GB2082425A - Equipment for single side band multiplexing through digital processing - Google Patents

Abstract

Equipment for SSB multiplexing and demultiplexing base-band signals uses the techniques of digital signal processing. It is characterized in that the frequency modulation process of the base-band signals 1 is partly performed with a discrete Fourier Transform (D.F.T.) 4 and partly with modulators (multipliers) 6, some of which are of simple construction and whose number is lower than the number of signals to be multiplexed. The filtering operation is made through filters 8, 11, 14, 16 which derive their filtering function from a set of filters with different frequency repetition period and that, when cascade connected, produce a pass- band filter equal to the frequency band which characterizes every base-band signal. The frequency repetition period of the whole filter is equal to the sampling frequency of the multiplexed signal. <IMAGE>

Description

SPECIFICATION Equipment for single side band multiplexing through digital processing Background of the Invention The present invention concerns an equipment which allows, through digital processing, the SSB multiplexing and demultiplexing of a given number of baseband signals characterised by a frequency spectrum ranging from 0 to 4 kHz. Said base-band signals can be available as analog signals, which via a preprocessing network are sampled at 8 kHz frequency and processed in numerical way, or they can be already coded in numerical form and time multiplexed on one or more transmission paths, i.e. 24 or 30 per path, more generally known as a 24 or 30 channel PCM stream. After an eventual pre-processing, the above mentioned base-band signals can be SSB multiplexed through digital processing.The latter operation supplies a signal which by means of a digital to analog conversion and by means of subsequent modulations and filterings can be allocated in that frequency range most suitable for traiismission on frequency division systems (FDM systems).

Description of the Prior Art Systems which perform the above mentioned digital SSB modulation are already known; for example refer to the IEEE magazine "Transaction on Communications" of May, 1978 and to U.S.A. Patents No. 4,131,766 and 4,013,842. Among the already known methods the most apparent is that one whereby N signals are frequency multiplexed with a discrete Fourier Transform (DFT), the dimension of which is at least equal to N and which corresponds to a modulation, and the signals leaving the processor which executes the discrete Fourier transform (DFT) are filtered through N filters which can be implemented as a single variable coefficient filter; the above-mentioned filters are derived from a single filter with the frequency repetition period of its filtering function equal to the sampling frequency of the frequency multiplexed signal.

Summary of the Invention The present embodiment still utilizes a single basic filter; however, said filter is split into a cascade connection of various filters that can generally be advantageously implemented with simple multiplying coefficients. The number of different types of filters is reduced with respect to the number of signals to be frequency multiplexed.The frequency modulation process is partly carried out with a reduced number of modulators (multipliers) with respect to the number of signals to be multiplexed, and said modulators are for the most part of simple implementation, and partly via a discrete Fourier transform processor the dimension of which is reduced with respect to the number of signals to be multiplexed and which operates in an identical manner on groups of signals to be multiplexed, each group containing a number of signals equal to the number of signals to be multiplexed divided by a power of two.Said filters with different frequency repetition period of their filtering function are used, together with modulators, to build a tree structure of filters and modulators, and such a tree structure has many inputs and only one output, and is repeated twice to process the real and, respectively, imaginary samples of the signals. The tree structure of the filters and modulators is modified so as to efficiently exploit the filters arranged on the side of the structure having more input ports.One of the greatest advantages of the present embodiment, as compared with the already known methods, is comprised of the fact that the design of the digital filters is highly flexible so that it is possible to have simple multiplying coefficients in the filters themselves; moreover, both the modulations and the Discrete Fourier Transform, necessary for the system, are simplified thereby facilitating their implementation. A description of the system is included herein and subsequently the basic theories are introduced on the basis of which the equipment is implemented.

An equipment used to frequency multiplex a given number of base-band signals must also be capable of carrying out the reverse function which, known the direct functional mode of operating, can be derived according to the general reversibility principle where applicable. This principle is applied to the embodiment herein, therefore a detailed explanation will be given of that part of the equipment which, starting from the 0-4 kHz base-band signals, SSB multiplexes the above-mentioned signals. The demultiplexing procedure of the equipment will also be explained.

Description of the Drawings Figure 1 depicts the multiplexing side of the equipment along a preferred implementation form.

Figure 2 gives a schematic representation of: frequency spectrum of a base-band signal to be multiplexed (a); the same type of spectrum as in (a) but shifted by 2 kHz towards lower frequencies (b); the frequency shape of the equivalent filter that is used, together with its frequency shifted version, to separate a 4 kHz band in a 512 kHz wide frequency range for every base-band signal (c); the spectrum of the complex multiplexed signal (d); the spectrum of the real multiplexed signal (e).

Figure 3 depicts the decomposition of a filter (d) into a cascade connection of filter with decreasing frequency repetition period of their response, and some of these filters are depicted in lines (a), (b), (c).

Figure 4 explains how a modulator can be removed from a filter and the related input signal.

Figure 5 depicts a modulating and filtering part of the equipment in its more straightforward derivable form.

Figure 6 depicts the time sequence of samples transiting through some points of the structure of Fig. 5 and Fig. 1.

Figure 7 depicts a non-recursive filter used as part of the multiplexing side of the equipment, and in a form suitable to be time-shared among different signals.

Figure 8 depicts the signal samples coming out from outputs of the filter of Fig. 7, when such filter is used on the multiplexing side of the equipment along the structure of Fig. 1.

Figure 9 depicts the shift of a complex modulator from output to input of a filter, in case the modulator performs a frequency shift equal to half the frequency repetition period of the filter frequency response.

Figure 10 depicts the merging of the two non-recursive filters of Fig. 9-b together with the summing node, into a single filter with two inputs and one output.

Figure ii depicts the receiving side of the equipment, used to demultiplex a signal into its constituents base-band signals.

Figure 12 depicts a time sequence of the samples of some signals pertaining to the demultiplexing side of the equipment.

Figure 13 depicts the filtering and modulating part of demultiplexing side of the equipment, in a more straightforward derivable form.

Fig. 1 illustrates that part of the equipment which performs the frequency multiplexing, starting from the base-band signals. The equipment of this embodiment can be implemented with a number of base-band signals which are equal to a power of two, for example: 16, 32, 64 are the most frequently recurring numbers though, as usual in this type of equipment, the number of signals really used is lower i.e. 12, 24, 60 respectively.

The 64 signal system is described herein for reasons of clearness and by way of example.

Sixty, out of the 64 signals are really utilized and they correspond either to two PCM streams entering the transmission side each having 30 channels, or to 60 analog voice channels to be allocated in the 312-552 kHz band according to the FDM systems procedure. Sixtyfour of said signals appear on input 1 of Fig. 1, either on two paths if it concerns PCM signal streams already sampled, coded and time multiplexed, or on 64 paths (60 effective) should it concern 0-4 kHz band allocated analog signals.

Each incoming path will, if analog, be sampled at 8 kHz in block 2 of Fig. 1 hence with a spectrum which, as per the PCM signals, will be frequency-recurrent as indicated in Fig. 2a) in compliance with the usual representation procedure.

Furthermore block 2 transforms the signals according to the already known procedures in order to suit them to the next processing step; at the output they will appear as linear coded digital signals the spectrum of which recurs with an 8 kHz period but shifted by 2 kHz towards the low frequencies (Fig. 2b).

