WO1991008615A1

WO1991008615A1 - Method and apparatus for generating a composite and pulse shaped frequency sweep signal

Info

Publication number: WO1991008615A1
Application number: PCT/NO1990/000174
Authority: WO
Inventors: Karsten Husby
Original assignee: Sinvent AS
Current assignee: Sinvent AS
Priority date: 1989-11-24
Filing date: 1990-11-23
Publication date: 1991-06-13
Anticipated expiration: 1992-05-24
Also published as: NO894710L; NO894710D0

Abstract

Method for generating a composite and pulse shaped frequency signal. The signal is built up by taking as a basis an elementary signal block (B2) comprising a small number of frequency sweep signals and having a limited extent as to period time (Ts) and period bandwith (Bs). An in the principle infinite number of elementary signal blocks (B2) are assembled with coinciding frequency and phase at the transitions between the elementary blocks, so that there is generated a sum of continuous frequency sweep signals by repeating of the elementary block (B2) both in time and frequency.

Description

METHOD AND APPARATUS FOR GENERATING A COMPOSITE AND PULSE SHAPED FREQUENCY SWEEP SIGNAL.

This invention relates to an essentially new method for generating a composite and pulse shaped frequency sweep signal (chirp signal) , and means for carrying out the method. A primary use of the resulting sum of frequency sweep signals is to multiply these by another analog signal in order to perform a CFT transform. The invention is not, however, restricted to this specific use, but has potential interest in all relationships where it is desired to employ a sum of overlapping frequency sweep signals.

The invention is, i.a. , particularly useful within the field of satellite communication, and in such case imple- mentet onboard a communication satellite, but the invention can also be employed in connection with other electronic equipment as for example radio links, mobile telephones and base stations.

In particular the invention is intended for appli¬ cations within the field of communications, where a large bandwidth and a low power consumption are important.

An interesting and usual utilization of the invention will be as a part of a CFT (Chirp Fourier Transform) which is an analog CZT (Chirp Z-Transform) . Such a CFT combines elements from digital signal processing (in order to attain flexibility) with analog techniques (in order to attain a large bandwidth) . The frequency sweep generator can be a part of such a CFT arrangement. Because of the large bandwidths and the long integration times which it is desirable to use, the time-bandwidth product will be high. This implies that the digital memory will be large, and the sampling frequency high. In particular the sampling frequency can become so high that components having a large power capacity must be used. For performing such a CFT there has up to now been a necessity to employ a relatively complicated linear multiplier.

At this point it is noted that methods for generating frequency sweep signals on an individual basis are previously known and published, and reference is made here to US patents 3.794.995 and 3.852.746. It is obvious, however, that these known methods are not directed to generating a sum of overlapping or simultaneously running frequency sweep signals, but exclusively separate or discrete frequency sweep signals at certain times. According to the US patents the sampling takes place in accordance with the Nyquist criterion, so that the sampling frequency is equal to, or higher than, the bandwidth of the frequency sweep signal. As will appear from the following description, the sampling is effected also according to the present invention in complience with the Nyquist criterion, but in such a manner that the sampling frequency is typi¬ cally lower than the bandwidth of the frequency sweep signals. In other words, the invention implies a form of undersampling in order to reduce both the sampling frequency and the number of sampling points. This utilization of undersampling with resulting aliasing gives the high number of signals and frequences which it is desired to achieve here.

The invention has for an object to reduce the size of the required digital memory in the frequency sweep generator, to eliminate the need for an accurately con¬ trolled amplitude of the frequency sweep signal whether this be generated in a digital or an analog manner, to reduce the intermodulation, to reduce the sampling rate as well as to replace the linear mulitiplier by a non-linear multiplier in the case of multiplication as with CFT.

