The invention relates to a method for transmitting a signal over a channel, which signal consists of signal pulses a(m) appearing at sampling moments with mutual distances of T seconds.

The telecommunication technique is now in a transition period from analog signal transmission of audio and video signals to digital signal transmission; besides that the need for data trans¬ mission from, to and between computers plays an increasing role. Within said development there exists a discrepancy between on the one hand the availability of a number of analog signal transmission systems with sometimes very high channel capacity, a high quality and a large capital and intrinsic value and on the other hand the strong increasing need for digital transmission systems, also on that transmission ways where now analog systems are installed on a large scale. Although it is true that at the moment new digital trans- mission systems are developed for consisting cables, in many cases one does not obtain therewith the same channel capacity (for instance measured in the number of telephone signals which can be transmitted) as with the analog system which is replaced. Furthermore in many cases there is a need for transmission of both analog as well as digital signals over a cable. That leads however, to conflicting situations.

The object of the invention is known to encode digital as well as analog signals such that the line signal resulting from said en¬ coding makes a very efficient use of the available channel capacity of an analog transmission channel. Thereby band width and dynamics can be interchanged with each other.

In agreement with said objects the above mentioned method for transmitting a signal over a channel, which signal consists of pulses appearing at sampling moments with mutual distances of T seconds is according to the invention characterized in that a channel is selected of which the band width is smaller than the band width which can be considered as essential for the signal contents of the signal pulses to be transmitted; on the basis of the impulse response k(i) of the channel on p successive sampling moments the series of signal pulses a(m) at the transmitting side is encoded into an encoded

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series of signal pulses using the algorithm

P b(m) = [a(m) - k(i)b(m-i)] i=1 in which "cod.s" is a periodical encoding function as for instance is illustrated in fig. 3. The value a(m) should be within the period of said function. At the receiving side the signal is sampled and processed with an inverse function "decs". The inverse function of fig. 3 is equal to the function itself. Application of the invention can, because of the band width restricting effect thereof, lead to a significant decrease in the capital investment in telecommunication networks for digital signal transmission. Furthermore the decision about general introduction of digital transmission can be taken in an earlier stage. Furthermore specific features, related to the applicated algorithm, can be used for obtaining effects such as:

- cryptography

- efficient source encoding

- realising signals fitting onto a predetermined time-amplitide- frame after passing a band width limiting filter or channel.

It is remarked that the algorithm itself is already described in the literature by Tomlinson in his article "New Automatic Equaliser Employing Modulo Arithmetic" published in Electronics Letters, No. 5/6, March 1971, Vol. 7, pages 138-139 and by Hiroshi Harashi a and Hiroshi Miyakawa in the article "Matched-Transmission Technique for Channels with Intersymbol Interference" published in IEEE Trans¬ actions on Communications, Vol. COM-20, No. 4, August 1972, pages 774-780.

In said publications equalizers are described which are in fact used for compensating deviations of the transmission function of an existing transmission channel. In contrast therewith the invention points in another direction. According to the invention one does not try to equalize an existing non ideal channel as good as possible, but one intεndedly creates a channel which is in fact not suited for transferring the signal to be transmitted. According to the invention the signal is adapted to the characteristics of said channel such, that transmission is possible thereafter.

Because of the invention it is now possible to significantly restrict the channel band width which is in the now existing systems necessary for transmitting analog and digital signals. The result thereof is that in channels with a relatively large dynamic range in comparison with the dynamics of the signal in fact the capacity of the existing channel is more efficiently used by application of the invention.

The invention will be explained in more detail with reference to the attached drawings. Fig. 1 shows a general sche atical diagram of a signal trans¬ mission system.

Fig. 2 illustrates a more detailed diagram of the processor 1 in the system of Fig. 1.

Fig. 3 shows a possible encoding function "modulo s" which can be used in the system according to the invention.

Fig. 4 illustrates a more detailed diagram of a transmission system for transmitting analog signals in agreement with the invention.

Fig. 5 illustrates the adaption of an existing channel in agree- ent with the invention.

Fig. 6 illustates the spectrum shaping feature which can be realised by signal processing in agreement with the invention. Fig. 7 illustrates another decoding function. Fig. 8 illustrates a further decoding function. Fig. 9 illustrates a system in which the privacy of the signal to be transmitted is quaranteed.

