Method and device for speech encryption and decryption in voice transmission5778073Abstract A digitized real voice signal is converted via complex filtering into a complex signal that is subjected to sampling rate reduction, the bandwidth of the respective complex filter corresponding to the sampling rate. The complex signal is phase-modulated by means of a code signal generated by a random-number generator and additively combined with a pilot signal (likewise phase-modulated in a random distribution) to form an encrypted useful signal for transmission. The useful signal is sequentially transmitted together with a preamble for synchronization and signal equalization at the receiver end. At the receiver end, clock synchronization is forced for a phase-modulated pilot signal produced at the receiver end and equalizer coefficients for an equalizer at the receiver end are calculated from the digitized received signal after complex filtering and corresponding sampling rate reduction, during a preamble recognition phase, at which point the phase of the useful signal decryption is initialized. The encrypted, transmitted signal is separated from its phase-modulated pilot signal, which is superimposed at the transmitter end, by linking to the synchronized pilot signal, which is produced at the receiver end, and the phase-modulated, encrypted digital speech signal thus obtained is subsequently decomposed by the code signal produced at the receiving end and clockcontrolled by the preamble. Claims What is claimed is: Description BACKGROUND
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Sampling frequency: 8 kHz
Word length: 16 Bit
Decimalization filter
Pass band: 0 to 3.7 kHz
Ripple: .+-.0.2 dB
Reverse attenuation: 65 dB
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For further details of the construction and operation of the analog front end 22, reference should be made to Ref. 1! and Ref. 2! of the bibliography specified in the Annex. The digitized input signal c(.nu.) acts on a first complex input filter 30 to suppress the lower sideband. The filter 30 also insures that the bandwidth of the input signal (digitized voice signal) is limited to one that corresponds to that of the transmission channel (i.e. 2.667 kHz in the present exemplary embodiment.) The complex first input filter 30 produces, from a real input signal, a complex output signal consisting of a real part and an imaginary part with a phase shift of 90.degree. existing (analytical signal) between the real and imaginary parts for any desired frequency. At the same time, spectral elements outside the usable bandwidth of the transmission channel are suppressed. Preferably, and in the tested embodiment of the invention, the first complex input filter is a higher-order Hilbert filter (as is the complex input filter at the receiving end; cf. below). The first Hilbert filter 30 at the receiving end is a recursive filter whose transfer function is given by ##EQU1## The structure of this filter is illustrated in FIG. 7. The input signal to the Hilbert filter 30 is, as mentioned, the sampled, real received signal c(.nu.). The recursive part of this filter has only real coefficients b.sub.i, so that only real operations are required. The transverse part has complex coefficients a.sub.i. The design of the first Hilbert filter 30 is based on that of an elliptical low-pass filter. The low-pass filter is converted into a Hilbert band-pass filter by transformation in the frequency domain. The frequency response of the Hilbert filter 30 implemented in the prototype of the invention is shown in FIG. 8. The band-limited output signal d(.nu.) of the first complex input filter (Hilbert filter) acts on a functional block designated as sampling rate reduction 31 in which the sampling clock is reduced by a specific, preferably integer factor. In the present exemplary embodiment, the sampling clock is reduced by the factor 3 to 2.667 kHz. Suitable dimensioning of the first Hilbert filter 30 on the input side assures that no aliasing effects occur. The combination of the Hilbert filter 30 and the sampling reduction 31 causes any randomly selected frequency band of 2.667 kHz width to contain all of the useful information. In principle, only every third output value of the input-side signal c(.nu.) of the Hilbert filter 30 is used for sampling rate reduction. In practice, this is implemented by operation of the transverse part of the Hilbert filter 30 at 8/3 kHz. As such, the filter output values are calculated and further-processed only with every third clock pulse of the 8 kHz sampling clock. The pilot signal generator 20 produces a pilot signal q(n) used at the receiving end for clock slaving. The pilot signal is produced by phase modulation as described below. The (pseudo-) random-number generator 34 (refer to FIG. 6), a part of the code signal generator 23, produces equally distributed numbers in the range from, for example, 1 to 64. Such numbers select random values from a field of 64 complex values (refer to "data set" block of FIG. 6). Two code signals z.sub.s (n), Z.sub.p (n) are derived from the selected values, one of which (z.sub.s (n)) is used for phase modulation of the information signal and the second (z.sub.p (n)) used to produce the pilot signal q(n). The random-number