On the above background the essential novelty and fundamental of the method for generating a composite and pulse shaped frequency sweep signal, mainly consists therein that the signal is built up by taking as a basis an elementary signal block comprising a small number of frequency sweep signals and having a limited extent as to period time (T_s) and period bandwidth (B_s) and that a number of elementary signal blocks being in the principle an infinite number, are assembled with coinciding frequency and phase at the transitions between the elementary blocks, so that there is generated a sum of continuous frequency sweep signals by repeating of the elementary block both in time and frequency.

More definite statements of other aspects and specific features of the method and means for carrying out the method, are found in the claims.

In the following description the invention shall be explained more closely with reference to the drawings, in which:

Fig. 1 is a frequency-time diagram of a sum of frequency sweep signals with indications of an elementary block or blocks being a fundamental elementary building block for the sum of signals shown, Fig. 2 shows a similar diagram as in Fig. 1, but with an enlarged elementary block as represented by an oversampling factor C₀ = 3, Fig. 3 shows a simplified block diagram of a feasible form of generator/multiplier based on a time variable phase twister, for example for performing a CFT, Fig. 4 shows simplified curve shapes of signals at certain points in the diagram of Fig. 3, Fig. 5 in block diagram form shows another embodiment of a frequency sweep signal generator/multiplier with complex digital generation and harmonic pulsed local oscillator, Fig. 6 shows simplified curve shapes of signals at certain points in the diagram of Fig. 5, Fig. 7 shows still another apparatus for carrying out the method according to the invention, namely a generator/multiplier based on a SAW filter as a main component, Fig. 8 shows simplified curve shapes of signals at certain points in the diagram of Fig. 7, Fig. 9 shows a block diagram of still a further form of generator based on a D/D converter, Fig. 10 illustrates simplified curve shapes of signals at certain points in the diagram of Fig. 9, Fig. 11 is an example of a generated sum of frequency sweep signals with C_n = 11, i.e. consisting of 11 band pass pulses having different phase, Figs. 12A and 12B show the same signals as in fig. 11, but here in the form of amplitude and phase values respectively, Fig. 13 is a polar diagram of a generated frequency sweep signal with C_n = 11, and Fig. 14 is a polar diagram of another (narrow band) frequency sweep signal with C_n = 11. Furthermore, reference is here made to the following appendixes at the end of this description:

Appendix I is a listing of a FORTRAN program BEVIS which serves to substantiate some of the mathematical background behind the method according to the invention.

Appendix II is a listing of a BASIC program for calculating function values according to the mathematical background given in the following description,

Appendix III is an example of running of the BASIC program with the result printed out, and

Appendix IV is another example of running the BASIC program with the result printed out.

Reference is now made to Fig. 1. A frequency sweep signal is an electric oscillation with a lineary increasing frequency as a function of time. A single sweep or signal variation is shown as the line SI in Fig. 1. According to the invention, such signals can be described by means of an elementary signal block as shown at B2 in the figure. This elementary block can serve as a "building block" for a sum of frequency sweep signals. The time dimension or extent of the elementary block is the period time T_s which is the shortest required time cycle for generating the frequency sweep signal. At the other hand, the elementary block has an extent in frequency referred to as the period band B_s which corresponds to the lowest required sampling frequency for generating the frequency sweep signal. This can be expressed as follows:

B_s = c₀μτ_s (1)

where μ is the sweep rate, i.e. change of frequency per second and C₀ is the "oversampling factor" seen in relation to the frequency spacing between the individual sweeps, i.e. B_s in Fig. 1.

As will appear from Fig. 1, a complete frequency sweep signal (in the theory) can consist of a sum of infinitely many overlapping frequency sweeps, having a frequency from - » to + oo. According to the invention, this is generated by copying or repeating the elementary block both along the frequency and the time axis. Just this is achieved by complex sampling of a periodic signal, which constitutes a substantial feature of the method according to the invention.

A mathematical treatment of these fundamental relation¬ ships in connection with the invention follows below.

