CA2110218C - Method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal - Google Patents
Method of generating a correction function for an elimination of phase and amplitude errors of a compressed signalInfo
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- CA2110218C CA2110218C CA 2110218 CA2110218A CA2110218C CA 2110218 C CA2110218 C CA 2110218C CA 2110218 CA2110218 CA 2110218 CA 2110218 A CA2110218 A CA 2110218A CA 2110218 C CA2110218 C CA 2110218C
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Abstract
In a method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal a reference function (hi(t)) is generated in accordance with patent application P 41 17 849.1-35 and a reference function (hf(t)) is generated by the optimum filter theory. Furthermore, the reference functions (hi(t) and hf(t)) of the ideal filter or optimum filter are fourier-transformed; the reciprocal value (1/Hf) of the one fourier-transformed signal (Hf) is multiplied by the other fourier-transformed signal (Hi), and the signal (Hi/Hf) obtained by the multiplication is subjected to an inverse fourier transformation for generating a correction function (hcorr(t)) in the time domain.
Description
~ ~ ~ Q ~
Method of generating a correction function for an 1 elimination of phase and amplitude errors of a compressed signal BACXGROUND OF THE INV~TION
1. Field of the Invention The invention relates to a method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, a reference function Hi(t) of an ideal filter being generated and a r~ef~ce function hf(t) being generated in accordance with the optimum filter theory.
SUMMARY OF THE INVENTION
The invention has as its object the extension of the concept of the ideal filter so that phase and amplitude errors can be eliminated with an already compressed signal ff(t) after a pulse compression in accordance with the theory of the optimum filter has already been carried out.
as The invention therefore provides a method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, in which for generating a reference function (hi(t)) an error-free frequency-modulated signal (so(t)), a signal (Sf(t)) containing phase and amplitude errors, a reference signal (ho(t)) corresponding to a conjugate complex time-inverted function of the error-free signal (sf(t)) and a reference signal (hf(t)) corresponding to the conjugate complex time-inverted input signal (Sf(t)) are each fourier-transformed to respective signals (SO, Sf, Ho and Hf) in FFT units (6.2, 6.5), then in each B
Method of generating a correction function for an 1 elimination of phase and amplitude errors of a compressed signal BACXGROUND OF THE INV~TION
1. Field of the Invention The invention relates to a method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, a reference function Hi(t) of an ideal filter being generated and a r~ef~ce function hf(t) being generated in accordance with the optimum filter theory.
SUMMARY OF THE INVENTION
The invention has as its object the extension of the concept of the ideal filter so that phase and amplitude errors can be eliminated with an already compressed signal ff(t) after a pulse compression in accordance with the theory of the optimum filter has already been carried out.
as The invention therefore provides a method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, in which for generating a reference function (hi(t)) an error-free frequency-modulated signal (so(t)), a signal (Sf(t)) containing phase and amplitude errors, a reference signal (ho(t)) corresponding to a conjugate complex time-inverted function of the error-free signal (sf(t)) and a reference signal (hf(t)) corresponding to the conjugate complex time-inverted input signal (Sf(t)) are each fourier-transformed to respective signals (SO, Sf, Ho and Hf) in FFT units (6.2, 6.5), then in each B
.
case two of the signals (Sf, Hf; SO' Ho) are multiplied 1 together and the reciprocal value of the signal (Ff) arising from the first multiplication is multiplied by the output signal (Fo) arising in the second multiplication and thereupon said signal (Fo/Ff) is multiplied by the fourier-transformed signal (Hf), and the signal (Hi) thus obtained is subjected to an inverse transformation for generating the reference function (hi(t)) in the time domain, and furthermore a reference function (hf(t)) is generated by the optimum filter theory, wherein the reciprocal value (1/Hf) of the one fourier-transformed signal (Hf) is multiplied by the other fourier-transformed signal (Hi), the signal (Hi/Hf) obtained by the multiplication is subjected to an inverse fourier transformation in the time domain in a following IFFT unit (6.7) for generating the correction function (hCorr(t))~ and a signal (ff(t)) containing phase and amplitude errors and the correction function (hCorr(t)) are convoluted in the time or frequency domain for generating an error-free signal ~fo(t))~