By this operation it is to be understood that the samples of each signal are alternatively to be regarded as real and imaginary. Each path can now be characterised by the individual spectrum within the - 2 kHz and + 2 kHz limits around a frequency multiple of 4kHz. The equipment makes, through digital filtering, a selection of one of the above-mentioned bands for every channel, at a frequency multiple of 8 kHz, that is different for each channelsee Fig. 2d). The signals numbered from 32 to 63 have an inverted spectrum with respect to the position at equal frequency in the periodic recurrence of the base-band signal spectrum as it can be deduced from the comparison with signal 32 operating at 256 kHz of Fig. 2b with respect to the position at a similar frequency of a generic signal shown in Fig. 2b).

Signals 32 to 63 necessitate a spectrum reversal which is obtained by modulating with a 4 kHz the base-band signal and this is achieved by changing the sign of one out of two samples.

The signals leave output 3 of block 2 as per the herein-above-described configuration, preferably as time-multiplexed signals. By ck it is meant (k variable from 0 to 63) a generic set of 64 adjacent samples of the above-mentioned time multiplexed signal; a particular value of index k assigns the sample characterised by it to the signal which will occupy a corresponding position (see Fig. 2d) in the frequency-multipíexed signal.

Values c, are on the whole arranged in sets of eight adjacent samples each, and are arranged in each set so as to subsequently correspond to signals of spectral position 64 kHz apart; the first sample of each set corresponds to signals having an 0,4,2,6,1,5,3,7 spectral position.

According to the present invention, the discrete Fourier transform (DFT) is performed in block 4 on each of the sets of eight adjacent samples in Ck, being the DFT of dimension eight, i.e. the powers of the complex number exp (j27r/8) = (1 + j)/2 are used in it as multiplying coefficients. In this phase the incoming samples can be always regarded as real. Sequences of eight samples are available at the output of block 4; some of the cited samples are real and others complex, but from this point onwards they can be all regarded as complex and the next block 5 will arrange the outgoing samples in a serial form, if not already so arranged, at the output block 4 which operates the DFT. Hence, the samples will appear at the input of block 6 in a time serial form.A generic set of 64 adjacent complex samples, which are in correspondence with the previous ck samples, can be denoted with dk, where "ko" and "i" assume a value from 0 to 7, and "k," characterises the set of eight adjacent samples on which DFT has been performed and "i" characterizes the eight transformed samples in each set, arranged as per the rule usually applied when writing the expression relative to an eight data DFT.

Block 6 contains a multiplier which multiplies the incoming samples by exp (jkoi27r/64): indices "ko" and "i" have been defined above. The multiplying constants used by multiplier 6 are supplied by block 7 usually comprised of a read-only memory (ROM).

The complex samples leaving multiplier 6 are split into real (Re) and imaginary parts (Im) and these are separately forwarded into two identical sets of filters and modulators, and only one of these sets is, for reasons of simplicity, depicted in Fig. 1, and which is inclusive of blocks 8 through 17, and is regarded as that which operates on the real part of the signals.

Upon separating the real part from the imaginary one at the output of multiplier 6, bear in mind that the samples, entering block 4 and related to the single base-band signal are alternately real and imaginary, hence it will be necessary to exchange, at the output of multiplier 6, the real and imaginary parts every one out of the two blocks of 64 complex samples and alternating the sign of the imaginary part leaving multiplier 6.

By sko.i is meant the real part of the samples leaving multiplier 6 and in a one-to-one relation with samples dko.i and entering the cascade of filters and modulators belonging to the real section, where "ko" and "i" have the same meaning of the aforementioned designations. The Sko.i, time samples are simultaneously forwarded on two paths; on the first they find the multiplier Mo, and on the other the delay elements R1 and R2 and each one of them time shifts the samples by 8 times the distance between two consecutive Sko.i samples, in this case shift 7 corresponds to the period of the frequency 512 kHz with which the serially arranged samples are routed throughout the equipment. At the output of delay R1, the samples are sent to multiplier M, and at the same time to delay R2 at the output of which they find the multiplier M2.

The samples sk , which flow into the three multipliers Mo, M1, M2, are multiplied by the latter by a series of eight coefficients (some of which could be zero) which are cyclically repeated in synchronism with indix "i" appearing as pedix to samples 5k,,i' each multiplier being supplied with a different set of coefficients. Multiplier M2 assumes opposite signs for sequences having k0 = 0,1,2,3 and k0 = 4,5,6,7.The three sample sequences leaving filter 8 enter multiplexer 9 that connects inputs A, B, C, to outputs E, with an O to 7 variable "r" index, in such a way that the 8 adjacent samples Sko.i (now modified by multipliers Mo, M1, M2) are connected to input Er in such a way that r is equal to index "ko" in 5,,i it must be taken into account that a sequence of eight adjacent samples sk (i = 0 . . 7), marked by a given value of "ko" appears in B delayed by 8T with respect to A, and in C by 16T with respect to A.If To is a time interval equal to 87, then in eight consecutive To time intervals, arranged so that each can contain eight Sko.i samples with an O to 7 variable "i' 's, the connection between inputs A, B, C and outputs E, is made as per the table hereunder:: TABLE 1 To Sequence A B C O Eo E7 E3 1 E4 E0 E, 2 E2 E4 Eo 3 Ee E2 E4 4 E, E6 E2 5 E5 E, E6 6 E3 E5 E1 7 E7 E3 E5 The eight outputs of multiplexer 9 are sent in pairs to four identical devices 10 which sum and difference the incoming signals, specifically, added S, sums the signal leaving E0 to the one leaving E4, similarly for the other outputs, while added S2 subtracts the signal leaving E4 from the one leaving E,. similarly for the other three pairs of signals. The four pairs of new signals are sent to each one of the four identical non-recursive filters implemented along the first canonical form.Said filters have a frequency period of 64 kHz but operate at a 512 kHz rate, and should each one be expressed as

where z = exp (j2rw/w0), being w the frequency and w0 corresponding to 51 2 kHz, then the sum signal leaving blocks 10 is for example, forwarded to the h, multiplier coefficients with even order r, and the difference signal to the h, multiplier coefficients with odd order r.As seen in Fig. 1 two of the filters 11 are connected to a modulator 1 2, the multiplying coefficients of which cyclically assumes values 1, j, - 1, - j, but said coefficients change value at a 64 kHz rate, therefore, the signal samples which transit in those modulators are multiplied in sets of eight adjacent samples with the same value. Since the multiplying coefficients of said modulators also assume imaginary values, the output must also be forwarded to the block of filters and modulators which processes the imaginary samples. Similarly, the corresponding multiplier on the block which processes the signal's imaginary parts or samples, when the multiplying coefficients assume an imaginary value must also send its output signal to the block which processes the real parts or samples.

The two following blocks 1 3 operate on the pair of incoming signals with the same modality of blocks 10, similarly for the identical filters 14 and 22 which operate in the same manner as filters 11, the only difference being that the filters contained in blocks 14 and 22 have a frequency repetition period of their filtering function equal to 32 Khz.

The output of filtering block 22 is connected to modulator 21, the multiplying coefficient of which assumes the consecutive powers of the number (1 + j)/ < 2 and, as per modulators 12, it maintains a constant multiplying coefficient for eight consecutive signal samples and it varies its coefficient values at a rate of 64 Khz. Block 1 5 operates like blocks 10 and 1 3 and its two output signals enter filter 1 6 which is eventually of the non-recursive type, and has frequency repetition period of its filtering function equal to 1 6 Khz. The output port of filter 1 6 is connected to filter 1 7 implemented in a recursive form owing to its steep transition between the pass-band and the stop-band.The frequency repetition period of said filter is equal to 8 Khz. As already stated, the cascade of elements from block 8 to block 1 7 is duplicated to permit the real and imaginary parts of the signals to be processed.

