Method and devices for the translation along the frequency axis of the modulus of the transfer function of a filter

The invention relates to a method for shifting in frequency the module of the transfer function of a filter of the digital type and with transverse structure; it also relates to devices for implementing said method.

Frequency filters of electrical signals are used in many fields of electronics and in particular in the processing of radar signals to eliminate for example fixed echoes or to detect echoes having determined characteristics such as a radial speed. This processing mode is for example used in coherent Doppler radars with pulses at constant ambiguous speed which make it possible, by taking advantage of the Doppler effect, to detect mobile obstacles which give rise to radar signals of low amplitude in the middle of fixed obstacles corresponding to large amplitude radar signals. Indeed, in these pulse radars the waves received after reflection on the moving obstacles are affected by a phase which varies from one repetition period to the next while the waves received from the fixed obstacles do not exhibit such a variation in the phase shift. . As a result, the signals corresponding to the mobile obstacles have, after demodulation, components which vary sinusoidally at a frequency fd called the Doppler frequency, which is linked to the radial speed v and to the wavelength e of the radar by the formula Fd = 2v / e. The signals which correspond to fixed obstacles have a constant amplitude and their spectrum consists of a series of discrete lines at frequencies O, Fr 2Fr, ... nFr, Fr being the repetition frequency of the pulses emitted. Furthermore, the spectrum of signals corresponding to moving obstacles is made up of discrete lines of the mFr - + Fd type.

It is then understood that it is possible to eliminate the signals corresponding to the fixed obstacles by using a filter for eliminating the fixed echoes which does not allow the signals of frequency O, Fr, 2Fr, ... nFr to pass. It is also desirable to eliminate in certain radars, such as air traffic surveillance radars, mobile obstacles which have low Doppler velocities compared to the echo velocities of interest, for example clouds, or even fluctuating fixed obstacles with a certain Doppler speed, such as wind-blown trees. These various parasitic echoes at low speed are better known by the English term "clutter" which has been translated by the term "clutter". These examples show that it would be advantageous to have filters in the field of radars, the transfer function of which could be easily and simply modified along the frequency axis to eliminate not only fixed or pseudo-fixed echoes but also those whose radial speed is very different from that of the targets we are interested in.

In radars, the filters are often made in digital form, that is to say that the signals to be filtered are sampled at a frequency equal to the repetition frequency of the pulses emitted by the radar, then the amplitude of the samples is coded so as to obtain a succession of digital codes; finally, these codes are multiplied by coefficients whose values ​​define the characteristics of the filtering to be obtained.

These so-called digital filters are produced for example using memories arranged in series which each record the codes of all the samples of a repetition period, multiplier circuits arranged at the output of said memories to multiply the codes read from the memory associated by an appropriate coefficient and an addition circuit to sum the codes resulting from the multiplications.

Such digital filters can be used in fields other than that of radars, for example in that of high-fidelity signals, in particular when such signals are in digital form. In these fields, there is also a need to modify the transfer function of the filters on the frequency axis without however profoundly modifying the structure of the filters, for example to extend the rejection band of the filter.

An object of the present invention is therefore to implement a method which makes it possible, in a transverse filter, to shift in frequency the module of the transfer function of said filter.

Another object of the invention is to provide devices for implementing the method which, for certain values ​​of the frequency offset, are simple to carry out.

The invention relates to a method for shifting in frequency by a value Fd the modulus of the transfer function of a transverse filter with n cells whose multiplication coefficients are KO ... Ki ... Kn characterized in that it consists in multiplying the coefficient of rank i by a factor<maths id="math0001" num=""><math display="block"><mrow><msup><mrow><mtext>e</mtext></mrow><mrow><mtext>j (ni) r</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0001.tif" /></maths> with i varying from o to n and<maths id="math0002" num=""><math display="block"><mrow><mtext>r = 2πFd.Tr</mtext></mrow></math><img file="EP0333566B1_D0002.tif" /></maths> if Tr is the period of repetition of the samples applied to the transverse filter so as to obtain new coefficients K′O ... K′i ... K′n.