A requirement for carrying out the method according to the invention is however that the amount ( I + Q ) of the compressed signal ff(t~ is not formed so that said signal ff(t) is present as complex function. With the aid of the reference function hi(t) of the ideal filter a correction function hCorr(t) is then calculated which is convoluted with a compressed signal ff(t). The result of such a convolution is an error-free pulse response fo(t) because the phase and amplitude errors of the functions ff(t) are eli~inated by the calculated functi~n hCorr(t)-According to a modified further development of the method of generating a correction function for the elimination of phase and amplitude errors of the -compressed signals, the phase and amplitude errors may 1 be removed from the actual compressed signal ff(t) if a pronounced point target response is present in the compressed signal ff(t). The selected pronounced point target response is then employed to determine the function hCorr(t)~ In this case the replica Sf(t) of the transmitted pulse is not required. The advantage of such a configuration of an ideal filter resides in that the information of the phase and amplitude errors can be taken from the compressed signal ff(t) and that the processing can be carried out in accordance with the concept of the ideal filter dir~ctly with the compressed signal or the corresponding image data.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be explained in more detail hereinafter with reference to preferred embodiments and with the aid of the attached drawings, wherein:
Fig. 1 shows in the form of a block diagram an apparatus for carrying out a pulse compression in the time domain using the method according to P 41 17 849.1-35 for obtaining an ideal pulse response in spite of an erroneous frequency-modulated input signal;
Fig. 2 shows in the form of a block diagram an apparatus for generating an ideal pulse response, a pulse compression being carried out in the processing in the frequency domain;
Fig. 3 shows in the form of a block diagram an apparatus for generating a reference function hi(t);
4 Z ~ ~2~
Fig. 4 shows in the form of a block diagram a 1 further apparatus for generating a reference function hi(t);
Fig. 5 shows in the form of a further block diagram an apparatus for carrying out a pulse compression using the concept of an ideal filter according to the invention, a correction of phase and amplitude errors of a compressed signal ff(t) being carried out by convolution with a correction function - hcorr(t);
Fig. 6 is a block diagram of an embodiment for performing the method of generating the correction function hCorr(t) for eliminating phase and amplitude errors of the compressed signal ff(t) and Fig. 7 is a further block diagram of an embodiment for implementing the method of generating the correction function hCorr(t) for eliminating phase and amplitude errors of the compressed signal ff(t).
DESCRIPTION OF THE PREFERRED EMBODIMENTS
When using the method, acting as a sort of ideal filter, for generating a reference function hi(t) as will be described below, a sin(x)/x function can be obtained independently of the phase and amplitude errors present in the received signal. A received signal Sf(t) containing phase and amplitude errors is convoluted in Fig. 1 in a convolution unit 1 with the aid of a reference function hi(t), as will be described below. In Fig. 1 a pulse response fo(t) obtained by the convolution then has the form of a sin(x)/x ~~~
"- 2 ~I lo21~
function if no amplitude weighting is additionally 1 carried out for suppressing sidelobes.
In Fig. 2 implementation of a me~od of performing a pulse comp~ession is illustrated, the pulse compression being shown in the frequency domain by means of a reference function generated according to P 41 17 849.1-35. ~ received signal Sf(t) and the reference function hi(t), the determination of which will be explained in detail below with the aid of Fig. 3 or 4, are each-fourier-transformed by FFT units 2.1 and 2.3 respectively, the spectra Sf and Hi thereby being obtained. The two spectra Sf and Hi are multiplied together in a multiplying unit 2.2 and then subjected to an inverse fourier transformation (IFFT) by an IFFT
unit 2.4 and thereby transformed to the time domain.
The pulse response fo(t) present at the output of the IFFT unit 2.4 then has the form of a sin(x)/x function.
The reference function hi(t) m~st then be determined by performing a pulse compression. In Fig. 3, in the form of a block diagram an embodiment is illustrated for determining the reference function hi(t) with the aid of a fast fourier transformation (F~T). By FFT units 3.1 to 3.4 the signals applied Sf(t), so(t), hf(t) and ho(t~ are fourier-transformed to the frequency domain.
The two signals so(t) and sf(t) here relate to the backscattering of only a single point target. The signal Sf(t) therefore corresponds to the replica of the transmitted pulse and is measured directly on reception whilst the signal so(t) can be determined from parameters such as the modulation rate and duration of the frequency modulation, contains no phase and amplitude errors and exhibits a linear frequency modulation. The reference functions hf(t) and ho(t) are determined from conjugate complex functions of the signal Sf(t) and the signal so(t) respectively.
B
6 211021~
1 As can be seen from Fig. 3, signals Ff and Fo are obtained by multiplying the spectra Sf and Hf and SO
and Ho in multiplying unitS3.5 and 3.6. The signal Ff thus corresponds to the fourier-transformed pulse response ff(t) whilst the signal Fo corresponds to the fourier-transformed pulse response fo(t)~
A reciprocal value l/Ff of the signal Ff formed in a unit 3.7 is multiplied by the signal Fo in a further multiplying member 3.8 so that the signal Fo/Ff is obtained which plays the part of a correction signal.