Fig. 10 illustrates a time-amplitude-frame. If in Fig. 4 the parts 31, 37, 38 and 39 are deleted a system remains by means of which a signal can be generated, which signal after passage of the channel 36 or a filter 36 fits onto a predetermined time-amplitude- frame which is illustrated in Fig. 10.

Fig. 11 illustrated a transmission system in which the signal a(m), consisting of a series of signal pulses appearing at sampling moments with mutual distances of T seconds, should be transmitted over channel 2. The channel 2 has the normalized impulse response [1, k(l), k(2), ...k(p)] onto an elementary pulse from the series b, assuming the channel output is sampled every T seconds. The signal

a(m) to be tansmitted is preprocεssed before transmission over the channel 2 in a processor 1, in which the signal b(a) to be trans¬ mitted is formed out of a(m) as well as out of p preceding values of b(m) according to

⁵ P b(m) = ^a(m) - .£ k(i)b(m-l) I cod.s

This process will be explained in more detail on the basis of the encoding function "mod.s" illustrated in fig. 3. In that case it 10 is true that:

P b(m) = a(m) - £ k(i) b(m-l) J mod.s (1)

¹ i=1

As result of the modulo s processing the signal b(m) has always a 15 value between -s/2 and +s/2 and -s/s. If a(m) is also situated between those values, than (1) can be written as

P a(m) = b(m) + k(i) b(m-i) mod.s (2) i=1

20 The signal b(m) is now transmitted over channel 2. At the output of channel 2 a signal c(t) is received which, after sampling every. T seconds has the values c(m), which can be written, taking into account the predetermined channel impulse response, as: c(m) -= b(m) + k(l)b( -l) + k(2)b(m-2) + ... +k(p)b(m-p) ^■ 25 '

= b(m) + £ k(i)b(m-i) (3) i=1

In the hereby used example of the mod.s encoding function this signal is now in the decoder subjected to a further mod.s processing 30 resulting into the output signal a(m):

i(m) = c(m)| mod.s =j b( ) +j*_ k(i)b(m-i)J mod.s (4)

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Comparing (4) with (2) shows that δ(m) = a(m), which means that at 35 the output of the decoder the input signal is found back.

Fig. 2 illustrates a more detailed diagram of a possible im¬ plementation of the processor 1. The incoming signal series a(m) is

supplied to an adder 10, receiving also the output signals of the multipliers 13- _j _, 132..«13 _p . The output signal of the adder 10 is subjected to a modulo s process. Fig.3 illustrates in a graphical way a possible modulo s processing function. The output signal of the modulo s processing stage 11 is on the one hand the output signal b(m) of the processor and is on the other hand supplied to the series circuit of the signal delay stages 12-^, 122«.«12p, each delay¬ ing the signal at the input over a time period of T seconds. The outputs of said delay stages 12-^, 122.-.1 _p are connected to inputs of a series of multipliers 13_, 13 - ..13 _p , in the way illustrated in the figure, which multipliers each multiply the received input signal with a constant factor -k^, -k2,.--- _p . The output signals of said multipliers are delivered to the adder 10. One can derive from Fig. 2 that

P b(m) - [a(m) -£k(i)b(m-i)] mod.s

1=1

This relation corresponds to relation (1) . According to the invention a channel is now used of which the band width is smaller than the frequency spectrum of the signal to be transmitted. Fig. 4 illustratesd a structure of a complete system in which the invention is applicated. In Fig. 4 the analog input signal a(t) is sampled every T seconds in the sample and hold stage 31, so that the signal pulse series a(m) appears at the output. With the process which is already described referring to Fig. 2 the signal b(m) is obtained by means of the adder 32, the modulo s stage 33, the signal delaying elements 34_, 342.«.34 _p and the multipliers 35^, 352« .-35 _p . The output signal b(m) of the modulo s stage 33 is supplied to the channel 36 of which the band width is smaller than the band width of the signal a(t). The output signal c(t) is sampled every T seconds in the sample and hold stage 37. The output signal c(m) of said sample and hold stage 37 is in the modulo s stage 38 subjcted to a modulo s processing. Finally the output signal of the modulo s stage 38 is supplied to a filter 39 for interpolating the output signal of the modulo s stage 38 into a continuous signal. The signal processing in the processor 32, 33, 34, 35 has to be carried

out synchroniously with the sampling in the stage 31 and also syn- chroniously with the sampling of the continuous signal c(t) into c(m) in the sampling stage 37. That means that in one way measures have to be taken for maintaining the synchronization between the transmitter and the receiver.