The real (Re) and imaginary (Im) signals leaving filter 1 7 relative to the real part and the related filter relative to the imaginary one both enter modulator 18 as a complex signal. Said complex signal has a periodic spectrum with a 512 kHz period as indicated in Fig. 2d) for frequencies within 0 and 512 kHz.Modulator 1 8 causes a 2 kHz frequency shift towards the higher frequencies, which is obtained by multiplying the adjacent samples of the complex signals by the consecutive powers of the exp(j2sr/4N) number, said consecutive powers being supplied by the ROM memory 1 9 to multiplier 1 8. Only the real section of the signal is kept at the output of said multiplier 18, the spectrum of which assumes a configuration which is symmetric with respect to the 256 Khz frequency. Said signal is the final frequency multiplexed signal in a sampled form.

Block 20, the operating procedures of which are already known, processes said signal in an analog form so that the 8 Khz to 248 Khz signal spectrum, corresponding to a 60 channel multiplexed signal, is traslated, after digital to analog conversion, filtering and modulation, into the 312 kHz-552 kHz band.

Even if the principles stated herein are not binding, a theoretical description is given of the embodiment in compliance with the designations adopted by the literature available on this subject. Fig. 2c) schematically illustrates the amplitude response versus frequency of a digital filter H(z), where z = exp(j2mnr/w,) and w0 is the sampling rate of the frequency multiplexed digital signal, the aforestated filter having a bass-band within - 2 Khz and + 2 Khz around the frequencies that are multiples of w", that correspond to 512 KHz in case of 64 channels, and said filter properly attenuates all other frequencies. Filter H(z) is preferably designed as a recursive filter, and if numerator and denominator are of identical degree, equal to I, it can be expressed as:

Each denominator factor of the previous expression has a 1 - x form, and since N is equal to a power of 2, i.e., N = 2', the following relation is valid 1 (1 +x) (1 +x2) (1 +x4). . z z (1 + xn/2) (1) 1 -x 1 x By applying the above equation (1) to each denominator factor of the H(z) expression, we can factorise H(z) as follows: H(z) = Ko(z)K,(z2)K2(z4). .. K(zN) (2) In Equation (2) the H(z) filter is decomposed in a cascade of filters, the first of which, K,(z), has a frequency period equal to wO, and the second equal to wo/2 and so on, the last K,(zN) (with L = log2N) has a frequency repetition period equal to Wo/N = Q which is the sampling frequency of the base band signals, in this case 8 Khz.

The aforementioned filters, except for K,(zN) are of the non-recursive type, while K,(zN) is purely recursive, i.e. the numerator is a constant. The decomposition (2) permits a thorough analysis of the principle on which the embodiment is based, starting from a filter H(z) the design of which is done following known procedures; however, the explanation of the K,(Z2') filters performance allows a lot of flexibility in filter design.This explanation is given by Fig. 3, more specifically Fig. 3a) schematically depicts the attenuation of filter Ko(z) the function of which is to allow the frequencies allocated within a - 2 kHz and + 2 kHz range and around the w0 multiple frequencies to transit, and to appreciably attenuate the frequencies allocated in the above-indicated range around the odd order multiples of the wo/2 frequency. Similarly, K,(z2) the transfer function of which is schematically depicted in Fig. 3b), allows the transmission of the 4 kHz bands around even multiples of the 128 kHz frequency, while it attenuates similar frequency bands around the odd multiples of 128 kHz.

The same explanation is applicable for the other filters too, of which filter K2(z4) is schematically represented in Fig. 3c). Filter K,(zN) is purely recursive, it attenuates the 4 kHz wide frequency bands centred around the 4 kHz odd order multiplies and permits similar frequency bands centred around the 4 kHz even multiples to transit.

The pass-bands of the filters obtained from decomposition (2) can have large amplitude variations with respect to frequency, nonetheless their cascade connection supplies the total filter H(z) depicted at Fig. 3d). The explanation given for filters Kr(z2') permits to design them without having to recur to the exact decomposition (2), hence each filter can be designed according to the specific attenuation requisites mentioned above. Moreover, each filter can be of the non-recursive or recursive type, including filter K,(zN).

An advantage of this invention is that there are procedures and possibilities to design nonrecursive and recursive filters in compliance with the expected attenuation requisites and the multiplying coefficients thereof can be very simple and particularly convenient to implement, especially when adopting serial arithmetic (as to this, refer to the article by D.J. Good man-M.J. Carey on Nine Digital Filters for Decimation and Interpolation", IEEE Transaction on Acoustic Speech and Signal Processing, April 1977 page 121, and the article by W.

Wegener on "Design of Wave Digital Filters with Very Short Coefficient Word Lengths" Proceedings of International Symposium on Circuit and Systems, 1976 page 473). For reasons of clarity the case of 64 signals is taken as a reference, where N = 64 = 26, and H(z) is obtained as a product of 7 filters from: H(z) = Ko(z) K, (z2) K2(z4)K3(z8) K4(z' 6) K5(Z32) K6(z64) (3) A certain number of filters of the set of seven filters on the right side of (3) and starting from the left, in this case three non-recursive filters, are decomposed according to the following expression:

This decomposition is straightforward since the aforementioned filters are non-recursive, hence their expression is a polynomial in the variables, respectively, z-1, z-2, z-4.

According to a general principle, the frequency multiplexing of N signals as per the configuration of Fig. 2d) can be accomplished by filtering each of the base-band signals (the spectrum of which is denoted by Xk (zN), being index k bound to the desired channel frequency location as per fig. 2d)), with the H(z) filter (u= 8 kHz) KS2 shifted on the frequencies axis; the analytic expression of said frequency shifted filter, called Hk (z) can be obtained from H(z) where the variable z is substituted by zexp( - j2" k/N); the exp(j2sz/N) complex number shall be called WN.Let us suppose that the complex signal relative to the base-band signal is called XK(ZN) and that it will have a final location around the k# frequency and that it has already a properly oriented spectrum; the complex signal of Fig. 2d) can then be expressed as:

Due to expression (3) and (4) and by the fact that WNN = 1, the result is that

Expression (5) of filter K6 (z64) can be moved outside the summation hence arranged, let us say, at the output of the structure which carries out the operation indicated by expression (5).

If by Y(z) is indicated the signal at the input of filter K8(z84)... expression (5) is also applied to it but with factor K6(z64) excluded. Before proceeding, index k is broken-down into two variables, that is k=ko+8 k, thereby dividing the 64 signals into eight sets of eight signals, each set being characterized by one of the values within 0 to 7 which k0 can assume, in accordance with the comment made to Fig. 1; index k, also assumes the values from 0 to 7 and characterizes a signal available inside each of the aforesaid set of signals in an ascending order with frequency.

Note that since WN64=1 then WN-8kr = WN-8(ko + 8k@)r = WN-8kor moreover, in expression (5) the summation on index k can be split into two summations on the indices k0 and k1. The expression of Y(z) at the input of filter K6(z64) can be written as:

with

The summation with respect to index k, at the far right of expression (7) shows a DFT on the samples of the set of eight signals, such set having a constant k0 index; the transform is of dimension eight wherein WNki (N = 64) can be substituted by W8Xl, W8 being the eighth root of unity given by W8 = exp (j27r/8).