Phase and amplitude errors in the pulse compression can be eliminated by means of this correction signal. In a further multiplying member 3.9 the correction signal Fo/Ff is multiplied by the fourier-transformed signal Hf.
For pulse compression in the frequency domain the signal Hi can be multiplied by the signal Sf in the multiplying unit 2. If a pulse compression is to be carried out in the time domain as well, the signal Hi is fourier-transformed by an IFFT unit 3.10, thereby obtaining the reference function hi(t).
A further generation of the reference function hi(t) of the ideal filter is illustrated in Fig. 4. The signal Sf(t) here corresponds to the replica of the transmitted signal and thus contains all the phase and amplitude errors which have occurred on transmission and reception. The signal ho(t) corresponds to the error-free reference function so(t) with a linear frequency modulation. Signals Ho and Sf are generated from the signals ho(t) and Sf(t) by the FFT units 4.1 and 4.2. The signal Ho is then supplied to an intensity-forming unit 4.3, thereby obtaining the signal Ho 7 211~13 -A reciprocal value l/Ff of the signal Sf formed in a 1 unit 4.4 is multiplied by the signal Ho in a further multiplying member 4.5, thereby obtaining a fourier-transformed reference function Hi of the ideal filter. An inverse fourier transformation may then be carried out by an IFFT unit 4.~ ~o that at the output of the IFFT unit 4.6 the reference function hi(t) of the ideal filter is obtained for pulse compression in the time domain.
~ith the aid of the block diagram in ~ig. 5 a pulse compression will be described corresponding to the theory of the optim~m filter. This pulse compression is carried out by means of a convolution unit 5.1, the input signal Sf(t) applied and the reference function hf(t) of the optimum filter applied, as well as the compressed output signal ff(t) of the convolution unit 5.1, each containing phase and amplitude errors. If the phase and amplitude e~rors of the input signal Sf(t) are known, a correction function hçorr(t) can be determined by means of which these errors can be eliminated in accordance with ~he concept of the ideal filter. An error-free pulse response fo(t) càn then be obtained by a further convolution unit 5.2 in which the signal ff(t) applied is convoluted with the correction functiOn hCorr(t)-The following relationship can be derived from a comparison of Figs. 1 and 5:
hi(t) = hf(t) ~) hkorr( ) ' where ~ is the convolution operator. It can be 1 seen from the above equation that the reference function hi(t) of the ideal filter contains two terms.
The first term hf(t) ensures the compression of the reception signal Sf(t) in accordance with the theory of the optimum filter and the second term is hCorr(t)~ ah additional correction term by which phase and amplitude errors are eliminated.
Hereinafter, with reference to Figs. 6 and 7 two embodiments will be described for implementing the method of generating the correction functions hCorr(t).
In a generating unit 6.1 the reference function hf(t) of the optimum filter is generated, the reference function hf(t) being determined from the conjugate complex and time-inverted replica Sf(t~ of the transmitted signal. The reference function hi(t~ of the ideal filter is generated as described above with the aid of the block diagrams of Figs. 3 or 4 and in Fig. 6 is combined i~ a generating unit 6.4. The signals hf(t) and hi(t) are fourier-transformed by FFT
units 6.2 and 6.5 so that the spectra Hf and Hi are obtained at the output of said FFT units. In a unit 6.3 forming a reciprocal value the reciprocal value l/Hf of the fourier-transformed signal Hf is formed.
The reciprocal value 1/Hf is multiplied in a further multiplying unit 6.6 by the output spectrum Hi of the FFT unit 6.5 and consequently at the output of the multiplying unit 6.6 the signal Hi/Hf = HCorr is present which is inversely fourier-transformed by an IFFT unit 6.7 to give the correction signal hCorr(t)~
If a convolution operation is carried out in the time domain by means of a time correlation by ~he convolution unit 5.2, the signal hCorr(t) is taken from the output of the IFFT unit 6.7 and supplied to said convolution unit 5.2, the phase and amplitude errors 9 211021~
then thereby being eliminated. If the convolution 1 operation by the convolution unit 5.2 is carried out in the frequency domain, the signal hCorr is taken from the output of the mutiplying member 6.6 fo~ a spectral multiplication by the fourier-tranformed signal of the compressed erroneous signal ff(t) at the output of the convolution uni~ 5.5. After spectral multiplication of the signal hCorr by Ff an IFFT operation is carried out, the error-free pulse response fQ(t) then once again being obtained.