In reality the channel 36 can for instance be embodied in the way as is illustrated in Fig. 5. A filter 36a is connected in series with an existing channel 36b, for instance an existing transmission path. Said filter 36a ensures that the channel 36 as a whole has a desired transfer function which eventually can be determined solely by said filter. The total band width can be smaller than the band width which is normally necessary for the usual transmission of an analog signal a(t). The impulse response k(i) of said channel 36, comprising of the normal channel 36b and the filter 36a, is now de- termined for instance by supplying a unity impulse to the input and registrating the response at the output. From said response the multiplying coefficients ~*~_ _} -k2...-k _p of the multipliers 35-^, 352«.«35 _p can be determined. After adjusting said multi- pliers using the coefficients determined in this way the system is ready for use.

As result of the preprocessing in the processor, in which the signal a(m) is transformed into the signal b(m), it is possible to transfer a signal over a channel of which the band width is in fact much too small in comparison with the band width of the signal to be transmitted. Ifowever, said signal band width restriction is realized at the expence of the signal dynamics. The dynamics in the signal c(m) will be much larger than the dynamics in the signal a(m). That effect is for instance very strong if one starts with a binary digital signal. A binary digital signal a(m) has because of his binary character a very small resolution and needs a relatively large band width for transmission. After encoding in the processor and after transmission over the channel the band width is signific¬ antly decreased, on the other hand requires the signal processing of c(t) at the receiving side a larger resolution. Fig. 6 illustrates the spectrum shaping effect which can be obtained by means of the signal processing according to the Invention, leaving out spectra around 1/T and multiples thereof. The

spectrum of the signal b(m) will, neglecting the influence of the shape of the local elementary pulse, tend to become a flat spectrum, because there exists little or no correlation between the successive values b(ra). The spectrum of c(t) will therefore almost exclusively be determined by the channel 36 and will yet represent the Inform¬ ation in a(t). Applying this transformation feature will in certain cases be more favourable as starting point for digital encoding of the signal a(t). In that case the "channel" 36 is not considered anymore a transmission channel, but is in fact a spectrum shaping filter, which can eventually be implemented using a digital processor.

The system illustrated in Fig. 4 can be used for transmission of for Instance a telephone signal having a band width of 4 kHz over a channel having a band width of 2 kHz, implying that the effective capacity of the existing transmission channels can be extended by means of systems according to the invention. By delimiting a number of separated frequency ranges within the frequency band of the exist¬ ing transmission path by means of filters a number of signals can be transmitted simultaneously over said existing transmission path using the method according the invention. Furthermore it is possible for instance to transmit signals having a very large band width, such as televsion video signals, over relatively small channels without taking into account the disadvantages of the known band width compression measures. It is indicated above that of the "mod.s" function Is used as encoding function, then -s/2 < _^ a(m)- _\ s/2. Because of influences of the channel noise and tolerances in the instrumentation of the system there is a chance that, when a(m) is In the close neighbourhood of one of the boundery values -s/2 or s/2 for a certain m, a large error will result in decoding a(m) out of c(m) at the receiving side, because c(m) is transferred to another interval of the modulo s decoding function. In a preferred embodiment of the invention said chance is now strongly reduced by restricting a(m) to -s/2 + r< ^" a(m)- _ι s/2-r whereby τj.0 is determined dependent on the strongth of the mean value of the noise onto the transmission channel and the tolerances in the instrumentation.

Such errors, caused by noise, can be eliminated completely of

the decoding function Is modified in the way as is illustrated In Fig. 7. According to the therein Illustrateed function a signal d(m) is derived from c(m) on the basis of the relation d(m) + [c(m)j tri s. The encoding algorithm should of course be adapted correspondingly.

Furthermore it is possible to use a decoding function il¬ lustrated in Fig. 8, with the result that the noise is proportional with the amplitude of the signal to be transmitted. Said decoding function can be written as d(m) — f([c(m)] mod s) whereby f is unambiguous in the range between -s/2 and s/2 and ]f'(x)j is increasing with jx|.