Hence:

Signals Y,(z8) have argument z8 which denotes that the samples of the aforestated signals flow at a 64 kHz rate, since signals Pk (z64 at a rate of 8 kHz also transit along filters H,(Z8 which interpolate the incoming signal on the time axis thereby supplying at the output a sample every 8T time interval (being 7 the period which corresponds to the 51 2 kHz frequency).

By using expression (8), expression (7) of Qi (z8) is split into two summations, one for the even values of index k0 and one for the odd values and the cited even and odd indices can be expressed as 2 k0 and 2 k0 + 1, where k0 will now become 0,1,2,3, Therefore:

The two summations have different filter sets which however can become identical by applying to the second summation of expression (9) the equivalence between structures "a" and "b" of Fig. 4, within which modulator 23 multiplies the subsequent signal samples at a rate of 512 kHz by the subsequent powers of WN, Fig. 5 shows inside block 28 the structure comprised of filters and modulators to be obtained; modulator 24 shown in Fig. 5 is similar to modulator 23 of Fig. 4 except for the signal flow which in Fig. 5 is at a rate of 64 kHz, hence modulator 24 will encounter non-zero samples only at 8T intervals hence the time adjacent samples are multiplied by the powers of W8. The introduction of modulator 24 of Fig. 5 enables to remove filtering block 25 on the path followed by the signals which correspond to the two summations of expression (9) and which carries out the filtering function given by K5(z32).

Going on, index k0 which appears in (9) is split again in even and odd values, whilst modulator 23 of Fig. 4 multiplies the adjacent samples by the powers of W2n which for Fig. 5 with signals at a 64 kHz rate entails, for the modulators, multiplying the adjacent transiting samples by the consecutive powers of W4 = exp(j2sr/4).

A further subdivision on index k0 completes the structure of block 28 depicted in Fig. 5 at the inputs of which arrive signals Pk with constant "i" and owing to the 8 values assumed by index k0 of the signals (8).

Block 28 should be repeated eight times in correspondence to the eight "i" values having to introduce at the output of each block an element which shall supply a delay of i7, hence proceeding to sum the outputs of the aforestated delays in order to obtain signal Y(z) in compliance with expression (6). Each of the aforementioned blocks must be then repeated twice for each value of index "i" in order to filter the real and the imaginary component of the signals.

The cited block can be reduced to two, one for the real part and the other for the imaginary part of signals Pk , if the signals are time multiplexed.

Fig. 6a) shows the samples with a time T interval which corresponds to an 8 kHz period of any one Pk i signals for any fixed value of k0 and i; Fig. 6b) shows the samples leaving block 28 of Fig. 5 at a rate of 64 kHz owing to the zero value of index i; Fig. 6c) shows the samples leaving the same structure relative to a generic value of index i different than zero and at the output of said structure is inserted an element with an i7 delay.

Should the i7 delay element be shifted at the input of every input 27 (Fig. 5) each one of said inputs shall, owing to the eight structures corresponding to the eight values of index "i" receive the samples sequentially in time with a 7 delay as indicated in Fig. 6d) for a generic value of index ko.

The samples of signals Pk @ arranged in a time sequence as per index i, can transit in only one structure, i.e., block 28 of fig. 5 which shall now operate at a rate of 512 kHz and within which filter 29 H;(Z8) must change its multiplying coefficients at a 512 kHz rate. Obviously, since signals Pk are complex, two similar structures must be provided, i.e., one for the real samples of the signal and one for the imaginary samples. Signal Y(z) is now available at the output of block 28 and will transit through filter 17 which will once again be split into two identical filters, i.e., one for the real part and the other for the imaginary one.

A further simplification is obtained if the samples belonging to signals Pk, (for a fixed k0 and changing from 0 to 7 said samples being illustrated at Fig. 6.d) are delayed by a multiple of 8T for a given value of index ko, i.e., they enter inputs 27, of block 28 shown at Fig. 5, with the following order of ko.; 0,4,2,4,1,6,3,7. Specifically, in order that a sample for every signal #ko.i (i = 0,...7) enters the pertaining ko input 27, a time period T, equal to the 8 kHz frequency period, is needed.This will mean that the samples of signals Xk(z 4) can be sent in a serial manner to input 3 of Fig. 5; processor 4 performs a DFT on 8 consecutive samples block with an 8T period, and the outputs of processor 4 are serially arranged, then the samples transit through multiplier 6; consequently, multiplexer 30 will allot the samples of signals Pk,,i' with a constant value of ko, in a time sequence tothe proper input of the filters and modulators block 28.

Filter 17 is inserted at the output of the cited block, the digital modulator 31 follows, at the output of which only the real samples are considered.

Reference has been made herein to a preferred embodiment, in particular to the case wherein it is wished to frequency multiplex 64 base-band signals. However, the equipment can be implemented for a number N of signals, equal to a power of 2. Said number N is split into the product of numbers p and q, i.e., N = p.q, where p and q are still powers of 2. Should # be the sampling frequency of each base-band signal, then the frequency multiplexed signal will have an N# frequency repetition period equal to its sampling frequency. p sets of q signals are now formed, the latter having a pE2 interval upon reaching their definite frequency allocation after multiplexing.

The samples of each set of q signals are transformed via a DFT of dimension "q" and the output complex signals are multiplied by the WN I factor, where "k," ranges from 0 to p - 1, and "i" from 0 to q - 1. The samples are then sent to a filter and modulator network with p inputs, and said network is foreseen to filter and modulate the real and the imaginary components. Before inputting into said network, the real and imaginary signal components exchange their role as per the aforestated procedure and reason. The complex signal undergoes a comples S2/4 modulation at the output of the filter and modulator block in order to be properly frequency allocated.

Various types of simplifications are possible on block 28 of Fig. 5, moreover, the functions carried out by the various blocks can be of different configuration depending on the preference and on the evolution of the digital components used in the equipment implementation.

Two main simplifications are stated herein which render the invention particularly advantageous with respect to others.

The first simplification arises from the fact that the first filters of the set K,(z). K1(z2)...KL(zN) appearing in expression (2), are particularly simple, i.e., of low degree; specifically when breaking-down expression (4), filters Hj(z8) have few terms, and this will mean that the set of Hj(z8) filters of block 29 in Fig. 5 can be implemented as a single filter with coefficients changing at a rate of 512 kHz. If this new single filter receives, at the beginning of the time T interval, a sequence of eight samples relative to signals Pk,,i with "ko" constant and "i" variable from 0 to 7, it will empty its delay elements content before the incoming of the next set of samples pertaining to the same ko value.

For example, with 64 signals a possible set of filters is: Ko(z) = (1 + z-1)2 K1(z2)=(1 + Z-2)3 (10) K2(Z4) = (1 + Z-4)3 and the product of the three previous filters supplies a filter

where the values of coefficients h, are as per the following Table II: TABLE II ho = 1 hs 22 h16 =9 h,= 2 hg =24 h,7=6 h2 = 4 h10 = 24 h16 =4 h3= 6 h11 = 24 h,g=2 h4 = 9 h,2= 22 h20 = 1 h5 = 12 h13 = 20 h6=16 h,4= 16 h7 = 20 h15 = 12 The above table gives in each row, from top to bottom, the coefficients of filters H,(z8) with "i" variable from 0 to 7. Data scaling is not set forth in this description since it belongs to the normal practice in designing digital filters.

Each of the filters 29 in Fig. 5 can be implemented according to the diagram of Fig. 7. Let us assume that said filter is the one inserted in put 27 and which in Fig. 5 has been attributed with value "0" of index k,; then it receives at its input 37 a sequence of samples as indicated by Fig.