It may happen in some cases that the replica sf(t) of the transmitted signal is not available. With the aid of Fig. 7 a method will therefore be described with which the correction function hCorr is determined from a selected point target response Zf(t) of the erroneous compressed signal ff(t). The selected point target response must have a pronounced backscattering to ensure that the backscattering of the background can be neglected compared with the backscattering of the point target response. If this condition is not fulfilled the phase and amplitude errors cannot be taken from the selected point target response. Experience ~ith practical data have shown that the peak value of the selected point target response must be at least 25 dB
above the mean value of the background backscattering to enable the influence of the background to be neglected.
Selection of the point target response may be carried out automatically by a simple search method by checking the 25 dB suppression of the background in the vicinity of pronounced ~oint target responses. Such a search method is carried out in a unit 7.1 in Fig. 7, thus giving at the output thereof a selected point target response Zf(t~ and the mean background backscattering Zm In a su~traction unit 7.2 the calculated mean background back~c~ring Zm is subtracted from the lO 211021~
-backscattering of the selected point target response 1 Zf(t) so that at the output thereof the signal Zh(t) is available (Zh = Zf ~ Zm) This subtraction gives a more exact determination of the actual pulse response with phase and amplitude errors.
The signal Zh(t) is fourier-transformed to the frequency domain by an FFT unit 7.3 and the reciprocal value l/Zh is formed by a reciprocal-forming unit 7.4.
The error-free pulse response fo(t) required for determining the correction function hCorr(t) is generated by convolution of the error-free replica so(t) of the transmitted signal sf(t) in the unit 7.5.
The nominal parameters of the frequency modulation of the transmitted signal Sf(t) are employed to determine so(t) whilst the reference functions ho(t) are determined from the conjugate complex and time-inverted function of the replica fo~t)~ The pulse response fo(t) is fourier-transformed to the frequency domain by an FFT unit 7.6 so that the signal Fo is available at the output of the FFT unit 7.6. ~he signal Fo/Zh playing the part of the fourier transformation of the correction function hCorr(t~ is then present at the output of a multiplying member 7.7 in which the signal Fo is multiplied by the reciprocal value 1/Zh The point target response Zf(t) having a limited number of points was used to generate the signal Fo/Zh at the output of the multiplying member 7.7. Due to the limited number of points irregularities occur with regard to the selected data set Zftt) and lead in the signal Fo/zh to interference components with higher frequency components. To reduce these irregularities a weighting function w(t) is generated ih a unit 7.8, for example in the form of a Hamming weighting, the point number of the weighting function w(t) being the same as that of the FFT operation in the FFT units 7.3, 7.6 and 7.9. By the FFT unit 7.9 the weighting function w(t) 11 211021~
,_ is fourier-transformed to the weighting function W
1 which is available at the output of the FFT unit 7.9.
In a multiplying member 7.1 the product of the weighting function W and the signal Fo/Zh is formed so that at the output thereof the actual fourier transformation hCorr = W . Fo/Zh of the correction signal is formed. By a further IFFT unit 7.11 the correction signal hCorr(t) is generated in the time domain. For eliminating the phase and amplitude errors the correction signal hCorr(t) is applied to the convolution unit 5.2.
case two of the signals (Sf, Hf; SO' Ho) are multiplied 1 together and the reciprocal value of the signal (Ff) arising from the first multiplication is multiplied by the output signal (Fo) arising in the second multiplication and thereupon said signal (Fo/Ff) is multiplied by the fourier-transformed signal (Hf), and the signal (Hi) thus obtained is subjected to an inverse transformation for generating the reference function (hi(t)) in the time domain, and furthermore a reference function (hf(t)) is generated by the optimum filter theory, wherein the reciprocal value (1/Hf) of the one fourier-transformed signal (Hf) is multiplied by the other fourier-transformed signal (Hi), the signal (Hi/Hf) obtained by the multiplication is subjected to an inverse fourier transformation in the time domain in a following IFFT unit (6.7) for generating the correction function (hCorr(t))~ and a signal (ff(t)) containing phase and amplitude errors and the correction function (hCorr(t)) are convoluted in the time or frequency domain for generating an error-free signal ~fo(t))~