Other characteristics and advantages of the present invention will appear on reading the following description of particular embodiments, said description being made in relation to the accompanying drawings in which:<ul id="ul0001" list-style="dash"><li>FIG. 1 is a block diagram of a transverse filter for eliminating fixed echoes,</li><li>FIG. 2 is a diagram showing the module of the transfer function of the transverse filter of FIG. 1,</li><li>FIG. 3 is a vector diagram showing two positions of a radar signal vector in the complex plane,</li><li>FIG. 4 is a diagram of the canonical structure of a transverse filter according to the invention,</li><li>FIG. 5 is a diagram showing the module of the transfer function of a transverse filter according to the invention, which eliminates echoes of Doppler frequencies close to -Fr / 4,</li><li>FIG. 6 is a diagram showing the module of the transfer function of a transverse filter according to the invention which eliminates echoes of Doppler frequencies close to + Fr / 4 and FIG. 7 is a diagram of embodiment of two filters transverse to frequencies + Fr / 4 and -Fr / 4.</li></ul>

The invention will be described in a particular application which is that of radar signal filtering.

In the processing of these signals, it is known to filter them, in particular to eliminate the fixed echoes, by using a device whose block diagram is given in FIG. 1. This device comprises several delay lines, for example three, LR1 , LR2 and LR3 arranged in series, each delay line introducing a delay equal to the repetition period Tr of the pulses transmitted at frequency Fr. Each delay line output as well as the input of the first LR1 is connected respectively to a multiplication or weighting circuit MO, M1, M2 and M3 in which the amplitude of the signal is multiplied or weighted respectively by a coefficient K0, K1, K2, and K3. The outputs of the multiplication circuits are connected to a summing circuit S which performs the sum of the weighted signals so as to obtain a filtered signal. To eliminate fixed echoes the values ​​of the coefficients K0, K1, K2 and K3 can be 1, -3, 3 and -1 respectively and the frequency transfer function of such a filter is of the form<maths id="math0003" num=""><math display="block"><mrow><mtext>| sin πFd.Tr | ³</mtext></mrow></math><img file="EP0333566B1_D0003.tif" /></maths> formula in which Fd is the Doppler frequency of the echo. The modulus of the frequency response curve of such a filter is given by the diagram in FIG. 2. In the field of radars, such a filter is known by the name of transverse filter and is of the type with cancellation on four pulses. , which corresponds to the Anglo-Saxon expression of "four-pulse canceler transverse filter".

In modern radars, such a filter is performed digitally, which means that the radar video-frequency signals are sampled at the frequency Fr, and digitally coded to obtain Xi codes. These codes are recorded in memories which produce the delay lines LR1, LR2, and LR3 of FIG. 1. The multiplication circuits MO, M1, M2 and M3 as well as the summation circuit S are also produced digitally so that for a code Xi at the input of the delay line or memory LR1, a code Si is obtained. the output of circuit S.

More precisely, at a given instant ti + 3, the signal S_{i +3} at the output of the summing circuit S will be given by:<maths id="math0004" num=""><math display="block"><mrow><msub><mrow><mtext>S</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> = KO.X</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> + K1.X</mtext></mrow><mrow><mtext>i + 2</mtext></mrow></msub><msub><mrow><mtext> + K2.X</mtext></mrow><mrow><mtext>i + 1</mtext></mrow></msub><msub><mrow><mtext> + K3 X</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0333566B1_D0004.tif" /></maths> formula in which:    X_i is the amplitude of the sample at time t of the recurrence of rank (i)    X_{i + 1} is the amplitude of the sample at time t of the recurrence of rank (i + 1), i.e. a period Tr later,    X_{i + 2} is the amplitude of the sample at time t of the recurrence of rank (i + 2), ie two periods Tr later,    X_{i + 3} is the amplitude of the sample at time t of the recurrence of rank (i + 3), that is to say three periods Tr later.