generator 34 implemented in the present embodiment is based on linear congruence. The random values r(n) are calculated in accordance with the rule r(n)=(a.multidot.r(n-1)+c) mod m n=1, 2 (2) The start value r(0) is in general unimportant since all m possible values are produced before the random sequence is repeated, provided that the constants a and c are suitably selected. The random numbers generated are distributed uniformly from 0 to (m-1). In the tested embodiment, m=2.sup.32 was employed, allowing a long sequence to be produced. In addition, the Modulo function of equation 2 can then be simply implemented by the signal processor 1. Constants a=1664525 and c=32767 were selected in accordance with Knuth's rule (cf. Ref. 6!). To obtain uniformly distributed random numbers between 1 and 64, it is sufficient to consider 6 bits of the respective random value r(n), using them as a random number. In a current embodiment, 6 bits are employed for generation of random numbers for "scrambling" (the phase modulation) of the information signal x(n) and 6 bits for the generation of random numbers for scrambling (the phase modulation) of pilot tone p(n). Thus, the random-number generator 34 supplies two random numbers r.sub.s (n) and r.sub.p (n) in each case per clock cycle. After each transmission of a preamble, the random-number generator 34 is reinitialized with a defined start value x(0). The control values for the phase modulators 32 and 33 are represented by a data set of 64 complex values. The random-number generator 34 selects values from this set and produces a random signal for phase modulation. The 64 complex values ##EQU2## are used as the data set. The control or input values z.sub.s (n) and z.sub.p (n) are all of amplitude "1" and differing phases. The random-number-controlled phase modulators 32, 33 are discussed in greater detail below. Two phase modulator units 32 and 33 are required for the transmission section of the SE module (FIG. 6). One phase modulator 33 is required for encryption of the information signal x(n) by a code signal z.sub.s (n) supplied by the random-number generator 34. The other phase modulator 32 generates the pilot signal q(n) from the pilot tone p(n), supplied by the pilot-tone generator, with the aid of the other code signal z.sub.p (n). Since the code signals z.sub.s (n),z.sub.p (n) are random sequences of complex values of the same amplitude but different phases, each phase modulator 32, 33 carries out a complex multiplication of the respective input signal value by the respective code signal value. If, as FIG. 6 illustrates, the signal values of the analytical filter output signal are designated by x(n) and the signal values of the associated code signal by z.sub.s (n), then, for the signal values of the phase-modulated information signal: y(n)=x(n).multidot.z.sub.s (n) (4) The phase-modulated information signal y(n) resembles a noise signal. The information contained in the information signal is completely distributed over a frequency band with a width of 2.667 kHz. It should be noted that phase modulation according to the invention possesses a certain similarity to a 64-stage PSK modulation as employed in digital transmission technology. However, its purpose is quite different. In digital data transmission using PSK modulation, the phase of a carrier signal is keyed at the sampling clock rate (Phase Shift Keying). The phase of the carrier signal thus contains the digital information to be transmitted. At the receiving end, the phase of the carrier is determined at defined sampling times. A discriminator assigns the corresponding digital information to each determined phase and thus obtains the transmitted information. On the other hand, in phase modulation according to the invention the signal to be modulated carries the information to be transmitted, rather than the modulation signal. This information is predetermined by its quasi-continuous signal profile. The phase modulation is employed solely for changing the signal to be transmitted to make it no longer possible to deduce the original signal profile. A voice signal thus becomes completely incomprehensible. The useful information is encrypted by the phase modulation. At the receiving end, the useful information can be recovered by the inverse operation of equation 4 ##EQU3## Complete recovery is possible only when two conditions are satisfied. First, the received signal y(n) must correspond with the (phase-modulated) transmitted signal y(n). Second, the modulation signal, i.e. the code signal z.sub.s (n), must be known at the receiving end. The first requirement depends upon equalization of the transmission channel at the receiving end. The second requirement depends upon knowledge of the code signal and exact synchronization at the receiving end. While the number of values of the code signal z.sub.s (n) is defined by the number of steps in the modulation (64 in this case), the number of possible values for x(n) and y(n) is determined by word length in the signal processing. If the signal values of the generated pilot tone are designated by p(n) and the signal values of the associated code signal by z.sub.p (n), then the signal values of the pilot signal are given by the relationship q(n)=p(n).multidot.z.sub.p (n) (6) Thus, due to properties of the selected random-number generator 34, the pilot signal q(n) generated comprises white noise. Transmission of the analytical signal generated at the clock frequency of 2.667 kHz requires that the transmitted signal be matched to the transmission channel. In the illustrated example, the sampling frequency predetermined by the analog front end 22 is 8 kHz. Accordingly, the sampling rate must first increase to 8 kHz. The increase in the sampling rate by a factor of 3 (i.e. from 2.667 kHz to 8 kHz) is accomplished by the insertion of two signal values, in each case of value 0, between two existing signal values. Thus, d.sub.s (.nu.)