A requirement for carrying out the method according to the invention is however that the amount ( I + Q ) of the compressed signal ff(t~ is not formed so that said signal ff(t) is present as complex function. With the aid of the reference function hi(t) of the ideal filter a correction function hCorr(t) is then calculated which is convoluted with a compressed signal ff(t). The result of such a convolution is an error-free pulse response fo(t) because the phase and amplitude errors of the functions ff(t) are eli~inated by the calculated functi~n hCorr(t)-According to a modified further development of the method of generating a correction function for the elimination of phase and amplitude errors of the -compressed signals, the phase and amplitude errors may 1 be removed from the actual compressed signal ff(t) if a pronounced point target response is present in the compressed signal ff(t). The selected pronounced point target response is then employed to determine the function hCorr(t)~ In this case the replica Sf(t) of the transmitted pulse is not required. The advantage of such a configuration of an ideal filter resides in that the information of the phase and amplitude errors can be taken from the compressed signal ff(t) and that the processing can be carried out in accordance with the concept of the ideal filter dir~ctly with the compressed signal or the corresponding image data.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be explained in more detail hereinafter with reference to preferred embodiments and with the aid of the attached drawings, wherein:
Fig. 1 shows in the form of a block diagram an apparatus for carrying out a pulse compression in the time domain using the method according to P 41 17 849.1-35 for obtaining an ideal pulse response in spite of an erroneous frequency-modulated input signal;
Fig. 2 shows in the form of a block diagram an apparatus for generating an ideal pulse response, a pulse compression being carried out in the processing in the frequency domain;
Fig. 3 shows in the form of a block diagram an apparatus for generating a reference function hi(t);
4 Z ~ ~2~
Fig. 4 shows in the form of a block diagram a 1 further apparatus for generating a reference function hi(t);
Fig. 5 shows in the form of a further block diagram an apparatus for carrying out a pulse compression using the concept of an ideal filter according to the invention, a correction of phase and amplitude errors of a compressed signal ff(t) being carried out by convolution with a correction function - hcorr(t);
Fig. 6 is a block diagram of an embodiment for performing the method of generating the correction function hCorr(t) for eliminating phase and amplitude errors of the compressed signal ff(t) and Fig. 7 is a further block diagram of an embodiment for implementing the method of generating the correction function hCorr(t) for eliminating phase and amplitude errors of the compressed signal ff(t).
DESCRIPTION OF THE PREFERRED EMBODIMENTS
When using the method, acting as a sort of ideal filter, for generating a reference function hi(t) as will be described below, a sin(x)/x function can be obtained independently of the phase and amplitude errors present in the received signal. A received signal Sf(t) containing phase and amplitude errors is convoluted in Fig. 1 in a convolution unit 1 with the aid of a reference function hi(t), as will be described below. In Fig. 1 a pulse response fo(t) obtained by the convolution then has the form of a sin(x)/x ~~~
"- 2 ~I lo21~
function if no amplitude weighting is additionally 1 carried out for suppressing sidelobes.
In Fig. 2 implementation of a me~od of performing a pulse comp~ession is illustrated, the pulse compression being shown in the frequency domain by means of a reference function generated according to P 41 17 849.1-35. ~ received signal Sf(t) and the reference function hi(t), the determination of which will be explained in detail below with the aid of Fig. 3 or 4, are each-fourier-transformed by FFT units 2.1 and 2.3 respectively, the spectra Sf and Hi thereby being obtained. The two spectra Sf and Hi are multiplied together in a multiplying unit 2.2 and then subjected to an inverse fourier transformation (IFFT) by an IFFT
unit 2.4 and thereby transformed to the time domain.
The pulse response fo(t) present at the output of the IFFT unit 2.4 then has the form of a sin(x)/x function.
The reference function hi(t) m~st then be determined by performing a pulse compression. In Fig. 3, in the form of a block diagram an embodiment is illustrated for determining the reference function hi(t) with the aid of a fast fourier transformation (F~T). By FFT units 3.1 to 3.4 the signals applied Sf(t), so(t), hf(t) and ho(t~ are fourier-transformed to the frequency domain.
The two signals so(t) and sf(t) here relate to the backscattering of only a single point target. The signal Sf(t) therefore corresponds to the replica of the transmitted pulse and is measured directly on reception whilst the signal so(t) can be determined from parameters such as the modulation rate and duration of the frequency modulation, contains no phase and amplitude errors and exhibits a linear frequency modulation. The reference functions hf(t) and ho(t) are determined from conjugate complex functions of the signal Sf(t) and the signal so(t) respectively.
B
6 211021~
1 As can be seen from Fig. 3, signals Ff and Fo are obtained by multiplying the spectra Sf and Hf and SO
and Ho in multiplying unitS3.5 and 3.6. The signal Ff thus corresponds to the fourier-transformed pulse response ff(t) whilst the signal Fo corresponds to the fourier-transformed pulse response fo(t)~
A reciprocal value l/Ff of the signal Ff formed in a unit 3.7 is multiplied by the signal Fo in a further multiplying member 3.8 so that the signal Fo/Ff is obtained which plays the part of a correction signal.
