CA2214287A1 - Method and apparatus for encoding a signal using pairs of its sub-band signals for quadrature amplitude modulation - Google Patents

Abstract

Improved transmission or storage of signals, such as high speed transmissions insubscriber loops of telecommunication systems, is facilitated by apparatus which includes an encoder for encoding the signal before application to the transmission/storage medium and a decoder which decodes the signal received from the medium. The encoder comprises an analysis filter which analyzes the input signal (Si) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and a device for combining at least one pair of said sub-band signals to provide an encoded signal comprising two adjacent spectral lobes each comprising information from both sub-bands. The decoder comprises a filter for extracting the pair of sub-band signals from a received encoded signal; and a synthesis filter, complementary and substantially inverse to the analysis filter, for processing the extracted pair of sub-band signals to produce a decoded signal corresponding to the input signal. The sub-band signals may be used to modulate in-phase and quadrature components of a common carrier signal to produce the combined signal. One of thespectral components may be removed before transmission/storage of the encoded signal.

Description

-METHOD AND APPARATUS FOR ENCODING A SIGNAL USING PAIRS OF ITS
SUB-BAND SIGNALS FOR QUADRATURE AMPLITUDE MODULATION
DESCRIPTION
TECHNICAL FI~LD:
The invention relates to a method and apparatus for encoding signals, whether digital or analog, for tr~n~mi~ion and/or storage. The invention is especially, but not exclusively, applicable to the encoding of digital signals for tr~nsmic~ion via communications channels, such as twisted wire pair subscriber loops in telecommunications systems or to storage of signals in or on a storage medium, such as 10 video signal recordings, audio recordings, data storage in com~,ller systems, and so on.

BACKGROUND ART:
Embo lim~nt~ of the invention are especially applicable to Asynchronous TransferMode (ATM) telecommunications systems. Such systems are now available to transmit 15 millions of data bits in a single second and are expected to turn futuristic interactive concepts into exciting realities within the next few years. However, deployment of ATM
is hindered by expensive port cost and the cost of running an optical fiber from an ATM
switch to the customer-premises using an architecture known as Fiber-to-the-home.
Running ATM traffic in part of the subscriber loop over existing copper wires would 20 reduce the cost considerably and render the connection of ATM to customer-premises feasible.
The introduction of ATM signals in the existing twisted-pair subscriber loops leads to a requirement for bit rates which are higher than can be achieved with conventional systems in which there is a tendency, when tr~nsmitting at high bit rates, 25 to lose a portion of the signal, typically the higher frequency part, causing the signal quality to suffer ~ignific~ntly. This is particularly acute in two-wire subscriber loops, such as so-called twisted wire pair cables. Using quadrature amplitude modulation (QAM), it is possible to meet the requirements for Asymmetric Digital SubscriberLoops (ADSL), involving rates as high as 1.5 megabits per second for loops up to 3 30 kilometers long with specified error rates. It is envisaged that ADSL systems will allow rates up to about 8 megabits per second over 1 kilometer loops. Nevertheless, these rates are still considered to be too low, given that standards currently proposed for ATM
basic subscriber access involve rates of about 26 megabits per second.