= . . . , w(n-1),0, 0, w(n), 0,0, w(n+1) (7) The sampling rate increase is done in conjunction with a first complex output filter 35 for matching the analytical transmitted signal to the transmission channel. The real part of the analytical output signal from the complex output filter 35 is supplied to the analog front end 22. The first complex output filter 35 initially produces an analytical signal, whose real part and imaginary part are phase-shifted through 90.degree. for any given frequency, from a complex input signal d.sub.s (.nu.). A real output signal c.sub.s (.nu.) is provided from the analytical signal. At the same time, spectral elements outside the useable bandwidth of the transmission channel are suppressed. The first complex filter 35 on the output side is preferably a (second) Hilbert filter, i.e. a recursive filter, whose structure is shown in FIG. 9. The input signal d.sub.s (.nu.) to the second Hilbert filter 35 is, as mentioned, an analytical signal; the output signal c.sub.s (.nu.) is a real signal. The design of the filter is based on an elliptical low-pass filter. The low-pass filter is subsequently converted into a Hilbert band-pass filter by transformation in the frequency domain. The frequency response of the (second) Hilbert filter 35 on the output side at the transmitting end is shown in the graph of FIG. 10. The conversion of the digital output signal c.sub.s (.nu.) from the second Hilbert filter 35 into an analog output signal is carried out in the output section of the analog front end 22 (reference block 22b of FIG. 3) and includes level matching. In the implementation, the D/A converter unit 3 (FIG. 1) of the analog front end 22 (without detailed illustration) consists of a D/A converter, an analog smoothing filter, a programmable amplifier and a differential amplifier. The following specifications apply to the output of the analog front end 22 in the illustrated exemplary embodiment of the invention:
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Clock frequency: 8 Khz
Word length: 16 bits
Gain: Adjustable in the range
from -15 dB to +6 dB
Interpolation filter
Frequency response:
0 to 3.7 kHz
Ripple: .+-.0.2 dB
Reverse attenuation:
65 dB
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Once again, reference should be made to Ref. 1! and Ref. 2! for more detailed information on the transmitting-end output at the analog front end 22. The preamble generator 24 generates a preamble at the start of transmission via radio or telephone channel. In order to connect to an ongoing transmission at the receiving end, the generation of a preamble is initiated at fixed time intervals. The preamble employed consists of two successive signal sections. The first signal section is a so-called CPFSK (Continuous Phase Frequency Shift Keying) signal. The second section comprises a noise-like signal. The first part is employed in the receiver to detect the preamble and to synchronize the receiver. The second signal part is employed to equalize the transmission channel. The CPFSK signal is generated by CPFSK modulation of a special data frequency. The length of the sequence may be, for example, 240 bits and the transmission rate 1.778 kbit/s. The structure of the data sequence is selected so that very reliable detection of the preamble can be accomplished employing a special method at the receiving end. Once again, reference is made to U.S. Pat. No. 5,267,264 (Ref. 4!) and to Ref. 5! for further details. The duration of the preamble of the example is approximately 230 ms. Two different operating modes of the SE module can be distinguished at the receiving end. One is the preamble recognition phase, during which the SE module is in the clear position, and the other is the decryption phase. Likewise, three types of signal processing, namely analog signal processing, digital signal processing at the 8 kHz clock rate and digital signal processing at the clock rate of 2.667 kHz can be distinguished as in the case of the transmitting end. Calculation of the equalizer coefficients runs in the background, without linkage to a specific sampling clock. After the apparatus has been switched on, the SE module remains in the preamble recognition phase. FIG. 11 is a functional block diagram of such signal processing. In this phase, the received signal passes only through the analog front end 52 with its filter. The received signal remains essentially uninfluenced by the SE module. The sampled received signal (8 kHz sampling frequency, 16 bit word length) is supplied to a second complex input filter 40, preferably a third Hilbert Filter (band-pass filter), at the