Frequency sweep signal number n in Fig. 1 having a frequency from - oo to + oo can be written mathematically as follows:

C_n(t) = _eJ τr(t+nT_s)2 ₍₂₎ where eO = the complex exponential function

μ = sweep rate [Hz/s]

T_s = sweep period [s] n = frequency sweep number t = running time from - oo to + ∞ [s] A sum of frequency sweeps can be expressed as: n=m cm(t) - ]^> cχι(t) n=l

A sum of oo many sweeps can be written as follows: c (t) = J C₀ lim c^tj /m m→ oo

It can be shown that: c(t) - 5(t-(k-D)T_s/C_n)_e3 7r(p(k,C_n/C₀)+D)2(T_s/C_n)2 ₍₃₎

wherein k = ... - 3, -2, -1.0,1,2,3 ... 1 x = 0 δ (x) = 0 x = 0

Accordingly, a sum of many frequency sweeps can be expressed as a series of pulses. These pulses can have shapes as for example illustrated in the diagrams of Figs. 11 to 14 of the drawings. This can be shown by means of a FORTRAN program BEVIS as listed in Appendix I. In this program the bandwidth of the frequency sweep signal is limited by a Banning window so that in the time domain the pulses will be sufficiently separated from each other. The deduction above applies to the idealized case. In practical implementation there will take place a filtering which can be expressed by a given impulse response h(t) , which means that the sum of frequency sweeps in practice will be c_p(t)=c(t)*h(t). T_S ² = C_n/C₀

where C_n is the number of samples per cycle of duration T_s and C₀ is the oversampling factor. C_n and C₀ are relatively primic integers having a highest common divisor equal to 1.

0 C_nC₀=2 N N=l,2,3 ...

D = 1/2 C_nC₀=2N+l N=l,2,3 ... p(k,C_n,C₀) = C₀A where A is an integer within the interval (0,C_n-l) and A = (k-NC_n)/C₀ N is an integer.

For a given k there exists an integer N which gives an integer A within the interval (0,C_n-l). The tables below show how the function p(k,C_n,C₀) can be expressed for C_n,C₀=13.3 and C_n,C₀=11.4.

In the above tables it is reason to note that for example p(2,13,3)=15, p(10,13,3)=36, p(4,ll,4)=4 and p(10,ll,4)=32.

The function values c(t) according to equation (3) above can, thus, be calculated. Appendix III recites a computer program written in BASIC which performs this calculation. The BASIC program works in the following manner:

Lines 110 to 130: Read desired value of period time T_s and an interval which indicate desired minimum and maximum limit of the sweep rate μ . Lines 140 to 190: Calculate the smallest possible C₀ which gives a sweep rate μ in compliance with the maximum and minimum values. At the same time, calculate C_n so that C_n and C_Q become relatively primic. Lines 200 to 240: The most important parameters of the frequency sweep signal are then determined. Print out these. Lines 250 to 290: Calculate the function p(k,C_n,C₀). Lines 300 to 310: Calculate D and the time spacing between sample number 0 and the instant where the sweep signals have the frequency nC_n/(T_SC₀) n=... -3,-2,-1,0,1,2,3 ... Lines 330 to 380: Calculate the phase of all samples from number 0 to sample number C_n-1 and simultaneously normalize the phase so that sample number 0 has always the value 0 degrees. The amplitude of all samples is equal.

Whereas the elementary signal block B2 in Fig. 1 comprises a single sweep, Fig. 2 shows an embodiment having an enlarged elementary block B12 based on CO = 3. The total sum of frequency sweep signals can be regarded as composed of a number of individual sweeps Sll in analogy to the individual sweep SI in Fig. 1. Within the elementary block B12 there is here included three individual sweep lines and the complete signal which it is desired to generate, is provided by repeating this elementary block in time and frequency.

In practice the invention is carried out by first calculating the phase values in the elementary block by means of a program as for examle the BASIC program in Appendix II. Then these values are applied to a suitable apparatus which can also simultaneously bandlimit the frequency sweep signal by letting the pulses extend somewhat in time. The desired sum signal is then obtained by generating these pulses at the desired sampling rate (C_n/T_s) and period time (T_s) .

