodiment of the invention is illustrated in fig 6 and 7, in which an object 17 moves and transmits through a transmitter 1 8 signals having a frequency f varying over the time t according to what is shown in fig 7. These analogue signals are reflected by a stationary object 19 and the reflected signal is received by a receiver 20 of the moveabie object, whereupon a signal processing in the form of Discrete Fourier Transformation having a restricted word length with error correction according to the invention is applied on this signal for carrying out a frequency analysis of the signal. The signal transmitted by the transmitter 18 at a determined instant is compared with a signal received at the same instant by the receiver 20, and the signals will then have different freque ncies, as illustrated through the arrow 21 in fig 7, and this frequency difference will be directly dependent upon the distance between the object 17 and the object 19. A certain noise may leak over from the transmitter 18 to the receiver 20, as indicated through the dashed line 21 . This noise will result in a difference signal having a comparatively low frequency, and when the object 17 arrives sufficiently close to the object 1 9 this leakage will seriously disturb the signal actually reflected from the object 1 9.

It is illustrated in fig 8 what the frequency spectrum of the application according to fig 6 and 7 look like for a not corrected 22 and a corrected 23 phase modulated signal after Doppler filtration. Furthermore, the corresponding is shown in fig 9 for an amplitude modulated signal after Doppler filtration. It appears therefrom that the strength of the undesired signal may through said error correction be restricted considerably by said error correction, and the frequencies at which another real "signal" may be discovered, i.e. not be buried by the undesired signal, get considerably lower than without such an error correction.

The invention is of course not in any way restricted to the preferred embodiments described above, but many possibilities to modifications thereof would be apparent to a man with skill in the art.

Claims

Claims:

1 . A method for signal processing, in which a Discrete Fourier Transformation (DFT) having a restricted word length is ap- plied on a signal in digital state, characterized in a) that a plurality of samples are taken from a signal in digital state and said Discrete Fourier Transformations are applied on these samples, b) that a mean value of the results of these transformations is calculated , c) that the calculated mean value is compared with a known ideal value for a result of a said transformation of said signal without any systematical errors emanating from a restricted word length, and that after that in connection with subsequent Discrete Fourier Transformations having a restricted word length of signals a cor- rection is made depending upon the deviation between said mean value and the ideal value established by said comparison.

2. A method according to claim 1 , characterized in that for a given Discrete Fourier Transformation having a restricted word length the systematical error resulting therefrom is determined by carrying out the steps a)-c) one single time, and that after that said correction is carried out at subsequent Discrete Fourier Transformations having a restricted word length of signals without any repetition of the steps a)-c).

3. A method according to claim 1 or 2, characterized in that the steps a)-c) are carried out on a signal of another type than the signal upon which a correction is later on applied.

4. A method according to any of claims 1 -3, characterized in that said correction in connection with said subsequent transformation of signals is made after said subsequent Discrete Fourier Transformations have been applied to the sig- nal in question .

5. A method according to any of claims 1 -3, characterized in that the corrections in connection with said subsequent transformation of signals is carried out on the signal in question before said subsequent Discrete Fourier Transformation having a restricted word length is applied thereon by forming an inverse transform for the Fourier Transformation being error corrected depending upon the result of step c) and applying this on the signal upon which said Fourier Transformation is to be applied.

6. A method according to any of the preceding claims, characterized in that said signals are created before said Discrete Fourier Transformation by applying an analog/digital- conversion on analog signals.

7. A method according to claim 6, characterized in that the analog signal is converted in the analog/digital conversion into a 8-bit digital signal.

8. A method according to claim 7, characterized in that the word length for the Discrete Fourier Transformation is less or equal to 12, preferably 8-10 bit.

9. A method according to any of the preceding claims, charac- terized in that said Discrete Fourier Transformation having a restricted word length is carried out according to the Cooley- Turkey-algorithm .

10. A method according to claim 9, characterized in that 64 samples are taken in connection with said subsequent Fourier Transformation .

1 1 . A method according to any of the preceding claims, characterized in that in step a) said plurality of samples is higher than 200, preferably higher than 400.

12. A method according to any of the preceding claims, characterized in that said subsequent Fourier Transformation of signals is made for applying a frequency analysis on the signals.

1 3. A method according to claim 12, characterized in that in connection with the said subsequent Fourier Transformation a partial Fourier Transformation of only certain selected frequency components of the signal is carried out.

14. A method according to claim 12 or 13, characterized in that said subsequent Discrete Fourier Transformation having a restricted word length is carried out for a signal obtained by transmitting a signal having a frequency varying over time from a moving object and receiving it after it has been reflected from a stationary object and then using it for forming said frequency signal having a frequency being equal to the frequency difference between a signal transmitted and received at a given moment and by that a measure of the in- stantaneous distance between the object moving and said stationary object.

5. A device for signal processing comprising an arrangement (4) adapted to apply a Discrete Fourier Transformation (DFT) having a restricted word length on a signal , characterized in that it comprises means (3) adapted to take a plurality of samples of a signal and send them to said arrangement, members (5) adapted to form a mean value of the results of the Discrete Fourier Transformation of said samples by the arrangement and members (5) adapted to compare said mean value with a known ideal value of a said transformation of said signal without any systematical error emanating from a restricted word length, and that the device comprises means (9, 12) adapted to obtain a correction depending upon the deviation between said mean value and the ideal value established through the comparison in connection with sub- sequent Discrete Fourier Transformations having a restricted word length of signals by the arrangement.

16. A device according to claim 15, characterized in that said means for taking samples and said members for forming an mean value and comparison are adapted to once determine the systematical error inherent in said Discrete Fourier Transformation having a restricted word length, and that said arrangement (4) is adapted to after that carry out said Dis- crete Fourier Transformation having a restricted word length for signals without any said sampling and in connection with a correction depending upon the comparison made once.

17. A device according to claim 15 or 16 , characterized in that said members (5) for forming a mean value are adapted to process another type of signal than the signal to be error corrected later on by the result of said mean value formation and comparison.

18. A device according to any of claims 1 5-17, characterized in that said arrangement (4) is adapted to utilise a Cooley- Turkey-algorithm for said Discrete Fourier Transformation.

19. A device according to claim 18, characterized in that said arrangement (4) is adapted to carry out a Discrete Fourier

Transformation having a restricted word length of at the most 12 bit of a digital signal having a word length of 8 bit.

20. A device according to any of claims 15-1 9, characterized in that it comprises an analog/digital-converter (1 ) adapted to convert analog signals into digital signals and send them to said arrangement (4) for said Discrete Fourier Transformation having a restricted word length.

21 . A device according to any of claims 1 5-20, characterized in that the arrangement (4) is adapted to carry out said subse- quent Discrete Fourier Transformations having a restricted word length on signals for obtaining a frequency analysis thereof.

22. A device according to claim 20, characterized in that the arrangement (4) is adapted to carry out a partial Fourier Transformation of only certain selected frequency components of the signal in connection with said subsequent Fourier Transformation.

23. A use of a device according to any of claims 15-22 for Discrete Fourier Transformation having a restricted word length of a frequency signal obtained by transmitting a signal with a frequency varying over time from a moving object (17) and receiving it after reflection from a stationary object (19) and using it for forming said frequency signal having a frequency being equal to the frequency difference between a signal transmitted and received at a given moment and by that a measure of the instantaneous distance between the moving object and said stationary object.