receiving end after filtering, and to a sampling rate reduction 43 to 2.667 kHz to the preamble recognition block 44. At the same time, the sample values of the received signal are buffer-stored in the buffer 41. The preamble recognition block 44 automatically and very reliably detects reception of the preamble. References can be found in Ref. 4! (U.S. Pat. No. 5,267,264) and Ref. 5!. The operation and structure of the second complex input filter 40 correspond essentially to the first complex input filter 30 at the transmission end, described above. Preamble recognition serves two functions: (1) detection of the reception of the preamble and the changeover to decryption; and (2) the preamble supplies an exact time reference, necessary for initialization and synchronization of the decryption process. Thus, initialization of a random-number generator 54 (at the receiver end) and a pilot-signal generator 50 occur with recognition of the preamble. In addition, a process is initiated for determining equalizer coefficients. The calculated coefficient set is used to set an equalizer 51 that is required for the decryption mode. The second section of the preamble, i.e., the noise signal, is evaluated to determine the equalizer coefficients. This requires waiting until a specific part of that section is in the buffer 41. The pulse response and the coefficient set for the equalizer filter 51 are then calculated with the aid of an FFT (Fast Fourier Transformation) and a nominal spectrum that is present in the receiver and stored in the program RAM 5 (FIG. 1). After recognition of the preamble, the SE module is in the decryption mode. FIG. 12 illustrates the signal processing in this phase. The flow chart of the functional sequence steps of the signal processing at the receiving end is presented in FIG. 14. The received signal is converted by the analog front end 52 into a digital signal with, for example, an 8 kHz sampling frequency and a 16 bit word length. This signal passes through the equalizer 51, whose object is equalization of the transmission channel as explained below. After filtering via the second complex input filter 40 (preferably a third Hilbert filter; band-pass filter; described in greater detail below) and a sampling rate reduction 43 by the factor 3, an analytical signal is provided of sampling frequency 2.667 kHz. Such signal s(n) consists of the encrypted information signal and the superimposed pilot signal. As described above, the pilot signal is phase-modulated. It is evaluated and separated from the information signal in the clock synchronization block 45. Decryption of the information signal is subsequently carried out by a phase demodulator (descrambler) 59. Once a sample rate increase 61 to 8 kHz and subsequent filtering using a second complex output filter 62, especially a fourth Hilbert filter (band-pass filter), has been performed, the conversion to an analog signal, the decrypted audio signal, takes place in the receiver-end analog front end 52. The operation and arrangement of the second complex output filter 62 correspond essentially to that of the first complex output filter 35. Evaluation of the pilot signal in the clock synchronization block 55 additionally provides a controlled variable for regulating out fluctuations of the sampling clock (clock correction). The regulation of the sampling clock is required because of the stringent requirements for synchronicity during decryption. Fluctuations in the sampling clock are caused by parameter variation between equipment and drifts of the crystal oscillators. To evaluate the pilot signal, the received signal s(n) passes through a phase demodulator (descrambler) 58 at a reduced sampling rate. The output signal q(n) of the phase modulator 58 consists of a carrier signal element and a superimposed signal element, such as a noise signal, produced from the information signal. The carrier signal is converted into the baseband signal by means of the signal generated by the pilot-tone generator 50. After an averager 56, an analytical baseband signal is provided whose real part is a measure of the level of the pilot signal and whose imaginary part is used as a control variable for regulating the sampling clock. Using the determined level of the pilot signal, the pilot-signal generator 50 and a phase modulator (scrambler) 57, a pilot signal q(n) is generated at the receiving end and is subtracted from the received signal s(n). In the ideal case, the generated pilot signal q(n) corresponds exactly to the received pilot signal so that the information signal is completely separated from the pilot signal by subtraction. If the equalization is optimal, then the signal y(n) obtained by subtraction corresponds, except for any superimposed noise signal, to the signal y(n) at the output of the phase modulator 33 of the transmitting end (cf. FIG. 6). The phase modulator 57 and the two phase demodulators 58, 59 are controlled by two (pseudo-) random-number generators 54. One random-number generator controls the phase modulator 57 and the phase demodulator 58 of the clock synchronization block 55. The other controls the phase demodulator 59 for decryption of the information signal y(n). The random-number generators correspond to those of the transmitting end; they are