The samples X_i at X_{i + 3} therefore correspond to a radar signal coming from a distance box located at a determined distance from the radar antenna equal to t / C if C is the speed of light.

What the invention proposes to achieve is to offset the transfer function of this filter, the frequency response of which is shown in FIG. 2, along the frequency axis by a value f, this offset being obtained from simple way with a minimum of additional means.

FIG. 3 makes it possible to understand the approach of the invention. In this figure, a radar signal Xi at the recurrence i can be represented in the form of a vector Vi defined by its components I and Q in the complex plane: Xi = Ii + JQi. At the next recurrence (i + 1), the vector will have become Vi + 1 and will correspond to the vector Vi but with a rotation r = 2πFd / Fr if Fd is the Doppler frequency of the echo. It will then be understood that this echo would be seen as a fixed echo if, at each recurrence, it was out of phase with the angle r which it would have rotated, which amounts to multiplying the radar signal:<maths id="math0005" num=""><math display="block"><mrow><msub><mrow><mtext>X</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> by 1</mtext></mrow></math><img file="EP0333566B1_D0005.tif" /></maths><maths id="math0006" num=""><math display="block"><mrow><msub><mrow><mtext>X</mtext></mrow><mrow><mtext>i + 1</mtext></mrow></msub><msup><mrow><mtext> by e</mtext></mrow><mrow><mtext>-jr</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0006.tif" /></maths><maths id="math0007" num=""><math display="block"><mrow><msub><mrow><mtext>X</mtext></mrow><mrow><mtext>i + 2</mtext></mrow></msub><msup><mrow><mtext> by e</mtext></mrow><mrow><mtext>-2d</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0007.tif" /></maths><maths id="math0008" num=""><math display="block"><mrow><msub><mrow><mtext>X</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msup><mrow><mtext> by e</mtext></mrow><mrow><mtext>-3d</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0008.tif" /></maths>

A frequency translation of the filter for eliminating fixed echoes would thus have been obtained with a value Fd. One way to achieve such a translation is to carry out the multiplications at the input of the transverse filter of FIG. 1, that is to say by preceding the delay line LR1 with a multiplication circuit 10 which has been represented by a dashed rectangle. Such a solution leads to a multiplication circuit 10 which is quite complex because the coefficient changes with each recurrence and which is quite costly in number of logic circuits and in processing time.

In the device of the invention, such a multiplication circuit 10 is no longer necessary and is replaced by new values ​​K′0, K′1, K′2, and K′3 of the multiplication coefficients used in the circuits M0 to M3, values ​​which are fixed and which, for certain values ​​of the frequency Fd, are easy to perform digitally.

The mathematical developments which will follow are intended to determine the coefficients K′0 to K′3. For this purpose, use is made of the z transform which is for example defined in the book entitled "THE NUMERICAL FILTERS" by R. BOITE and H. LEICH and published by MASSON in 1980 - chapter II.

The z-transform of a discrete-time signal (x_not) is defined by the series:<maths id="math0009" num=""><img file="EP0333566B1_D0009.tif" /></maths>

In the case of a radar signal, x_not corresponds to the series of samples separated from each other by a repetition period Tr.

The properties of the transform in z allow to demonstrate that the transfer function H (z) of the filter of figure 1 (without the multiplier circuit 10) is written in the form:<maths id="math0010" num="(2)"><math display="block"><mrow><mtext>H (z) = K0 + K1.z⁻¹ + K2.z⁻² + K3.z⁻³</mtext></mrow></math><img file="EP0333566B1_D0010.tif" /></maths>