As a supplement to the diagrams in Figs. 11, 12A and 12B, the diagrams in Figs. 13 and 14 are corresponding polar diagrams. Regarding the diagram in Fig. 13 it can be noted that the pulses are short, so that intersymbol interference is avoided. Such a frequency sweep signal can be handled non-linearly. In the diagram of Fig. 14 the frequency sweep signal is a narrow-band signal, so that the different pulses interfere with each other.

Advantages obtained: The invention makes it possible to generate a sum of several frequency sweep signals at sampling rates being much lower than the bandwidth of the sweep signals, without employing parallel processing. When used in connection with a CFT and without oversampling (Appendix III) the sampling frequency of the generator will be equal to the processed bandwidth irrespective of the bandwidth of the sweep signal. This is a great improvement from previous frequency sweep generators. Since the bandwidth of the sweep signal typically can be 8 times wider than the processed bandwidth in a CFT (the useful band¬ width) ,. the reduction of sampling frequency when using this invention will be correspondingly large. Also the memory requirements will decrease correspondingly. A further advantage consists therein that the amplitude of all sweep samples are equal, so that amplifiers having a non-linear characteristic can be used for amplifying and conveying the frequency sweep signal. In a CFT the frequency sweep signal shall be multiplied by the useful signal. Previously it was here necessary to have a linear multiplier because both the useful signal and the frequency sweep signal were analog composite signals with varying amplitudes. In the case of the present invention a traditional passive mixer can be employed for this operation. The fact that the frequency sweep signal consists of short pulses can also be utilized for simplifying the local oscillator which can be used for up-converting the frequency of the sweep signal to a suitable IF. It is not required that the local oscillator runs continuously, but it can be implemented by means of a band pass filter which is pulsed for each sample. The SAW filter can also be used as a frequency sweep generator directly. One pulse for each frame is emitted into a crystal, and this gives C_n pulses out, which can be limited in class C amplifiers (amplifiers having a high efficiency and a non-linear characteristic) . All the factors mentioned above are significant with respect to complexity, mass, volume and power consumption.

As a practical illustration of an important advantage as mentioned above, reference can be made to the implemen¬ tation of CFT processors. With a bandwidth of about 25 MHz, there must be generated frequency sweep signals with bandwidths of about 100 MHz. Based on techniques proposed previously, this has required sampling rates of about 200 MHz, which implies a need for very fast circuits involving a high power consumption. By means of the method according to this invention, the sampling rate can be reduced to about 30 MHz in such a practical case.

The fundamental method according to the invention opens up for a long variety of practical embodiments, and some variants of arrangements being suitable in certain uses, shall be discussed in the following description.

What is desired to be effected in for example a CFT, is to multiply an analog signal by a sum of several frequency sweep signals. Fig. 3 shows an apparatus which performs this. An analog band limited signal 1 is applied to a time varying phase twister 2 so that the relative phase between an output signal at 3 and the input signal at 1 will be given by the phase values, for examle from Appendix III. At the right instant of time a short pulse of signal 3 is admitted through sampler 4. The length and the shape of this pulse determines the spectral configuration of the output signal 5. Schematic curve shapes of the signals at 1,5,6 and 7 are shown in Fig. 4. For implementing the time varying phase twister 2 there can be employed multiplying D/A converters for example, or an analog band pass filter having a controllable phase characteristic can be used.