synchronized to the received signal, just as is the pilot-signal generator 50, by the recognition of a preamble. The objects and the implementation of the individual functional blocks of FIG. 12 are described in detail as follows: The input section of the analog front end 52 has the object of level matching, sampling the analog received signal, and conversion into a digital signal. An AD28msp02 chip may be utilized as the analog front end 52 in a prototype implementation (cf. Ref. 3!). Such a chip corresponds to the analog front end used in the ADSP-21msp55 signal processor. The analog front end 52 consists of two analog input amplifiers, a 20 dB preamplifier which can be connected and an A/D converter. The following specifications apply to the A/D converter section of the analog front end 52:
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Sampling frequency: 8 kHz
Word length: 16 Bit
Decimalization filter
Pass band: 0 to 3.7 kHz
Ripple: .+-.0.2 dB
Reverse attenuation: 65 dB
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The equalizer 51 is employed to equalize the frequency response of the transmission channel in the region of the transmission bandwidth from, for example, 300 Hz to 3 kHz. The transmission channel contains all assemblies from the first complex output filter 35 of the transmission section to the second complex input filter 40 of the receiving section (both inclusive). The equalizer 51 is implemented by a transverse digital filter having 128 stages. The equalizer 51 transfer function is: ##EQU4## The coefficients e.sub.i are determined during the reception of a single preamble. The second complex input filter 40 (Hilbert filter) is used to suppress the lower sideband of the input signal and to limit the bandwidth of the input signal (received voice signal) to approximately 2.66 kHz. The second complex input filter 40 (Hilbert filter) is a recursive filter whose structure corresponds to that of the input-side first complex filter 30. To such extent, reference can be made to FIG. 7. The input signal to the second complex input filter 40 is the real output signal c(.nu.) from the equalizer 51. The design of this filter is based on an elliptical low-pass filter. The low-pass filter is converted into a Hilbert band-pass filter by transformation in the frequency domain. A sampling rate reduction 43, for reducing the sampling rate in the illustrated example by the factor "3" to 2.667 kHz, is also carried out in the receiving section, in a manner analogous to the transmitting section. Suitable dimensioning of the second complex input filter 40 ensures that no aliasing effects occur. The combination of a complex input filter 40 and sampling rate reduction 43 results in any selected frequency band of 2.667 kHz bandwith containing all the useful information. In practice, the processing of each third output value of the second complex input filter 40 is accomplished as the transverse part of the filter is operated at 8/3 kHz. As a consequence, the filter output values are calculated and processed further only in every third clock cycle of the 8 kHz sampling clock. The pilot-tone generator 50 supplies an identical signal to the pilot-signal generator 37 at the transmitting end. This signal is required in the clock synchronization block 55 to convert the received and demodulated pilot signal q(n) into the baseband signal, and for receiving-end generation of a phase-modulated pilot signal q(n). As mentioned, the averager 56 is employed for averaging the analytical signal q(n) transformed to the baseband. In this way, the level of the received pilot tone is provided as the real part and a control variable for sampling clock slaving (clock correction) is produced as the imaginary part. Averaging is implemented so that, after every 128 sampling clock cycles, the mean is formed over the last 128 input signal values q(n), transformed into the baseband signal. The random-number generator 54 produces uniformly distributed numbers in the range from 1 to 64, entirely analogously to the operation of the random-number generator 34 of the transmitting end. The numbers are used to select random values from a field of 64 complex values. Once again, two code signals z.sub.p (n) and z.sub.s (n) are produced from the selected values. One of these (z.sub.s (n), is used for phase demodulation, i.e. for decryption of the information signal y(n), and the other, (z.sub.p (n)), is employed in the clock synchronization block 55 for decryption of the received pilot signal and for generation of the receiving-end pilot signal. Because of clock synchronization, the code signals are, of course, identical to the code signals z.sub.p (n) and z.sub.s (n) at the transmitting end. The implementation of the random-number generator 54 is identical to that of the transmitting section, whereby reference can be made to the above-described designs. The random numbers supplied to the phase modulator 57 and to the phase demodulators 58 and 59 consist of a set of 64 complex values from which discrete values are selected by the random-number generator 54. In an analogous manner to the transmitting end, the same 64 complex values ##EQU5## are employed as the data set. The two above-mentioned phase demodulators 58, 59 are required in the receiving section