If we introduce the multiplier circuit 10, it is written in the form:<maths id="math0011" num=""><math display="block"><mrow><msub><mrow><mtext>Hi (z) = KO.C</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> + K1.C</mtext></mrow><mrow><mtext>i + 2</mtext></mrow></msub><msub><mrow><mtext>.z⁻¹ + K2.C</mtext></mrow><mrow><mtext>i + 1</mtext></mrow></msub><msub><mrow><mtext>.z⁻² + K3.C</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>.z⁻³</mtext></mrow></math><img file="EP0333566B1_D0011.tif" /></maths> form in which Ci = (e^jr)ⁱ = (e^{j2πFd / Fr})ⁱ

The module Hi (z) is then given by<maths id="math0012" num=""><math display="block"><mrow><msup><mrow><mtext>Hi (z) = KO.e</mtext></mrow><mrow><mtext>j3r</mtext></mrow></msup><msup><mrow><mtext> + K1.e</mtext></mrow><mrow><mtext>j2r</mtext></mrow></msup><msup><mrow><mtext>.z⁻¹ + K2.e</mtext></mrow><mrow><mtext>jr</mtext></mrow></msup><mtext>.z⁻² + K3.z⁻³</mtext></mrow></math><img file="EP0333566B1_D0012.tif" /></maths> which corresponds to a transfer function filter H ′ (z) such that<maths id="math0013" num="(3)"><math display="block"><mrow><msup><mrow><mtext>H ′ (z) = KO.e</mtext></mrow><mrow><mtext>j3r</mtext></mrow></msup><msup><mrow><mtext> + K1.e</mtext></mrow><mrow><mtext>j2r</mtext></mrow></msup><msup><mrow><mtext>.z⁻¹ + K2.e</mtext></mrow><mrow><mtext>jr</mtext></mrow></msup><mtext>.z⁻² + K3.z⁻³</mtext></mrow></math><img file="EP0333566B1_D0013.tif" /></maths>

The comparison of formulas (2) and (3) shows that to achieve the frequency offset fd of the module of the transfer function, it is sufficient to modify the coefficients of the multiplier circuits M0 to M3 so that they become<maths id="math0014" num=""><math display="block"><mrow><msup><mrow><mtext>K′0 = K0.e</mtext></mrow><mrow><mtext>j3r</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0014.tif" /></maths><maths id="math0015" num=""><math display="block"><mrow><msup><mrow><mtext>K′1 = K1.e</mtext></mrow><mrow><mtext>j2r</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0015.tif" /></maths><maths id="math0016" num=""><math display="block"><mrow><msup><mrow><mtext>K′2 = K2.e</mtext></mrow><mrow><mtext>jr</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0016.tif" /></maths><maths id="math0017" num=""><math display="block"><mrow><mtext>K′3 = K3</mtext></mrow></math><img file="EP0333566B1_D0017.tif" /></maths>

FIG. 4 gives the canonical structure of such a transverse filter in the case of a weighting made on four pulses. In this figure, the delay lines LR1 to LR3 of FIG. 1 are shown diagrammatically by operators Z1 to Z3 in series which each carry out the transform z⁻¹, which corresponds to performing a delay Tr of each sample X_i because :<maths id="math0018" num=""><math display="block"><mrow><msup><mrow><mtext>z⁻¹ = e</mtext></mrow><mrow><mtext>-j2πFd.Tr</mtext></mrow></msup></mrow></math><img file="EP0333566B1_D0018.tif" /></maths>

The input of the operator circuit Z1 as well as the outputs of the operator circuits Z1, Z2 and Z3 are connected to multiplier circuits M′0 to M′3 which carry out the multiplication by the coefficients K′0 to K′3 respectively. The outputs of the multiplier circuits M′0 to M′3 are connected to an addition circuit S ′ which supplies a filtered signal S ′_{i + 3} defined by :<maths id="math0019" num=""><math display="block"><mrow><msub><mrow><mtext>S ′</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> = K′0.X</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> + K′1.X</mtext></mrow><mrow><mtext>i + 2</mtext></mrow></msub><msub><mrow><mtext> + K′2. X</mtext></mrow><mrow><mtext>i + 3</mtext></mrow></msub><msub><mrow><mtext> + K3.X</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0333566B1_D0019.tif" /></maths> that is to say a signal in which the echoes having Doppler Fd frequencies have been eliminated.