Known QAM systems tend to operate at the higher frequency bands of the channel, which is particularly undesirable for two-wire subscriber loops where attenuation and cross-talk are worse at the higher frequencies. It has been proposed, therefore, to use frequency division modulation (FDM) to divide the tr~n~mi~ion system S into a set of frequency-indexed sub-ch~nnel~. The input data is partitioned into te~llpoldl blocks, each of which is independently modulated and tr~nsmitted in a respective one of the sub-channels. One such system, known as discrete multi-tone tr~n~mi.~sion (DMT), is disclosed in United States patent specification No. 5,479,447 issued December 1995 and in an article entitled "Pelrol-nance Evaluation of a Fast Computation Algorithm for 10 the DMT in High-Speed Subscriber Loop", IEEE Journal on Selected Areas in Communications, Vol. 13, No. 9, December 1995 by I. Lee et al. Specifically, US
5,479,447 discloses a method and appal~lus for adaptive, variable bandwidth, high-speed data tr~n~mission of a multi-carrier signal over a digital subscriber loop. The data to be tr~n~mitted is divided into multiple data streams which are used to modulate multiple 15 carriers. These modulated carriers are converted to a single high speed signal by means of IFFT (Inverse Fast Fourier Transform) before tr~n~mi.~ )n. At the receiver, Fast Fourier Transform (FFT) is used to split the received signal into modulated carriers which are demodul~ted to obtain the original multiple data streams.
Such a DMT system is not entirely s~ti~f~çtory, however, especially for use in 20 two-wire subscriber loops which are very susceptible to noise and other sources of degradation which could result in one or more sub-channels being lost. If only one sub-channel fails, p~lhaps because of tr~n~mi~ion path noise, the total signal is coll~led and either lost or, if error detection is employed, may be retr~nsmitted. It has been proposed to remedy this problem by adaptively elimin~ting sub-channels, but to do so 25 would involve very complex circuitry.
A further problem with DMT systems is the poor separation between sub-channels. In United States patent specifi~tion No. 5,497,398 issued March 1996, M.A.
Tzannes and M.C. Tzannes proposed ameliorating the problem of degradation due tosub-channel loss, and obt~ining superior burst noise immunity, by replacing the Fast 30 Fourier Transform with a lapped transform, thereby increasing the difference between the main lobe and side lobes of the filter response in each sub-channel. The lapped transform may comprise wavelets, as been disclosed by M.A. Tzannes, M.C. Tzannesand H.L. Resnikoff in an article "The DWMT: A Mlllti~rrier Transceiver for ADSL

using M-band Wavelets", ANSI Standard Committee TlEl.4 Contribution 93-067, Mar.1993 and by S.D. Sandberg, M.A. Tzannes in an article "Overlapped Discrete Multitone Modulation for High Speed Copper Wire Communications", IEEE Journal on Selected Areas in Comm., Vol. 13, No. 9, pp. 1571-1585, Dec. 1995, such systems being 5 referred to as "Discrete Wavelet Multitone (DWMT).
A disadvantage of both DMT and DWMT systems is that they typically use a large number of sub-ch~nnel~, for example 256 or 512, which leads to complex, costly equipment and equalization and synchronization difficulties. These difficulties are exacerbated if, to take advantage of the better characteristics of the two-wire subscriber 10 loop at lower frequencies, the number of bits transmitted at the lower frequencies is increased and the number of bits tr~n~mitted at the higher frequencies reduced co~ ondingly.
It is known to use sub-band filterin~ to process digital audio signals prior to recording on a storage medium, such as a compact disc. Thus, US patent specification 15 number 5,214,678 (Rault et ar) discloses an arrangement for encoding audio signals and the like into a set of sub-band signals using a commutator and a plurality of analysis filters, which could be combined. As shown in their Figures 12 and 13 and described at column 15, lines 5-26, Rault et al use recording means which record the sub-band signals as multiple, distinct tracks. This is not entirely .~ti~f~ctory because each sub-band 20 signal would require its own recording head or, if applied to tr~n~mic~ion, its own tr~n~mi~ n channel.
United States patent specification number 5,161,210 (Druyvesteyn) discloses a similar analysis technique to that disclosed by Rault et al but, in this case, the sub-band signals are combined by means of a synthesis filter before recordal. The input audio 25 signal first is analyzed, and an identification signal is mixed with each of the sub-band signals. The sub-band signals then are recombined. The technique ensures that the identification signal cannot be removed simply by normal filtering. The frequency spectrum of the recombined signal is substantially the same as that of the input signal, so it would still be susceptible to co~lu~lion by loss of the higher frequency colllponents.
30 The corresponding decoder also comprises an analysis filter and a synthesis filter.
Consequently, the al)~al~ s is very complex and would involve delays which would be detrimental in high speed tr~n~mis~ion systems.