of the SE module. One phase demodulator 59 is used for decryption of the useful signal y(n) by one code signal z.sub.s (n). The other phase demodulator 58 is used for recovery of the pilot tone from the received pilot signal. As already mentioned, these code signals must be identical to the code signals at the transmitting end. If the signal values of the analytical input signal after the sampling reduction 43 are designated by s(n), the signal values of the code signal of the pilot tone are designated by z.sub.p (n), then, for the signal values at the output of the phase demodulator 58 in the clock synchronization block 55: ##EQU6## If the encrypted information signal is designated by y(n) and the code signal for the encryption is designated by z.sub.s (n), then, for the decrypted signal at the output of the phase demodulator 59: ##EQU7## The phase modulator 57 is used to generate the pilot signal from the pilot tone supplied by the pilot-tone generator 50. If the signal values of the generated pilot tone are designated by p(n), then the signal values of the phase-modulated pilot tone result from the relationship: q(n)=p(n).multidot.z.sub.p (n) (12) In order to convert the digital analytical signal x(n) generated at a clock frequency of 2.667 kHz into an analog signal, it is first necessary to carry out a sampling rate increase to 8 kHz. The increase in the sampling rate by the factor 3 (from 2.667 kHz to 8 kHz in the illustrated example) is carried out by inserting two signal values having a "0" value in each case between the two values, corresponding to the following relationship: d.sub.s (.nu.)= . . . , x(n-1), 0, 0, x(n), 0, 0, x(n+1), (13) A further (second) complex output filter 62, preferably a (fourth) Hilbert filter, converts the analytical output signal into a real output signal. This filter is used to limit the bandwidth of the output signal (voice signal) to approximately 2.667 kHz. The second complex output filter 62 is again a recursive filter whose structure corresponds to that of the first complex output filter 35 at the transmitting end and is illustrated in FIG. 9. The input to the second complex output filter 62 (fourth Hilbert filter) is again an analytical signal, the output signal a real signal. In the tested exemplary embodiment of the invention, the filter is based upon an elliptical low-pass filter. The low-pass filter is converted into a Hilbert band-pass filter by transformation in the frequency domain. The analog front end 52 at the output side converts the digital output signal into an analog output signal (audio signal) and also includes level matching. The D/A converter section (not shown in detail) of the analog front end 52 (output) consists of a D/A converter, an analog smoothing filter, a programmable amplifier and a differential amplifier. The following specifications apply to the output of the analog front end 52:
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Clock frequency: 8 kHz
Word length: 16 Bit
Gain: Adjustable in the range
from -15 dB to +6 dB
Interpolation filter
Frequency response:
0 to 3.7 kHz
Ripple: .+-.0.2 dB
Reverse attenuation:
65 dB
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The essence of the invention is in no way limited to the described embodiment of an SE module. Extensions of the invention, primarily directed to the security of encryption, will be appreciated by those skilled in the art. For example, while, in the described exemplary embodiment, only a simple (pseudo-) random-number generator is employed for generating the code signals, separate, different generators might be utilized to further improve encryption security. Further, while, in the described exemplary embodiment, it has been assumed that the random-number generator 54 is initiated at the same starting point on every resynchronization, security of encryption may be increased by changing the starting point on every resynchronization. This may be achieved by transmitting the starting point of the random-number generator 54 in the preamble. Other variations of the invention will, of course, be apparent to those skilled in the art. While the invention is defined by the following set of patent claims, all such variations are contemplated within the scope of such claims and their equivalents. BIBLIOGRAPHY 1! Analog Devices: ADSP-2100 Family User's manual. Prentice Hall, 1933. 2! Analog Devices: ADSP-21msp50/55/56 Datasheet, Mixed-Signal-Processor. 3! Analog Devices: AD28msp02 Datasheet, Voiceband Signal Port. 4! U.S. Pat. No. 5,267,264 issued in the name of inventors Erhard Schlenker and Gunter Spahlinger for "Synchronization and Matching Method For a Binary Baseband Transmission System" on Nov. 30, 1993. 5! E. Schlenker: A Method For Determining the Signal-Matched Receiving Filter and the Initial Synchronization of a Digital Receiver. Ein Verfahren zur Bestimmung des signalangepa.beta.ten Empfangsfilters und der Anfangssynchronisation eines digitalen Empfangers!. Dissertation, Stuttgart University, Network and System Theory Institute, Institut fur Netzwerk- und Systemtheorie! 1993. 6! D. E. Knuth: The Art of Computer Programming: Volume 2/Seminumerical Algorithms, Second Edition, Reading, MA: Addison-Wesley Publishing Company, 1969.
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