6d); every sequence of eight samples is orderly multiplied via multiplier 34, by the values of the first column at the left of table II and read from top to bottom.

The same samples available at input of multiplier 34 will be available at input of multiplier 35 after an 8T delay produced by delay element 32 and multiplied by multiplier 35 by the values of the second column of table II.

Similarly said samples shall appear at the input of multiplier 36 with a 16T delay as compared to input 37, this owing to the presence of delay elements 32 and 33 and multiplied by multiplier 36 with the coefficients of the last column on the right of table II, where the missing coefficients are to be considered zero. The samples outputting from paths 38, 39, 40 shall be joined on one single path, thereby supplying a 21-pulse sequence as shown in Fig. 8, line a), and forwarded to the next filtering block. t.ll the filtering blocks 29 arranged in a column (Fig.

5) are indentical; moreover, they operate in a similar manner on the eight incoming sample blocks and the outgoing sequences are shown on Fig. 8 from lines 'a' to 'h' Only one filtering block 27 of Fig. 5 instead of eight can now be used, and shall be implemented as per Fig. 7, since all the elements of Fig. 7 are used on each set of eight samples (see Fig. 6d) for a T/8 time only. In fact as the samples of signals Pk , flow in a time sequence with T/8 interval among groups of samples marked with different index ko value, they can all be sent to input 37 as long as outputs 38, 39, 40 are properly connected to inputs Ej of the following eight filtering blocks 41 of Fig. 5.By dividing the time interval T, which occurs between two incoming samples of the same pko.i, into eight To intervals numbered as per Fig. 8, this same Fig. 8 also gives the connections to be made between outputs 38, 39, 40 and inputs Ei. The connections have already been cited in table I where outputs 38, 39, 40 of Fig. 7 have been represented by letters A, B, C respectively. The filtering so performed corresponds to the cascade connection of the three filters definad by expression (10).This type of filtering causes a loss of iess than 0.05 dB at the + 2 kHz and - 2 kHz pass-band limits and an attenuation greater than 75 dB on the same frequency range located around th9 256 kHz frequency (where crosstalk is unintelligible) and greater than 85 dB abound the other frequencies which are integer multiples of 64 kHz.

The advantage of the embodiment lies in the fect that the simlifications set forth can be applied to a wide range cf cf 0 value's, nu;iber of paths to multiplex. To further elucidate: should N = 16 it will be possible, for example, to distribute the sixteen signals into four sets of four signals each, thereby performing a DFT on each of the aforestated sets.Since L = 1092 16 = 4, filter H(z) shall be factored as follows: H(z) = Ko(z) K1(z2)K2(z4) K3(z3) K@(z10) Where variable z is now exp(jw##/w1) @@@@sin w1 equal to 128 kH2, in this case it can be convenient to choose, by way of example Ko(z) = (1 + z-1)3 (11) K,(z)= - 1 + 9z-4 + 16 z-6 + 9 z-8-z-12 and the product of the aforecited filters yields a filter

the hr coefficients of which can be arranged as per Table Ill.

TABLE Ill ho = -1 h4 = 9 h8 = 57 h12 = -1 h1 = -3 h5 = 27 h9 = 43 h12 = -3 h2 = -3 h6 = 43 h10 = 27 h14 = -3 h3 = -1 h7 = 57 h11 = 9 h15 = -1 The above Table 111, read line by line from top to bottom, gives on each line the coefficients of filters H,(z4) wherein i = 0,1,2,3 for a decomposition similar to decomposition (4). The filter whose function is analogous to that ot the filter shown in Fig. 7 has three 4T1 delay elements where T1 is equal to the period of the 128 kHz frequency, and four multiplying elements the multiplying coefficients of which cyclically assume the values indicated in Table Ill and read along columns.

The loss at the edge of the pass-band ;.' the two filters' product (11) is now less than 0.04 dB and the attenuation in the 4 kHz frequency ranges centred around the 32, 64, 96 kHz frequency is greater than 78 dB.

A further simplification can be introduced in block 28 of Fig. 5 on the non-recursive set of filters the output signals of which are summed after one of them has passed through a modulator. Configurations similar to those illustrated in Fig. 9a) are depicted in block 28 of Fig.

5; in Fig. 9a) filters 44 and 45, which are alike, filter signals Xa(z8) e Xb(z8) connected to inputs 48 and 49, and the signal at the output filter 45 encounters multiplier 47 which frequency translates the signal spectrum by a quantity equal to half the frequency repetition period of the attenuation function of filter 45.

The structure of Fig. 9b) is equivalent to that of Fig. 9a) and now multiplier 47 has been shifted at the input of the filtering structure 45 which has become filtering structure 46 and which differs from the previous one in that its filtering function has been frequency shifted by half its repetition period; this is shown by changing the sign of argument z8r of the function itself.

Filters 44 and 46 of Fig. 9b, assumed to be of the non-recursive type, can now merge into one filtering function implemented according to the first canonical form as per Fig. 10, concerning a linear phase fourth-degree filter. The sum of signals Xa(z8) and X'b(z8) at the input ports of filters 44 and 46 of Fig. 9b) is sent to the input of the multipliers with even order coefficients 52 and 53, as illustrated in Fig. 10, and the difference is sent to the input of the multipliers with odd order coefficients; in the case of Fig. 10 only multiplier 54.

The transformation illustrated by Figs. 9 and 10 is applied in block 28 of Fig. 5 to all of the set of filters 41, 43 and 25, where output signals are summed after one of them has passed through modulators 42, 26 and 24. Specifically, modulators 42, the function of which is to multiply the subsequent samples of the signals transiting in them alternatively by + 1 and - 1, are also placed at the input of filters H,(z8) encountered on route. This produces two effects.The first is that since the function of multiplier 42 is to alternate the sign of the samples inherent to a Pk i signal, with k0 and i being constant and which are 8T apart, when said multiplier is placed at the input of filter Hi(Z8), the function of which is also that of an interpolator, the signal samples are at a T distance, hence they do not undergo any sign alternation, since said samples are in a time position to which the same sign always pertains. Said modulator 42, is now no longer necessary, therefore it is removed.The second effect is that the passage of modulator 42 at the input of filter H-(z8) fitted along its route, will cause said filter to change the argument sign as per Fig. 9; this means that multiplier 35 of Fig. 7 must change the sign of its multiplying coefficients when the samples of signals Pk i marked by the values of index k0 equal to 4,5,6,7, transit through it. Fig. 7 shows the structure assumed by the function of filters 29 of Fig. 5.

What has been mentioned so far clarifies the operating mode and the structure of that part of equipment illustrated in Fig. 1 the purpose of which is to SSB frequency multiplex 64 baseband signals. The normal technical know-how, the implementation of the equipment with a number of signals other than 64, as well as the technology and complexity of digital components available enable one to modify the equipment without altering the basic operating principles. For example, the duplication of the blocks of Fig. 1 from 8 through 1 7 is needed to filter and modulate the real and imaginary components of the signal and can be avoided when the speed of the digital components used is sufficient.In such a case all or a part of the abovecited blocks can process both the real samples and the imaginary ones which are serially arranged with time and are alternated, thereby doubling the operating rate of the blocks.

Obviously, the real and imaginary samples in modulators 1 2 and 22 of Fig. 1 provided with complex multiplying coefficients are synchronized again so that they can interact, hence they are arranged in an alternate time sequence. Moreover, the equipment used to process N signals, if allowed by equipment operating speed, can multiplex more than one set of N signals where the pertaining time samples will be serially time arranged.