Phase and amplitude errors in the pulse compression can be eliminated by means of this correction signal. In a further multiplying member 3.9 the correction signal Fo/Ff is multiplied by the fourier-transformed signal Hf.
For pulse compression in the frequency domain the signal Hi can be multiplied by the signal Sf in the multiplying unit 2. If a pulse compression is to be carried out in the time domain as well, the signal Hi is fourier-transformed by an IFFT unit 3.10, thereby obtaining the reference function hi(t).
A further generation of the reference function hi(t) of the ideal filter is illustrated in Fig. 4. The signal Sf(t) here corresponds to the replica of the transmitted signal and thus contains all the phase and amplitude errors which have occurred on transmission and reception. The signal ho(t) corresponds to the error-free reference function so(t) with a linear frequency modulation. Signals Ho and Sf are generated from the signals ho(t) and Sf(t) by the FFT units 4.1 and 4.2. The signal Ho is then supplied to an intensity-forming unit 4.3, thereby obtaining the signal Ho 7 211~13 -A reciprocal value l/Ff of the signal Sf formed in a 1 unit 4.4 is multiplied by the signal Ho in a further multiplying member 4.5, thereby obtaining a fourier-transformed reference function Hi of the ideal filter. An inverse fourier transformation may then be carried out by an IFFT unit 4.~ ~o that at the output of the IFFT unit 4.6 the reference function hi(t) of the ideal filter is obtained for pulse compression in the time domain.
~ith the aid of the block diagram in ~ig. 5 a pulse compression will be described corresponding to the theory of the optim~m filter. This pulse compression is carried out by means of a convolution unit 5.1, the input signal Sf(t) applied and the reference function hf(t) of the optimum filter applied, as well as the compressed output signal ff(t) of the convolution unit 5.1, each containing phase and amplitude errors. If the phase and amplitude e~rors of the input signal Sf(t) are known, a correction function hçorr(t) can be determined by means of which these errors can be eliminated in accordance with ~he concept of the ideal filter. An error-free pulse response fo(t) càn then be obtained by a further convolution unit 5.2 in which the signal ff(t) applied is convoluted with the correction functiOn hCorr(t)-The following relationship can be derived from a comparison of Figs. 1 and 5:
hi(t) = hf(t) ~) hkorr( ) ' where ~ is the convolution operator. It can be 1 seen from the above equation that the reference function hi(t) of the ideal filter contains two terms.
The first term hf(t) ensures the compression of the reception signal Sf(t) in accordance with the theory of the optimum filter and the second term is hCorr(t)~ ah additional correction term by which phase and amplitude errors are eliminated.
Hereinafter, with reference to Figs. 6 and 7 two embodiments will be described for implementing the method of generating the correction functions hCorr(t).
In a generating unit 6.1 the reference function hf(t) of the optimum filter is generated, the reference function hf(t) being determined from the conjugate complex and time-inverted replica Sf(t~ of the transmitted signal. The reference function hi(t~ of the ideal filter is generated as described above with the aid of the block diagrams of Figs. 3 or 4 and in Fig. 6 is combined i~ a generating unit 6.4. The signals hf(t) and hi(t) are fourier-transformed by FFT
units 6.2 and 6.5 so that the spectra Hf and Hi are obtained at the output of said FFT units. In a unit 6.3 forming a reciprocal value the reciprocal value l/Hf of the fourier-transformed signal Hf is formed.
The reciprocal value 1/Hf is multiplied in a further multiplying unit 6.6 by the output spectrum Hi of the FFT unit 6.5 and consequently at the output of the multiplying unit 6.6 the signal Hi/Hf = HCorr is present which is inversely fourier-transformed by an IFFT unit 6.7 to give the correction signal hCorr(t)~
If a convolution operation is carried out in the time domain by means of a time correlation by ~he convolution unit 5.2, the signal hCorr(t) is taken from the output of the IFFT unit 6.7 and supplied to said convolution unit 5.2, the phase and amplitude errors 9 211021~
then thereby being eliminated. If the convolution 1 operation by the convolution unit 5.2 is carried out in the frequency domain, the signal hCorr is taken from the output of the mutiplying member 6.6 fo~ a spectral multiplication by the fourier-tranformed signal of the compressed erroneous signal ff(t) at the output of the convolution uni~ 5.5. After spectral multiplication of the signal hCorr by Ff an IFFT operation is carried out, the error-free pulse response fQ(t) then once again being obtained.