Fig. 5 shows another embodiment. A clock signal 12 is generated by a circuit 11. The sequence circuit 14 which can be a common counter circuit, is clocked for example on a positive edge, whereas counter 13 can be clocked on a negative edge. Counter 13 has also particularly fast and precise drivers at its output. Therefore, this counter generates fast transitions 15 having a high bandwidth each time the signal 12 goes negative. The steep edges of signal 15 are filtered in a band pass filter 24 so as to result in short band pass pulses 16. In the ideal case this shall be a filter having a linear phase and a finite pulse response. If the pulse response of the filter is shorter than the period of clock 12, there will be no interference between the different band pass pulses 16. An amplifier having a non-linear characteristic therefore can be used for ampli¬ fying the frequency sweep signal. As this is effected, the pulses 16 are mutually displaced by 180 degrees. Signal 16 is then split in a 90 degree hybrid 37. Each of the two signals 8,9 are applied to a separate mixer 25,26. The signals 8,9 are mixed each with a signal 18,17 being proportional to sinus and cosinus of the phase angles as given for example by Table III. Sequence circuit 14 forms an address 10 which addresses two stores 31,32 for sinus and cosinus respectively. The digital representation 34,33 for sinus and cosinus is fed to two digital-analog converters 36,35 which generate the analog sinus and cosinus voltage 18,17. The mixing product 20,19 is a comlex representation of a sum of several frequency sweep signals as these are stored in stores 32 and 31 and adjusted with respect to frequency by filter 24. Mixing products 20,19 are added at 22 so as to give a real frequency sweep signal 27. This signal can be strongly amplified before it is conveyed to the mixer 23 which finally multiplies the frequency sweep signal by the input signal 28. Schematic curve shapes of the signals at 12,15,16,17,18,20 and 28 are shown in Fig. 6.

Fig. 7 shows a third alternative based on this invention. Here short pulses 42 are fed at a regular rate from a clock generator 41 into a SAW filter (Surface Acoustic Wave filter) . SAW filter 43 is configured in compliance with calculated phase values as described above. Pulses 42 are generated each T_s second. For each input pulse 41, the SAW filter generates a number C_n of pulses 44 out. The length of the pulse response of the SAW filter can be equal to T_s. Frequency sweep signal 44 can be non- linearly amplified before it is mixed with the input signal 45 in mixer 46 which can well be of the passive, non-linear type. Schematic curve shapes of the signals at 42,44 and 45 are shown in Fig. 8.

A fourth alternative is shown in Fig. 9. D/D- converters or socalled Digital-to-Delay-converters can be employed for generating digital pulses having controllable delays. Such pulses used for the excitation of a band pass filter can form the heart of a frequency sweep generator. Clock circuit 51 generates a clock frequency which forms the sampling rate for the desired frequency sweep. This clock is used for incrementing a sequence circuit 53 which can be a common counter. Sequence circuit 53 generates an address 54 which is used for making a table look-up in a storage circuit 55. D/D-converter 57 delays one edge of signal 52 in accordance with the digitally stored word 56. Circuit 59 generates a short pulse 60 each time the delayed transition 58 arrives. Pulse 60 is applied to band pass filter 61. The bandwidth of the filter must be much smaller than the center frequency. In the ideal case this shall be a filter having a linear phase and a finite pulse response. If the pulse response of the filter is shorter than the period of clock 52, there will be no interference between the various band pass pulses 62. An amplifier 63 having a non-linear characteristic can therefore be employed for amplifying the frequency sweep signal before it is conveyed further, for example to a non-linear mixer 65 of a conventional type. Schematic curve shapes of most of the signals in Fig. 9 are shown in Fig. 10. Finally mention shall also be made of the conventional digital frequency sweep generator which directly generates a frequency sweep by means of a D/A converter and band pass sampling. Such a generator can also make use of some of the advantages of this invention. The number of quantizing levels can for example be reduced to 2, which is the same as completely removing the D/A converter.

Appendix I

**************************************************************************

* Name: BEVIS

*

* Function performed: Prove that sum(exp (. j *u*pi* (t+n*Ts) **2) ) = . . .