Furthermore, with reference to Fig. 1, some of the filters considered therein as non-recursive can be implemented in a recursive form. For example block 1 6 of Fig. 1 has a filtering function with a 1 6 kHz frequency period. In order to have a simpler filter and to compensate for the losses on the pass-bands of the preceeding filters, said filter can be implemented as a recursive one; in this case the compactness of Fig. 10 is not possible, hence it will be necessary to use two separate filters for the real part of the signal and likewise for the imaginary part.

The following describes the demultiplexer i.e., that part which receives at its input the signal pertaining to several SSB frequency multiplexed signals, and which provides to split the signal thereby converting it into the base-band signals.

This part of the equipment is illustrated in Fig. 11.

If still considering the demultiplexing of 64 signals (60 real ones), the multiple signal shall be allocated at input 78 e.g., in the 312-552 kHz frequency band. Block 55 converts said signal into the 8-248 kHz frequency band according to standard norms via the modulating and filtering procedures; said signal is, therefore, sampled at a 512 kHz rate, it is digitally encoded and interpreted as a periodic frequency spectrum signal comprised of 64 4 kHz band signals 3llocltetll d an the 0 to 256 kHz band, and with the aforecited spectrum symmetrical with respect to odd multiples of the 256 kHz frequency.Said signal, at output of block 55 and at a sample rate of 51 2 kHz, enters the following multiplier 56 where it is 2 kHz frequency shifted towards the low frequencies via the multiplying of its subsequent real samples with subsequent powers of the complex exp(j27r/256) number; said values are yielded by the ROM 57 to multiplier 56.

The signals at the output of multiplier 56 are now complex and the subsequent parts of the equipment have to be split-up in order to separately process the real components (Re) parts and the imaginary components parts (Im) at a rate of 512 kHz, except where the aforementioned real and imaginary parts interact. Just as for the transmit section, the route followed by the real signal samples, which goes from block 58 (included) to block 83 (excluded) of Fig. 11, is described, because the imaginary samples are similarly processed.

The real part of the signal leaving multiplier 56 is sent to filter 58, the filtering function of which is similar to filter 1 7 of Fig. 1. The signal leaving filter 58 enters filter 59, where the signal is filtered and subsequently distributed on two outputs. Filter 59 is of the non-recursive type and is implemented according to the second canonical form; should

be the expression of its filtering function the signal at output 79 will only pass through even order multipliers, while that at output 80 passes through odd order multipliers. Block 60, which follows, makes a sum and difference between the cited signals, the difference being sent towards multiplier 63.Since the signal samples are at a rate of 512 kHz, the multiplier 63 shall multiply subsequent sets of eight samples each, by the subsequent power of the complex number W8 = (1 + j)/ < , each of the cited powers being cyclically repeated at an 8 kHz rate.

As already described for the transmission part, assuming the powers of W8 imaginary and complex values, an interaction occurs between the section which processes the real part and that which processes the imaginary part.

The signals reaching the two filters 61 are processed in the manner already described for blocks 59, 60 and 63 until arriving at the input of multiplexer 67 where the signal is split on eight different paths. Said multiplexer 67 connects inputs Ei to outputs A, B, C as per modality adopted by multiplexer 9 of Fig. 1. The signals outputting from multiplexer 67 find three multipliers 68,68.70 in the variable coefficients filter which follows; the multiplying coefficients of said multipliers take on the same values of the analogous multipliers of filter 8 shown at Fig.

1, except that said coefficients are now cycled in the reverse order; moreover, the multiplying coefficients of multiplier 69 change sign when the multiplier itself is multiplying samples coming from Eo E1, E2, E3 as compared to when it multiplies samples coming from inputs E4, E5, E6, E7.

The samples coming from multiplier 70 are forwarded to the delay element 71 with an 8T delay wherein they are added in adder 72 with samples coming from multiplier 69. The samples leaving element 72 are forwarded in a second delay element 73 with a delay equal to 8T and by means of adder 74 are added with samples coming from multiplier 68. The samples outputting from filter 81 are forwarded to multiplier 83 together with the imaginary samples from the analogous filter provided for the imaginary samples. As for the transmission section the subsequent sets of 64 real samples outputting from filter 81 are indicated as go ,. Index ko assumes values from 0 to 7 thereby distinguishing the 8 time consecutive samples which transit through the abovecited Er paths.

Furthermore, note that multipliers 68, 69, 70 must modify their eight multiplying coefficients in synchronism with the variations of index "i" which in gk,i distinguish the eight samples which have consecutively passed through each E, path. A similar procedure is applied to the 64 consecutive imaginary samples, subdivided into eight equal groups which are synchronous with the pertaining real samples groups. In subsequent blocks of N complex samples, at the input of multiplier 83, the role of real and imaginary parts is alternately changed, changing also the sign of that component which will, after the above change, assume the role of the real part.At this point, multiplier 83 multiplies the complex sample (now called ssk ) by the WNk(BI) complex number, being the above cited complex coefficient supplied to multiplier 83 by the ROM 84.

Processor 85 which follows, performs a DFT of dimension eight on complex signals ak (= ssk WN (8~j), which leave multiplier 83, processing them in groups of 8, with the foflowing ordering of k0 index: 0,4,2,6,1,5,3,7. Only the real value is considered at the output of processor 85 which performs the DFT.

The samples leaving processor 85 are parallel time arranged into groups of eight and at a 64 kHz rate; said samples are newly serially arranged by element 86. This parallel-to-series conversion is necessary if the DFT calculation is performed in such a way that the transformed data simultaneously appear at the output on eight paths. Data outputting from block 86 can be represented by k +8k, since they are serially arranged with respect to k0 as cited above, and with respect to index k, according to the correspondence between index "i" and index k, determined by the DFT operation.As already described, the k +8k real samples are arranged in 64 consecutive blocks, and in said subsequent blocks the samples of same k0 and k1 indices are the 8 kHz rate samples of the single base-band signal to which a frequency position on the multiple signal was due (re. description in the transmission section and Fig. 2d). The abovementioned samples of each single base-band signal, are to be alternately regarded as real and imaginary due to the alternating of real and imaginary parts at the input of multiplier 83. Said samples at 8 kHz rate represent a base-band complex signal with frequency spectrum arranged as per Fig. 2b, eventually shifted by 4 kHz for signals which positions were assigned from 32 to 63 in the multiplexed signals, according to Fig. 2d.Block 87 of Fig. 11 performs inverse transforms on the above-cited signals with respect to the TX block 2 of Fig. 1 thereby restituting the PCM streams or the base-band analog signals to the output.

To better explain the operating mode of the equipment section schematically shown in Fig.

11, concerned with the demultiplexing of the signal into single base-band signals, a theoretical description of the above equipment operating mode is given hereinafter.

The multiplexed complex signal at the output of multiplier 56 of Fig. 11 is denoted by Y(z) having said multiplier shifted by 2 kHz the input signal spectrum towards low frequencies, as shown in Fig. 2e). Said Y(z) signal is split into eight Y,(z8) signals where "i" varies from 1 to 8; each Y1(z8) signal contains different samples of the original signal, at a reciprocal distance of 8T, hence said signals are sampled at a rate of 64 kHz; with respect to a reference sequence of samples of Y(z), spaced by 8r and which constitute the signal Y8(z), a signal Yj(z) contains samples which are time shifted by jT, towards increasing time.Fig. 12a) schematically represents the complex samples of signal Y(z), which samples are time spaced by ; Fig. 12b) denotes the samples of a generic Y,(z) signal with i other than 8; Fig. 12c) illustrates the samples of signal Y8(z). The connection among signals Y(z) and yj(z8) is given by:

The KS2 frequency shifted version of the filter H(z), called Hk(z), is used to separate a single SSB signal to be translated into its base-band frequency allocation.