The description of the invention has been made in the particular case of a transverse filter treating four pulses, but it is clear that the invention can be implemented for any number of pulses. Thus, for a number L of pulses to be processed simultaneously, we have the following transfer functions in z according to the structures:<ul id="ul0002" list-style="none"><li>(A) classical structure for eliminating fixed echoes:<maths id="math0020" num=""><img file="EP0333566B1_D0020.tif" /></maths></li><li>(B) structure with head multiplications<maths id="math0021" num=""><img file="EP0333566B1_D0021.tif" /></maths></li><li>(C) structure with multiplication at output<maths id="math0022" num=""><img file="EP0333566B1_D0022.tif" /></maths></li></ul>

We then observe that Hi (z) and H ′ (z) have the same module, which means that we perform the same filtering with structure (C) as with structure (B) if we do not s 'is only of interest in the module, but in structure (C) the coefficients no longer depend on the rank of the sample in the repetition period and are therefore fixed values.

We note that, for certain values ​​of the Doppler frequency Fd with respect to the repetition frequency Fr, we obtain values ​​of the coefficients K′0 to K′3 which are integers leading to simple multiplications. This is so when Fd is equal to + Fr / 4 or -Fr / 4; in the first case, the four coefficients K′0 to K′3 can be respectively equal to one of the following four groups<ul id="ul0003" list-style="dash"><li>(-d, 3, 3d, -1)</li><li>(1, 3d, -3, -d)</li><li>(j, -3, -3d, 1)</li><li>(-1, -3d, 3, d)</li></ul> In the second case, they can be respectively equal to:<ul id="ul0004" list-style="dash"><li>(d, 3, -3d, -1)</li><li>(1, -3d, -3, j)</li><li>(-j, -3, 3d, 1)</li><li>(-1, 3d, 3, -d)</li></ul>

In the first case, the modulus of the frequency transfer function H ′ (f) is given by curve 12 in FIG. 5 which corresponds to curve 11 for eliminating fixed echoes in FIG. 2, but displaced by - Fr / 4 on the frequency axis. Such a transfer function, the maximum transmission of which is at + Fr / 4 makes it possible to eliminate the echoes corresponding to the Doppler frequencies close to -Fr / 4.

In the second case, the modulus of the frequency transfer function H ′ (f) is given by curve 13 in FIG. 6 which corresponds to curve 11 for eliminating fixed echoes but displaced by + Fr / 4 over l 'frequency axis. Such a transfer function whose maximum transmission is at -Fr / 4 allows the filter to eliminate the echoes corresponding to the Doppler frequencies close to + Fr / 4.

FIG. 7 is a diagram of a digital filtering device which implements the method of the invention in the case of simultaneous frequency shifts of + Fr / 4 and -Fr / 4 with processing on four pulses at using three memories each carrying a delay line.

The signal to be filtered is presented in the form of its two real components I and imaginary Q which are first processed in two separate channels and then in a common part. Each separate channel comprises a memory 20 (or 21) which is made up, in the case of simultaneous processing on four samples, of three identical elementary memories 22, 24, 26 (or 23, 25, 27) which are provided for recording each, in the case of a radar signal, the sample codes corresponding to a repetition period Tr. The outputs of memories 22 and 24 (or 23 and 25) are respectively connected to adder circuits 28 and 30 (or 29 and 31) which carry out the operation multiplication by the coefficient 3.