*

* **************************************************************************

INTEGER uendelig,n,u

REAL MY,TS,t,pi

COMPLEX j,s pi=3.1415926

WRITE(*,*) 'Chirp period : '

READ*,TS

WRITE(*,*) 'Chirp rate : '

READ*, Y

WRITE(*,*) 'Bandwidth : '

READ*,uendelig

OPEN (10,FILE='CHIRP.PRN') u=uendelig j=(0.0, 1.0) do 20 t=-ts/2.0,ts/2.0-ts/2048.0,tS/2048.0 s=(0.0,0.0) do 10 n=-uendelig,uendelig,1 s=s+cexp(j*my*pi*(t+n*ts)**2)*(l+cos((t+n*ts)/(u+.5)/ts*pi) ) 0 continue

WRITE(10,17)real(s) ,imag(s) 7 FORMAT(2(F10.5)) fase=atan2(real(s) ,imag(s) )*180/pi write(*,*) 't= ',t,' fase = ',fase,' amp = ',cabs(s) 0 continue close (10) END

Appendix II

100 DIM panel(256)

110 INPUT "Chirp period : ",ts

120 INPUT "Minimum chirp rate : ",mymin

130 INPUT "Maximum chirp rate : ", ymax

140 mymid=(mymin+mymax)/2

150 FOR co-1 TO 1000

160 cn=INT(co*mymid*ts^*2+.5)

170 my=cn/co/ts^*2

180 IF raymin < my AND my < mymax THEN GO TO 200

190 END FOR CO

200 PRINT "Calculated chirp rate : ";my/lE12;" Mhz/us"

210 PRINT "Number of complex samples in chirp = ";cn

220 PRINT "Chirp oversampling = ";co

230 PRINT "Sampling frequency - ";cn/ts/lE6;" MHz"

240 PRINT "Prosessed bandwidth - ";cn/ts/co/lE6;" MHz"

250 k«0

260 FOR i=0 TO cn*co-l STEP co

270 IF i-cn*k >=cn THEN k=k+l

280 panel(i-cn*k)=i

290 END FOR i

300 d=cn*co/2-INT(cn*co/2)

310 PRINT "Zero Hz time instant - ";INT(-d*ts/cn*lE9) ;

"ns relative to sample zero." 330 off*l80*my*(d*ts/cn)^*2

340 FOR i-0 TO cn-1

350 fase(i)=180*my*((panel(i)+d)*ts/cn) ^*2-off 360 fase(i)-INT(fase(i)/360+.5) *360-fase(i) 370 PRINT "Sampel = ";i," Phase = ";fase(i) 380 END FOR i

Appendix III

Chirp period = 8.333333 us

Calculated chirp rate : .1584 Mhz/us

Number of complex samples in chirp - 11

Chirp oversampling = 1

Sampling frequency - 1.32 MHz

Prosessed bandwidth = 1.32 MHz

Zero Hz time instant = -379 ns relative to sample zero^,

Appendix IV

_Chirp period *= 8.333333 us

_Calcu_lated chirp rate : .1536 Mhz/us

Number of complex samples in chirp = 32

_Chirp oversampling = 3

_Sampling frequency = 3.84 MHz

Prosessed bandwidth = 1.28 MHz

Zero Hz time instant = 0 ns relative to sample zero

118.125

112.5

-16.875

90

73.12501

-67.5

28.12501

1.525879E-5

-151.875

-67.5

-106.875

90

163.125

112.5

-61.875

0

-61.87499

112.5

163.125

90.00001

-106.875

-67.5

-151.875

0

28.125

-67.49998

73.125

90

-16.87498

112.5

118.125

Claims

1. Method for generating a composite and pulse shaped frequency sweep signal, characterized in that the signal is built up by taking as a basis an elementary signal block comprising a small number of frequency sweep signals and having a limited extent as to period time (T_s) and period bandwidth (B_s) and that a number of elementary signal blocks being in the principle an infinite number, are assembled with coinciding frequency and phase at the transitions between the elementary blocks, so that there is generated a sum of continuous frequency sweep signals by repeating the elementary block both in time and frequency.