Since the multiplexed signal Y(z) has 51 2 kHz sample rate, the same sample rate is also present at the output of filter Hk(z) which selects a single signal from the frequency multiplexed signal. Since the single filtered signal has a 4 kHz frequency band, it is sufficient that said signal has an 8 kHz sample sequence instead of 51 2 kHz, hence the single signal shall have a spectrum which is periodically frequency-recurrent with an 8 kHz period as indicated in Fig. 2b).

By using expression (3) for H(z) and by applying the decomposition (4), whereby index "i" is substituted by index "r" so as to distinguish it from index "i" used in expression (2), by splitting index "k", which indicates the single path to extract, into k0 + 8k1, and finally by expressing filter Hk(z) with the same modalities used for the transmission path, then a signal Xk,+Sk, to be separated, and which is sampled at 512 kHz, can be expressed by:

A first sample decimation of signal Xk +8k (z), is made by summing the spectrum of signal itself with its frequency translations along multiples of 64 kHz, thereby arriving at the conclusion that it is sufficient to consider the two summations in (13) with indices "i" and "r" linked by relation: i+r=8 i.e., index "r" can be substituted by index 8 - i, in expression (13) thus obtaining (disregarding an inessential delay z-8):

Relationship (14) expresses the fact that each signal y,(z8) is filtered by eight different filters distinguished, besides index "i", by index k0 which assumes the eight values from 0 to 7, thereby obtaining complex cr' signals at the output of the aforesaid filters. The filtering function that filters every signal y,(z8) can be implemented in a way similar to the one used for the multiplexing side, therefore obtaining the structure of filters and modulators depicted in Fig. 13, to be meant doubled to process real and imaginary signal components of the y,(Z8) signal.The structure of Fig. 1 3 has to be intended for the moment as pertaining to a specific value of index Said Said structure operates at a rate of 64 kHz and the identical filters 96 are marked by index 8-i, therefore, filter Hr(z8) belongs to signal yj(z8), according to the following Table IV, where in each column it is possible to find the correspondence between the value of "i" and the relative value of "r".

TABLE IV

i12345678 r 76543210 In Fig. 1 3 signal Yi(Z8) goes into input 98 where it finds filter 89 which performs the K6(z64) filtering function. At the output of said filter the signal is simultaneously sent along two paths, in one of which said signal encounters modulator 90 which multiplies the subsequent samples by the subsequent powers of the W8 = (1 + j)/2 number, said values having an 8 kHz repetition period. Hence, the signals transit in two identical filters 91, at the output of which the outgoing signals are again simultaneously sent along two paths.After the signals have passed through modulators 92 and 94 and through filters 93, 95, 96, the k c'k,,i signals will appear at outputs 97. As already stated, signals Yi(Z8) are complex, therefore the structure of Fig. 1 3 must be duplicated in order to process in an identical manner the real part and the imaginary part, having in mind the interactions between the two structures for real and imaginary samples at the output of multipliers 90 and 92, there being no interaction for multiplier 94 which assumes + 1 and - 1 real values.

The structure of Fig. 1 3 can be simplified along the same criteria used for block 28 of Fig. 5.

Specifically, multipliers 90, 92, 94 are transferred at the output of the filtering structures, i.e.

91, 93, and at the output of the cascade connected filters 95 and 96, changing furthermore the argument sign of the function representing the filter contained in the aformentioned blocks.

Those pairs of non-recursive filters 91, 93 and 95 having the same input signal can be merged into one filter of the second canonical form with two separate outputs, one for the sum of signals coming from even order coefficients and the other for the sum of signals obtained from odd order coefficients of the aforestated filter. The signals of the aforecited two outputs are combined into sum and difference signals.

The structure of Fig. 1 3 is duplicated for real and imaginary samples and is envisaged to operate on the samples of a signal yj(z8) at a rate of 64 kHz; but it can process signals Y(z8) for all of the values of "i" from 1 to 8, if said signals enter input 98 already time multiplexed, i.e., with the same structure of the original Y(z) multiple signal depicted in Fig. 12c); said structure shall now operate at a rate of 512 kHz.Filters 96 shall now have the multiplying coefficients varying with time at a rate of 512 kHz and cyclically assuming versus time the values belonging to filter Hr(z8) where r is pertaining to the samples subsequently transiting with a T time interval, - and distinguished by index "i" which is related to r as per relationship given in table IV.

Complex signals o'k,,i going out at a rate of 64 kHz from the real and imaginary block of the structure of Fig. 1 3 and pertaining to a constant "i" index, can be decimated at a rate of 8 kHz by cyclically extracting, at every T time interval from each output 97, only eight time-adjacent samples.

Every sequence of T spaced samples extracted from each output 97 belong to the same value of index i and constitute an 8 kHz rate signal which is denoted by

Relationship (14) can now be expressed as:

The whole set of signals

gives a time sequence of 64 sample blocks.

The samples of every block are denoted by Xk +8 and sskolr where indices k0 and k1 assign the samples to the respective time multiplexed signals. Samples ssk, are multiplied by the WNk(8-t values, hence becoming ako j.

A subsequent DFT is performed on every set of eight samples having a time distance of T and going out from one path 97 of Fig. 1 3 and to which a fixed value of index k0 belong.

The DFT can be expressed as:

By disregarding a phase rotation applied to the base-band signal, the aforecited operation can also be expressed as:

and supplies the samples of the base-band signal at a rate of 8 kHz, distinguished by fixed values of index k0 and k1. Since the DFT operation expressed by relationship (15) generates complex Xk,+8k, values, the real or imaginary values are alternately considered for every baseband signal, which represent the signal spectrum, according to the frequency allocation shown in Fig. 2).

A subsequent 2 kHz translation towards the high frequency supplies the desired spectrum of a base-band real signal sampled at 8 kHz. Alternatively, instead of considering the real and imaginary parts of the samples of each path alternately, the real value obtained from the block output performing the DFT can be taken, thereby switching the real and imaginary part as well as the sign, when needed, of the signal supplied to outputs 97 in blocks of 8 adjacent samples.

Said operations should be performed once out of two T time intervals. Since the blocks of 8 adjacent samples to be taken from each of the 8 outputs 97, at every T time interval, can be extracted during T/8 consecutive time intervals the filtering blocks 96 can be merged into one structure. It will assume the configuration illustrated by block 81 of Fig. 11, bearing in mind that the translation of multipliers 94 towards the outputs of the structure depicted by Fig. 1 3 (where they become useless and are so suppressed) involves the transformation of function Hr(z8) of blocks 96 into Hr( - z8). It results therefrom that the odd order coefficients of the aforesaid filter become negative hence multiplier 69 of block 81 of Fig. 11 must assume negative values when it deals with blocks of 8 consecutive samples belonging to paths 97 which in Fig. 11 have been designated as 4, 5, 6, 7.

The exemplifications and the remarks made in connection with the part required to frequency multiplex the incoming base-band signals are, obviously, applicable to the part required to demultiplex the aforementioned signals.