It is desirable to combine the sub-band signals in such a way as to reduce the risk of collu~lion resulting from part of the signal being lost or corrupted during tMn~mi~ion and/or storage.
It should be noted that, although Rault et a/ use the term "analysis filter" in their 5 specification, in this specification the term "analysis filter" will be used henceforth to denote a device which decomposes a signal into a plurality of sub-band signals in such a way that the original signal can be reconstructed using a complementary synthesis filter.
International patent application number .. (Agent's Docket No. AP487PCT) 10 filed at the C~n~ n Intellectual Property Office contemporaneously herewith) discloses a method and apparatus for encoding such signals which uses the sub-band signals to modulate carriers which are then combined into a single signal for tr~n~mi~ n orstorage. According to such international application, various kinds of modulation may be used. However, it has been discovered that quadrature amplitude modulation, when 15 used with sub-band filtered signals, may provide improved operation and reduced complexity/cost.

DISCLOSURE OF INVENTION:
According to one aspect of the present invention, appald~lls for encoding an input 20 signal for tr~n~mi~ion or storage and decoding such encoded signal to reconstruct the input signal, comprises:
an encoder comprising (i) analysis filter means for analyzing the input signal (S~ into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and (ii) means for combining at least one pair of said sub-band signals subst~nti~lly orthogonally to provide a combined signal comprising two orthogonal components each comprising information from both sub-bands, and using said combined signal to provide said encoded signal;
30 and a decoder comprising (iii) means for extracting said pair of sub-band signals from a received encoded signal; and (iv) synthesis filter means complementary and subst~nti~lly inverse to said analysis filter means for proces~ing the extracted pair of sub-band signals to produce a decoded signal c~ onding to the input signal.
It should be noted that the term "substantially orthogonally" embraces signals 5 which are orthogonal or pseudo-orthogonal.
According to second and third aspects of the invention, there are provided the afore-mentioned encoder per se and afore-mentioned decoder per se.
According to a fourth aspect of the invention, there is provided a method of encoding an input signal for tr~n~mis~ion or storage and decoding such encoded signal 10 to reconstruct the input signal, comprising the steps of:
at an encoder (i) using analysis filter means to analyze the input signal (S;) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a colles~nding plurality of fre~quencies (f); and 15 (ii) combining at least one pair of said sub-band signals substantially orthogonally to provide a combined signal comprising two orthogonal components each comprising information from both sub-bands, and using said combined signal to provide said encoded signal;
and at decoder, the steps of 20 (iii) extracting said pair of sub-band signals from a received encoded signal; and (iv) using synthesis filter means complementary and subst~nti~lly inverse to said analysis filter means, processing the extracted pair of sub-band signals to produce a decoded signal colr~s~,ollding to the input signal.
According to fifth and sixth aspects of the invention, there are provided the afore-25 mentioned encoding steps per se and aforementioned decoding steps per se.

BRIEF DESCRIPTION OF THE DRAWINGS:
The foregoillg and other objects, fealu~s, aspects and advantages of the presentinvention will become more apparent from the following detailed description, taken in 30 conjunction with the acconlpallying drawings, of l)rere led embo~liment~ of the invention, which are described by way of example only.
Figure 1 is a simplified block schematic diagram illustrating a tr~n~mi~ion system including an encoder and decoder according to the invention;