It may happen in some cases that the replica sf(t) of the transmitted signal is not available. With the aid of Fig. 7 a method will therefore be described with which the correction function hCorr is determined from a selected point target response Zf(t) of the erroneous compressed signal ff(t). The selected point target response must have a pronounced backscattering to ensure that the backscattering of the background can be neglected compared with the backscattering of the point target response. If this condition is not fulfilled the phase and amplitude errors cannot be taken from the selected point target response. Experience ~ith practical data have shown that the peak value of the selected point target response must be at least 25 dB
above the mean value of the background backscattering to enable the influence of the background to be neglected.
Selection of the point target response may be carried out automatically by a simple search method by checking the 25 dB suppression of the background in the vicinity of pronounced ~oint target responses. Such a search method is carried out in a unit 7.1 in Fig. 7, thus giving at the output thereof a selected point target response Zf(t~ and the mean background backscattering Zm In a su~traction unit 7.2 the calculated mean background back~c~ring Zm is subtracted from the lO 211021~
-backscattering of the selected point target response 1 Zf(t) so that at the output thereof the signal Zh(t) is available (Zh = Zf ~ Zm) This subtraction gives a more exact determination of the actual pulse response with phase and amplitude errors.
The signal Zh(t) is fourier-transformed to the frequency domain by an FFT unit 7.3 and the reciprocal value l/Zh is formed by a reciprocal-forming unit 7.4.
The error-free pulse response fo(t) required for determining the correction function hCorr(t) is generated by convolution of the error-free replica so(t) of the transmitted signal sf(t) in the unit 7.5.
The nominal parameters of the frequency modulation of the transmitted signal Sf(t) are employed to determine so(t) whilst the reference functions ho(t) are determined from the conjugate complex and time-inverted function of the replica fo~t)~ The pulse response fo(t) is fourier-transformed to the frequency domain by an FFT unit 7.6 so that the signal Fo is available at the output of the FFT unit 7.6. ~he signal Fo/Zh playing the part of the fourier transformation of the correction function hCorr(t~ is then present at the output of a multiplying member 7.7 in which the signal Fo is multiplied by the reciprocal value 1/Zh The point target response Zf(t) having a limited number of points was used to generate the signal Fo/Zh at the output of the multiplying member 7.7. Due to the limited number of points irregularities occur with regard to the selected data set Zftt) and lead in the signal Fo/zh to interference components with higher frequency components. To reduce these irregularities a weighting function w(t) is generated ih a unit 7.8, for example in the form of a Hamming weighting, the point number of the weighting function w(t) being the same as that of the FFT operation in the FFT units 7.3, 7.6 and 7.9. By the FFT unit 7.9 the weighting function w(t) 11 211021~
,_ is fourier-transformed to the weighting function W
1 which is available at the output of the FFT unit 7.9.
In a multiplying member 7.1 the product of the weighting function W and the signal Fo/Zh is formed so that at the output thereof the actual fourier transformation hCorr = W . Fo/Zh of the correction signal is formed. By a further IFFT unit 7.11 the correction signal hCorr(t) is generated in the time domain. For eliminating the phase and amplitude errors the correction signal hCorr(t) is applied to the convolution unit 5.2.
Claims (3)
1. A method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, in which for generating a reference function (hi(t)) an error-free frequency-modulated signal (so(t)), asignal (Sf(t)) containing phase and amplitude errors, a reference signal (ho(t))corresponding to a conjugate complex time-inverted function of an error-free signal (Sf(t)) and a reference signal (hf(t)) corresponding to a conjugate complex time-inverted input signal (Sf(t)) are each fourier-transformed to respective signals (So, Sf, Ho and Hf) in FFT units (6.2, 6.5), then in each case two of the signals (Sf, Hf; So, Ho) are multiplied together and a reciprocal value of a signal (Ff) arising from the first multiplication is multiplied by anoutput signal (Fo) arising in the second multiplication and thereupon a signal (Fo/Ff) is multiplied by a fourier-transformed signal (Hf), and a signal (Hi) thus obtained is subjected to an inverse transformation for generating the reference function (hi(t)) in a time domain, and furthermore a reference function (hf(t)) is generated wherein a reciprocal value (1/Hf) of the one fourier-transformed signal (Hf) is multiplied by another fourier-transformed signal (Hi), a signal (Hi/Hf) obtained by the multiplication is subjected to an inverse fourier transformation in the time domain in a following IFFT unit (6.7) for generating a correction function (hcorr(t)), and a signal (ff(t)) containing phase and amplitude errors and the correction function (hcorr(t)) are convoluted in a time or frequency domain for generating an error-free signal (fo(t)).