While the invention has been particularly shown and described with reference to a preferred embodiment thereof, it will be understood by those skilled in the art that the foregoing and other changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (9)

1 An equipment which SSB multiplexes and demultiplexes a given number of base-band signals equal to the power of 2 and whose multiplexing side is comprised of a circuit section which transforms the incoming base-band signals into a sampled digital form so that the spectrum of the signals is symmetrically arranged around the zero frequency, of a processor which performs the DFT, of digital filters and modulators and also includes a circuit section which converts the sampled signal, which is a frequency multiplexing of the incoming signals, into an analog form with suitable frequency allocation; elements similar to the abovementioned are also provided at the demultiplexing side, the operating mode of which is opposite to the previous one, and the whole equipment comprises at least: A) on the multiplexing path:: A. 1) a processor that performs a Discrete Fourier Transform (DFT) on the complex samples of the base-band signals, said signals being preferably in a time multiplexed format, and the abovecited DFT operates in an identical manner on groups of signal to be frequency multiplexed, every group of signal containing a number of signal equal to the total number of signal to be frequency multiplexed divided by a power of two, and at least two of the above groups of signals are provided, A.2) a multiplier which multiplies by complex numbers the complex samples going out of the above cited DFT processor hence frequency modulating the signal spectra, A.3) a pair of synchronously operating demultiplexers provided for the real and imaginary samples of the signals outgoing from the aforementioned multiplier; moreover, they allow the aforecited real and imaginary samples to cyclically time transit towards input ports of two filtering-modulating structures respectively provided for the real and imaginary samples of the signal, A.4) two identical filters and modulator structures provided to operate on real and imaginary samples of the signals respectively; each of the abovecited structures having only one output and a number of inputs equal to the number of groups of base-band signals dealt with in the same manner by the Fourier processor, thereby receiving each of said inputs in a serial manner and cyclically in time and via one of the aforecited multiplexers the real or imaginary samples of one of the cited group of signals; said filters are derived from a set of filters with pass-band equal to the band which characterizes each base-band signal and which when cascade connected supply one filtering function with a passband symmetrically arranged around the zero frequency, and around frequencies which are multiples of the sampling frequency of the frequency multiplexed signal; the provided modulators frequency-shift the signal spectra transiting through them by an amount equal to a power of two of a basic frequency which is equal to the sampling frequency of the original input signals multiplied by the number of signals contained in each group of signals processed in a likewise manner by the aforementioned processor; said filters and modulators having a tree-structure so that subsequent pairs of signals are forwarded to identical filters whose output signals are summed together after one of them has gone through one of the above-cited modulators, therefore by subsequently reducing the signal paths to a half, one single output signal is achieved; A.5) a modulator which frequency translates the complex signal, outputting from the two above cited filters and modulators structure, by 1 /4th of the sampling frequency of the original base-band signals, and the real samples outputting from said modulator represent SSB frequency multiplexing of the original base-band signals; and B) on the demultiplexing path:: B.1) a modulator which translates the spectrum of the sampled multiplexed signal by half of the frequency band pertaining to each of the signal to be frequency demultiplexed, thereby yielding a complex signal made up of real and imaginary samples, B.2) two identical structures of filters and modulators used to operate on the real samples and on the imaginary samples of the signals, each of the aforecited structures having only one input and a number of outputs equal to the power of two and at the most equal to half of the signals to be frequency demultiplexed; said filters are derived from a set of filters the pass-band of which is equal to the band which characterizes every signal which has to be base-band demultiplexed and which when cascade connected, supply a filtering function with pass-band symmetrically arranged around the frequencies zero and multiples of the sampling frequency of the frequency multiplexed signal; said pass-band range being equal to the frequency range which characterizes each of the single signals to demultiplex; said modulators frequency translate by a power of two of a basic frequency, which is the sampling frequency of the received multiplexed signal divided by the number of outputs of each of the aforecited structure of filters and modulators; said filters and modulators are arranged in a tree structure so that the signal, after going through a single filter, is sent toward two identical filters, one of these having a modulator at its output, and every one of these two new output signals is sent to a following couple of filters, one of these again provided with an output modulator, and so on till the needed number of output signals is obtained, B.3) a set of synchronous multiplexers which extract, in a cyclic manner and sequentially from each of the outputs of the above-cited filter and modulators, a number of time adjacent samples equal to the number of signals to demultiplex, divided by the number of outputs of each of the above mentioned structures, being said sets of real and imaginary samples forwarded towards a single output of the connection network, at the output of which there is a complex signal represented by real and imaginary samples; B.4) a multiplier that multiplies by proper complex numbers the real and imaginary samples coming out of the aforementioned multiplexers, which is equivalent to a frequency modulation, B.5) a processor which performs a DFT on the complex samples leaving the abovecited multiplier and which operates in an identical manner on the complex samples corresponding to a single output of the above cited structure of filters and modulators; the samples leaving the processor characterize the single base-band signals.

2. An equipment according to claim 1, wherein said frequency multiplexing is characterized in that only one of the filtering and modulating structures, implemented to process the real and imaginary samples of the signals, is used to process both the time sequentially arranged real and imaginary samples; moreover, means are used to time align said real and imaginary samples where interaction exists between said real and imaginary samples and to then set them in a time sequence after said interaction procedures.

3. An equipment according to claim 1 or 2 wherein more than one set of base-band signals are multiplexed and demultiplexed in it and that each set contains an equal number of signals to be multiplexed and demultiplexed and that the multiplexed signals are allocated in similar frequency bands and have the same sampling frequency, and the equipment works on the above-cited set of signals according to the time multiplexing principle.

4. Equipment according to any of the above-cited claims wherein those filtering elements on multiplexing side that receive input samples different from zero only for a small portion of the time interval between subsequent samples of the base-band signals are merged into a single variable coefficient filtering element which is provided of single input and many outputs, said input receiving the real or imaginary components of the complex samples coming out of the multiplier, and now the multiplexer is inserted between said variable coefficient filter and inputs to the remaining prt of the filtering-modulating structure.

5. Equipment according to any of the above cited claims, wherein in the block of filters and modulators on the demultiplexing path those filters inserted near the outputs and giving samples to the following block only for a fraction of the base-band signals sampling period merge in a single variable coefficient filter having several inputs and a single output; the inputs are connected to the preceding sets of filter and modulator through time variable connections, and the samples at the output are directly forwarded to the multiplier which is inserted before the DFT processor.

6. Equipment according to any of the above cited claims, wherein in those couples of filters on multiplexing path which output signals are summed together, after one of said signal has undergone a modulation, the multiplier performing said modulation is translated at the input of the pertaining filter, which must now have its frequency response shifted by half its frequency repetition period; the couple of filters merge now in a single filtering structure with one output and two inputs, and these inputs receive now the sum and difference of input signals to the previously separated filter, said sum and difference being done after one of said signal has passed through the shifted modulating element.

7. Equipment according to any of the above cited claims wherein, in the demultiplexing path and in those couples of filters which receive the same signal at their inputs, and after at input of one of the filters the signal has undergone a modulation, the modulating element is shifted at the output of the pertaining filter; after this shift the pertaining filter has its filtering function with a frequency translation equal to half the frequency period of said filtering function, the two filters merge now in a single filtering structure with one input and two outputs and sum and difference is made of the output signals, the difference passing through the shifted modulator.

8. The equipment and system complying with that substantially as decribed and/or illustrated herein.

9. Any novel feature(s) or integer(s), or any operative combination(s) thereof, substantially as herein described and/or illustrated in the accompanying drawings.