2. Method according to claim 1, characterized in that the composite frequency sweep signal is described by the following relation:

_Cp(t) = 5(t-₍k-D)T_s/C_n)_eJ π(p(k,C_n/C₀)+D)2(T_s/C_n)2_Λh(t)

where k = ... - 3, -2, -1,0,1,2,3 ...

1 x=0

5(x) -

0 x O

*h(t) denotes filtering with a given impulse response

μT_s2 = c_n/C₀

where C_n is the number of samples per cycle of duration T_s, and C₀ is the oversampling factor, whereby C_n and C₀ are relatively primic integers having a highest common divisor equal to 1, and μ is the sweep rate, 0 C_nC_Q=2 N N=l,2,3 ...

D = 1/2 C_nC₀=2N+l N=l,2,3 ... p(k,C_n,C₀) = C_QA where A is an integer within the interval (0,C_n-l) and A = (k-NC_n)/C₀ N is an integer.

3. Method according to claim 1 or 2, characterized in that the elementary signal block comprises a single frequency sweep.

4. Method according to claim 2 or 3, characterized in that the extent of the elementary block as to period time (T_s) and bandwidth/frequency (B_s) is brought to a minimum by finding the lowest values of the pair of relatively primic integers C_n and C_Q which give a desired period time (T_s) and sweep rate (μ) .

5. Method according to any one of claims 1 to 4, characterized in that the amplitude of the pulses in the composite frequency sweep signal is brought to be constant, whereas the phase is brought to vary from pulse to pulse.

6. Method according to claim 5, characterized in that the phase is brought to be linear within each pulse.

7. Method according to any one of claims 1 to 6, characterized in that the frequency sweep signal is gene¬ rated by means of periodic complex sampling, and that the sampling frequency corresponds to the period bandwidth (B_s) .

8. Method according to claim 7, characterized in that generating the frequency sweep signal in the first instance comprises calculation of the phase values thereof, and in the second instance loading or application of these phase values into circuit means adapted to deliver the sum of frequency sweep signals at its output.

9. Method according to any one of claims 1 to 8, characterized in that the generated sum of continuous frequency sweep signals is multiplied by an analog signal, for example for performing a CFT transform.

10. Apparatus for carrying out the method according to claim 8, characterized by comprising: a storage circuit (55) for storing said calculated phase values, a converter circuit (57) which receives signals corresponding to calculated phase values from said storage circuit (55) and to which also clock pulses (52) are being applied, in order to provide time delays depending upon received phase values, and has an output (58) connected to

- a circuit (59) adapted to generate pulses (60) suitable for the excitation of a following band pass filter (61) which delivers the desired sum of frequency sweep signals (62) . (Fig. 9) .

11. Apparatus for carrying out the method according to claim 8, characterized by comprising: storage circuits (31,32) for storing sinus and cosinus of said calculated phase values, a circuit (13) to which clock pulses are applied and which is adapted to generate pulses (15) suitable for the excitation of a following band pass filter (24) , a hybrid circuit (37) receiving pulses from the band pass filter (24) and delivering signals having a 90° split, to respective mixing circuits (25,26), to which mixing circuits there are also applied signals corresponding to said stored sinus and cosinus values, and an adding circuit (22) for forming the sum of the signals from said mixing circuits (25,26), this sum constituting said sum of continuous frequency sweep signals. (Fig. 5) .

12. Apparatus for carrying out the method according to any one of claims 1 to 6, characterized by a SAW filter (43) of suitable configuration and adapted to have short clock pulses (42) applied thereto at a regular rate corresponding to the period time (T_s) , so that the output (44) of the filter delivers a sum of continuous frequency sweep signals. (Fig. 7) .

13. Apparatus for carrying out the method according to claim 9, characterized by a time variable phase shifter circuit (2) adapted to have an analog signal (1) applied thereto and to be controlled by a signal (6) which represents said calcu¬ lated phase values, and a following sampling circuit (4) . (Fig. 3).