In case the elements of c(m) deviate somewhat from the Ideal value, for instance because of additive noise in the channel, or because of a non exact equalisation, a function of such a type has the advantage that with s small amplitude of a(m) these deviations only cause a small error in the transmitted channel, whereby for a large amplitude of a(m) a larger error will result. If in this way for instance a speech signal is transmitted then many people have the opinion that the received speech signal, comprising an error signal of this type, is much more pleasant to hear than a speech signal having an error signal of constant value. If this function is utilized then the processor should comprise a section having the Inverse transfer function f , which section should be inserted before the Input of the processor illustrated in Fig.2. Finally itis remarked that various coding and decoding functions are conceivable for "cod.s" and "decod.s", whereby for instance the interval s is shifted along the one or the other coordinate axis.

A further aspect can play a role in the choice of the channel respectively the way Into which the channel should be restricted, namely maintaining the secrecy of the information to be transmitted. Because in an increasing way normal telephone lines and other existing transmission channels are used for transmitting information, which should be kept secret for one reason or another there Is a strong need for encyphering systems or "scramblers". Said cramblers can be used for Instance if there is a chance that a telephone conversation will be tapped off, In which case the scrambled line signals do have no meaning for third parties. Scramblers are also

used in the data exchange between computers, which are connected to each other through a normal telephone line, whereby there is a chance that important information will come into the hands of third parties during the transmission thereof. These scramblers applications are not resticted to line connections but can also be used in radio channels within the scope of the invention.

Fig. 9 illustrates a system in which the signal a(m) is encoded in the processor 40 into a signal series b(m) in the already described way. Said signal series b(m) is now transmitted over the channel 41, in which signal b(m) is not subject to significant changes. A decyphering circuit 42 functioning as an extension of the transmission channel, is installed at the receiving side. This circuit 42 in fact determine the coefficients k(i) of the impulse response of the combination of the channel 41 and the circuit 42 in the same way as is explained for the filter 36a in Fig. 5. At the output of the circuit 42 therefore the signal c(m) is obtained, which is transformed into the original signal a(m), generated at the trans¬ mitting side, using the decod.s decoding stage 43 in the already described way. In this system the encoded series b(m) is transmitted instead of a(m) over a channel which does not have limitations, and said series appears as total nonsense for a third party who does have no knowledge of the method and no knowledge of the coefficients k(i), the value s and the function cod.s in the decyphering circuit at the receiving side, the decyphering circuit 42 can be implemented both analog and digital. If a software Implementation is used than a regular change of for instance the k-values of the code can be easily implemented.

It Is possible to use the method according to the invention in fact twice, whereby at the transmitting side first of all the signal to be transmitted is coded mainly with the purpose to realise a band width compression, whereafeter it is coded as second time mainly with the purpose to encypher the signal to be transmitted. At the receiving side the signal is first of all subjected to a decoding process for decyphering the received signal, whereafter a second de¬ coding process is used for retrieving the original signal. At the transmitting side a filter can be installed in front of the channel

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to restrict the signal band width sufficiently such that said band width equals the band width of the channel, whereas at the receiving side a circuit is inserted into which the value of k(i) for the en- cyphering decyphering processs are determined. Itis remarked that above two completely separated encoding/decoding processes are intended. It is however also possible to realise the complete processing in a smaller number of processing stages.

Furthermore the Invention can be used for recording and repro¬ ducing signals on respectively from a recording medium, whereby the recording medium has the function of the above mentioned channel. For recording and reproducing high frequency signals onto a magnetic tape using a tape recorder the tape transport speed should be increased significantly. For audio purposes that is in general sufficient to meet the frequency requirements, however, the mechanism has to meet very strong standards and furthermore the tape length is, as result of the increased speed, very significant.

For video applications various rescuing solutions are applied to keep the transport speed of the band _^ itself within acceptable limits and thereby only the relative speed of the band in relation to the recording/reproducing heads is made as large as possible, for instance by means of heads which are rotating transversely to the tape transport direction. The thereby appearing mechanical problems are significant and with much of these solutions the desired frequency limits are not reached. By using the invention it is now possible to transform the audio or video signal before recording this signal onto a tape recorder such that the highest frequency in the encoded signal is significant¬ ly lower than the highest frequency in the original signal. For recording/reproducing this encoded signal it is sufficient to use a significantly lower transport speed with the result that the transport mechanism can be simplified and the tape consumption is decreased.

It will be clear that in a similar way the Invention can also be used for other registration mediums, such as magnetic discs, drums etc.

Above the invention is explained with reference to a number of feedback embodiments. However, it is also possible to use embodiments

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with a transversal configuration, whereby if necessary the algorithm which is described above should be approximated.

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