The common part includes adder circuits 32 to 39 and two module calculation circuits. The adder circuits 32 to 35 and 36, 39 have a direct input + and a complementary input - which completes the code applied to it. More precisely, the inputs (-) of the adder circuits 32 to 35 are connected respectively:<ul id="ul0005" list-style="dash"><li>at the output of memory 26,</li><li>at the output of the adder circuit 31,</li><li>at the input of memory 22, and</li><li>at the output of memory 27.</li></ul>

Similarly, the outputs (+) of the adder circuits 32 to 35 are connected respectively:<ul id="ul0006" list-style="dash"><li>at the output of the adder circuit 28,</li><li>at the entry of memory 23,</li><li>at the output of the adder circuit 30, and</li><li>at the output of the adder circuit 29.</li></ul>

Each output of the adding circuits 32 to 35 is connected to one of the two inputs of one of the adding circuits 36 to 39. Thus, the output of the adder circuit 32 is connected to the inputs (+) of the adder circuits 36 and 37; the output of the adder circuit 33 is connected to the input (-) of the circuit 36 ​​and to the input (+) of the circuit 37; the output of circuit 34 is connected to the input (+) of circuit 38 and to the input (-) of circuit 31; finally, the output of circuit 35 is connected to the input (+) of circuits 38 and 39.

The outputs 42 and 45 of the circuits 36 and 39 are connected to the two inputs of the module calculation circuit 41 while the outputs 43 and 44 are connected to the two inputs of the module calculation circuit 40.

If IO, I1, I2 and I3 respectively call the sample codes at the input of memory 22 and at the outputs of memories 22, 24 and 26 and QO, Q1, Q2 and Q3 the sample codes at the input of memory 21 and at the outputs of memories 23, 25 and 27, we can see that we have the following codes at the output of circuits 36 to 39.<ul id="ul0007" list-style="dash"><li>at output 42 of adder circuit 36:    - I3 + 3I1 - QO + 3Q2;</li><li>at output 45 of adder circuit 39:    - Q3 + 3Q1 + IO - 3I2;</li><li>at output 43 of adder circuit 37:    - I3 + 3I1 + QO - 3Q2;</li><li>at output 44 of adder circuit 38:    - Q3 + 3Q1 - IO + 3I2.</li></ul>

It has been shown above that, in order to obtain a so-called + Fr / 4 filter, it was necessary, according to the invention, to multiply the complex samples X3, X2, X1, XO by the respective coefficients -1, 3j, 3, -j and sum the results of the multiplications, i.e. obtain: -1 (I3 + jQ3) + 3j (I2 + jQ2) + 3 (I1 + JQ1) - j (Io + JQo) is : -I3 + 3I1 + QO - 3Q2 + j (-Q3 + 3Q1-IO + 3I2), which corresponds for the real part to the output 43 of the circuit 37 and for the imaginary part to the output 44 of the circuit 38.

Regarding the filter called -Fr / 4, the respective coefficients which have been indicated above are -1, -3j, 3 and j, for the complex samples X3, X2, X1, XO. At the output of the summing circuit S ′ in FIG. 4, we obtain: -1 (I3 + jQ3) - 3j (I2 + jQ2) + 3 (I1 + JQ1) + j (Io + JQo) either: - I3 + 3I1 - QO + 3Q2 + j (-Q3 + 3Q1 + IO - 3I2) , which corresponds for the real part to the output 42 of the circuit 36 ​​and for the imaginary part to the output 45 of the circuit 39.

As a consequence of the above, the circuit for calculating the module 40 therefore gives the module of the signal corresponding to the filter + Fr / 4 while the circuit 41 gives the module of the signal corresponding to the filter -Fr / 4. The description which has just been made in relation to FIG. 7 shows that the application of the invention to particular cases of filters makes it possible to achieve simple digital devices, easy to produce and using only elementary circuits. .

The invention has been described in relation to a particular application in the field of radars. However, it is understood that the invention applies to the filtering of all types of electrical signals provided that they are sampled at a frequency at least equal to twice the maximum frequency of the useful spectrum so as to obtain the samples Xi separated by intervals of times equal to the sampling period.

Of course, to obtain a filter having a given transfer function by implementing the present invention, it is possible to put in parallel several transverse filters according to the invention, each transverse filter having an appropriate transfer function so that the sum transfer functions lead to the desired global transfer function.