2. A method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal, in which for generating a reference function (hi(t)) a reference signal (ho(t)) corresponding to a conjugate complex time-inverted function of an error-free frequency-modulated signal (so(t)) and a signal (Sf(t)) containing phase and amplitude errors are generated by a fourier transformation to signals (Ho, Sf) which correspond to the fourier transformation of the signals (ho(t)) and (Sf(t)), a squared signal ( Ho ) and a reciprocal value (1/Sf) of the other fourier-transformed signal (Sf) being multiplied together, and a signal (Hi) resulting from the multiplication being subjected in a time domain to an inverse transformation to generate the reference function (hi(t)) to generate a reference function (hf(t)) being generated wherein a reciprocal value (1/Hf) of a fourier-transformed signal (Hf) is multiplied by another fourier-transformed signal (Hi), a signal (Hi/Hf) obtained by the multiplication is subjected in a following IFFT unit (6.7) to an inverse fourier transformation to generate a correction function (hcorr(t)) in the time domain, and a signal (ff(t)) containing phase and amplitude errors and the correction function (hcorr(t)) are convoluted to generate an error-free signal (fo(t)) in atime or frequency domain.
3. A method of generating a correction function for the elimination of phase and amplitude errors of a compressed signal (ff(t)) in which from the compressed signal (ff(t)) a point target response with pronounced backscattering is selected and a mean backscattering (Zm) of the background around the point target response is formed; wherein the mean backscattering (Zm) of the background is subtracted from the backscattering of the selected point target response in a subtraction unit (7.2);
.
for generating an error-free pulse response (fo(t)) in the convolution unit (7.5) a convolution is performed between an error-free reference function (ho(t)) of the optimum filter and an error-free modulated signal (so(t));
the output signals (zh(t), fo(t)) of the subtraction unit (7.2) and a generatingunit (7.5 ) are fourier-transformed, a reciprocal value (1/Zh) of a fourier-transformed signal (Zh) is multiplied by a fourier-transformed signal (Fo), a weighting function (w(t)) is generated and thereafter fourier-transformed by an FFT unit (7.9); and a multiplication result (Fo/Zh) is multiplied by a fourier-transformation (W) of the weighting function (w(t)), a resulting product (W . Fo/Zh) is thereafter subjected to an inverse fourier transformation by an IFFT unit (7.11) for generating a correction function (hcorr(t)) in a time domain, and a signal (ff(t)) containing phase and amplitude errors and the correction function (hcorr(t)) are convoluted to generate an error-free signal (fo(t)) in atime or frequency domain.
.
for generating an error-free pulse response (fo(t)) in the convolution unit (7.5) a convolution is performed between an error-free reference function (ho(t)) of the optimum filter and an error-free modulated signal (so(t));
the output signals (zh(t), fo(t)) of the subtraction unit (7.2) and a generatingunit (7.5 ) are fourier-transformed, a reciprocal value (1/Zh) of a fourier-transformed signal (Zh) is multiplied by a fourier-transformed signal (Fo), a weighting function (w(t)) is generated and thereafter fourier-transformed by an FFT unit (7.9); and a multiplication result (Fo/Zh) is multiplied by a fourier-transformation (W) of the weighting function (w(t)), a resulting product (W . Fo/Zh) is thereafter subjected to an inverse fourier transformation by an IFFT unit (7.11) for generating a correction function (hcorr(t)) in a time domain, and a signal (ff(t)) containing phase and amplitude errors and the correction function (hcorr(t)) are convoluted to generate an error-free signal (fo(t)) in atime or frequency domain.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE4240225A DE4240225C2 (en) | 1991-05-31 | 1992-11-30 | Method for generating a correction function for eliminating phase and amplitude errors of a compressed signal |
| DEP4240225.5-35 | 1992-11-30 |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2110218A1 CA2110218A1 (en) | 1994-05-31 |
| CA2110218C true CA2110218C (en) | 1998-11-24 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA 2110218 Expired - Fee Related CA2110218C (en) | 1992-11-30 | 1993-11-29 | Method of generating a correction function for an elimination of phase and amplitude errors of a compressed signal |
Country Status (2)
| Country | Link |
|---|---|
| CA (1) | CA2110218C (en) |
| IT (1) | IT1261347B (en) |
-
1993
- 1993-11-29 CA CA 2110218 patent/CA2110218C/en not_active Expired - Fee Related
- 1993-11-29 IT ITTO930906 patent/IT1261347B/en active IP Right Grant
Also Published As
| Publication number | Publication date |
|---|---|
| ITTO930906A1 (en) | 1995-05-29 |
| ITTO930906A0 (en) | 1993-11-29 |
| IT1261347B (en) | 1996-05-14 |
| CA2110218A1 (en) | 1994-05-31 |
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