Figure 2 is a block schematic diagram of an encoder embodying the present invention;
Figure 3 is a block schematic diagMm of a corresponding decoder for decoding signals from the encoder of Figure l;
Figure 4A illustrates three-stage Discrete Wavelet Transform decomposition usinga pyramid algorithm to provide sub-band signals;
Figure 4B illustrates three-stage synthesis of an output signal from the sub-band signals of Figure 4A;
Figure 5 is a block schematic diagram of an encoder using a sub-band analysis 10 filter and quadrature amplitude modulation (QAM) of two sub-bands using components of a single carrier;
Figure 6 is a block schematic diagram of a decoder for decoding signals from theencoder of Figure 5;
Figures 7A, 7B and 7C illustrate the frequency spectrum of an input signal, and 15 two sub-bands before and after quadrature amplitude modulation;
Figure 8 illustrates, as an example, a very simple input signal Sj applied to the encoder of Figure 5;
Figure 9 illustrates the frequency spec~ "~ of the input signal Si;
Figures 10A, 10B, 10C and 10D illustrate the sub-band signals y0, Yl, Y2 and y3,20 respectively, produced by analysis filtering of the input signal S; of Figure 8;
Figure 11 illustrates the encoded signal S0 obtained by modul~ting sub-band signals y0 and Yl using QAM;
Figure 12 illustrates the frequency spectrum of the encoded signal SO;
Figure 13 illustrates the decoded signal S'i;
Figure 14 illustrates the frequency spectrum of an encoded signal sn0 following optional bandpass filtering; and Figure 15 illustrates the decoded signal S"; obtained by decoding the bandpass-filtered encoded signal S~O

A tr~n~mi~ion system embodying the present invention is illustrated in Figure 1. The system comprises digital input signal source 10, an encoder 11, tr~n~mi~ion medium 12, decoder 13 and signal destin~tion 14. Input signal Si from signal source 10 is applied to the encoder 11 which encodes it using sub-band filtering and quadrature amplitude modulation (QAM) and supplies the resulting encoded signal SO to tr~n~mi~ n medium 12, which is replesented by a tr~n~mi~sion channel 15, noise source 16 and summer 17, the latter combining noise with the signal in the trAn~mi~ion channel 15 5 before it reaches the decoder 13. Although a trAn~mi~cion medium is illustrated, it could be an analogous storage medium instead. The output of the decoder 13 iS supplied to the signal destinAtion 14. The usable bandwidth of channel 15 dictates the maximum allowable rate of a signal that could be transmitted over the channel.
A first embodiment of the encoder 11 is illustrated in more detail in Figure 2.
10 The input signal Si is applied via an input port 20 to analysis filter bank 21 which decomposes it into sub-bands to generate/extract a lowpass sub-band signal yO, bandpass sub-band signals y, - YN-2 and a highpass sub-band signal YN-I- The sub-band signals y, -YN-I are supplied to a multi-carrier modulator 22 which uses selected pairs of the sub-band signals to modulate a res~ ;live carrier of a selected frequency, as will be 15 explained later. The lowpass sub-band signal yO and first bandpass sub-band signal y, contain more low frequency colllpollents than the other sub-band signals so that pair is used to modulate a low frequency carrier fO. The bandpass sub-band signals Y2-YN-2 and highpass sub-band signal YN-I are used to modulate higher frequency carrier signals fi -fNn, r~sl)ec~ ely, of which the frequencies increase from fi to fN,2. The resnltin~
20 modulated carrier signals Y'o,l - Y'(N-2),(N-I) are combined by summer 23 to form the encoded output signal SO which is tr~n~mitted via output port 24 to tr~n~mi~ion medium 12 for tr~n~mi~ion to decoder 13 (Figure 1).
For reasons which will be explained later, the output of the summer 23 may be supplied to tr~n~mi~ion medium 12 by way of a filter 25, as shown in broken lines. In 25 this particular example, filter 25 is a bandpass filter.
A suitable decoder 13, for decoding the encoded output signal SO~ will now be described with reference to Figure 3. After passing through the trAn~mi~sion medium 12, the tr~n~mitted signal SO may be attenuated and contain noise. Hence, as received by way of port 30 of the decoder 13, it is identified as received signal S O (the prime 30 signifying that it is not identical to encoded signal SO) and supplied to a filter array 31.
Each of the filters in the array 31 corresponds to one of the frequencies fO - fN,2 of the multi-carrier modulator 22 (Figure 2) and recovers the corresponding modulated carrier signals. The recovered modulated carrier signals ynO,l - Yr(N-2),(N-l) separated by the array 31 are demodulated by a multi-carrier demodulator 32 to recover lowpass, bandpass and highpass sub-band signals y~0 - Y~N 1 corresponding to sub-band signals yO - YN-1 in the encoder 11. These recovered sub-band signals are supplied to synthesis filter bank 33 which, operating in a complementary and inverse manner to analysis filter bank 21, 5 produces an output signal S';, which should closely resemble the input signal Si in Figure 2, and supplies it to signal destin~tion 14 via output port 34. Usually, the signal S'; will be equalized using an adaptive equalizer (not shown) to co-,-pensate for distortion and noise introduced by the channel 12.
It should be noted that some of the sub-band signal pairs in Figure 2 may not 10 need to be tr~n~mitted, if they contain little tr~n~mi~sion power as compared with other sub-band signals. When these sub-band signals are not tr~n~mitted, the synthesis filter bank 33 shown in Figure 3 will insert "zero" level signals in place of the mi~sing sub-band signals. The reconstructed signal S'1 would then be only a close approximation to the original input signal S;. Generally, the more sub-bands used, the better the15 approximation.
Preferably, analysis filter 21 (Figure 2) is a multiresolution filter bank whichimplements a Discrete Wavelet Transform (DWT) such as is disclosed in C~n~ n patent application number 2,184,541 and International patent application No....(Agent's ref.
AP487PCT)... filed at the C~n~ n Receiving Office on August 29, 1997, to which the 20 reader is directed for reference.
In order to f~cilit~te a better understanding of the embo-liment~ which use DWT,a brief introduction to discrete wavelet transforms (DWT) will first be given. DWT
~resents an arbitrary square integrable function as the superposition of a family of basis functions called wavelets. A family of wavelet basis functions can be generated by 25 tr~n~1~tin~ and dilating the mother wavelet colres~llding to the family. The DWT
coefficients can be obtained by taking the inner product between the input signal and the wavelet functions. Since the basis functions are tr~n~l~tecl and dilated versions of each other, a simpler algorithm, known as Mallat's tree algorithm or pyramid algorithm, has been proposed by S. G. Mallat in "A theory of multiresolution signal decomposition: the 30 wavelet re~resenla~ion", IEEE Trans. on Pattern Recognition and Machine Intelligence, Vol. 11, No. 7, July 1989. In this algorithm, the DWT coefficients of one stage can be calculated from the DWT coefficients of the previous stage, which is expressed as follows:

WL (n~ , WL (m, j-1 ) h (m-2n) (la) m WH (n, j ) = ~ WL (m~ j -l ) g (m-2n) (lb) m where W(p,q) is thep-th wavelet coefficient at the q-th stage, and h(n) and g(n) are the dilation coefficients corresponding to the scaling and wavelet functions, respectively.
For computing the DWT coefficients of the discrete-time data, it is assumed thatthe input data l~plesellts the DWT coefficients of a high resolution stage. Equations la and lb can then be used for obtaining DWT coefficients of subsequent stages. In practice, this decomposition is performed for only a few stages. It should be noted that the dilation coefficients h(n) represent a lowpass filter, whereas the coefficients g(n) 10 l~present a highr~ filter. Hence, DWT extracts information from the signal atdifferent scales. The first stage of wavelet decomposition extracts the details of the signal (high frequency components) while the second and all subsequent stages of wavelet decomposition extract progressively coarser information (lower frequency components).
It should be noted that compactly supported wavelets can be generated by a perfect-15 reconstruction two-channel filter banks with a so-called octave-band tree-structured architect--re. Orthogonal and biorthogonal filter banks can be used to generate wavelets in these system. A three stage octave-band tree structure for Discrete Wavelet Transformation will now be described with reference to Figures 4A and 4B, in which the same co",pollents in the different stages have the same reference number but with the 20 suffix letter of the stage.
Referring to Figure 4A, the three decomposition stages A, B and C have differentsampling rates. Each of the three stages A, B and C comprises a highpass filter 40 in series with a downsampler 41, and a lowpass filter 42 in series with a downsampler 43.
The cut-off frequency of each lowpass filter 42 is substantially the same as the cut-off 25 frequency of the associated highpass filter 40. In each stage, the cut-off frequency is equal to one quarter of the sampling rate for that stage.
The N samples of input signal Si are supplied in common to the inputs of highpass filter 40A and lowpass filter 42A. The coirespollding N high frequency samples from hi~hp~c~ filter 40A are downsampled by a factor of 2 by downsampler 41A and the resl-ltin~ N/2 samples supplied to the output as the highpass wavelet y3. The N low frequency samples from lowpass filter 42A are downsampled by a factor of 2 by downsampler 43A and the resulting N/2 samples supplied to stage B where the sameprocedure is repeated. In stage B, the N/2 higher frequency samples from highpass filter 5 40B are downsampled by downsampler 41B and the resulting N/4 samples supplied to the output as bandpass wavelet Y2. The other N/2 samples from lowpass filter 42B are downsampled by downsampler 43B and the reslllting N/4 samples are supplied to the third stage C, in which highp~s filter 40C and downsampler 41C process them in like manner to provide at the output N/8 samples as bandpass wavelet Y1. The other N/4 10 samples from lowpass filter 42C are downsampled by downsampler 43C to give N/8 samples and supplies them to the output as low-pass wavelet y0.
It should be noted that, if the input signal segment comprises, for example, 1024 samples or data points, wavelets y0 and Yl comprise only 128 samples, wavelet Y2comprises 256 samples and wavelet y3 comprises 512 samples.
Instead of the octave-band structure of Figure 4A, a set of one lowpass, two bandpass filters and one highpass filter could be used, in parallel, with different downsampling rates.
Referring now to Figure 4B, in order to reconstruct the original input signal, the DWT wavelet signals are upsampled and passed through another set of lowpass and 20 highpass filters, the operation being e~plessed as:

wL(n~ Wr(k, j+1) h~(n--2k) +~ WH(1, j+1) g~(n--21) (2) where h'(n) and g'(n) are, respectively, the lowpass and highpass synthesis filters co.resl?onding to the mother wavelet. It is observed from e~uation 2 thatj-th level DWT
wavelet signals can be obtained from ~ + l)-th level DWT coefficients.
Compactly supported wavelets are generally used in various applications. Table I lists a few orthonormal wavelet filter coefficients (h(n)) that are popular in various applications as disclosed by I. Daubechies, in "Orthonormal bases of compactly supported wavelets", Comm. Pure Appl. Math, Vol. 41, pp. 906-966, 1988. These wavelets have the propelly of having the maximum number of v~nishin~ moments for30 a given order, and are known as "Daubechies wavelets".

Wavelets Coefficients Daub-6 Daub-8 h(O) 0.332671 0.230378 h(l) 0.806892 0.714847 h(2) 0.459878 0.630881 h(3) -0.135011 -0.027984 h(4) -0.085441 -0.187035 h(5) 0.035226 0.030841 h(6) 0.032883 0 h(7) -0.010597 Table I
An embodiment of the invention in which the higher sub-bands are not tr~n~mitted, and which uses discrete wavelet transforms for encoding a digital signal, will now be described with reference to Figure 5. In the encoder 11' of Figure 5, the 15 input signal S; is supplied via input port 20 to an octave-band filter bank 51 which applies a Discrete Wavelet Transform to the signal S; to generate lowpass sub-band wavelet signal yO, two bandpass sub-band wavelet signals, Yl and Y2, and the highpass sub-band wavelet signal y3. In this implementation, only sub-band wavelet signals yO and Yl are processed. Bandpass wavelet sub-band signal Y2 and highr~ sub-band wavelet 20 signal y3 are discarded. Interpolator means 52, interpolates each of the pair of sub-band wavelet signals yO and Yl, respectively, by the same factor M, where M is an integer, typically 8 to 24. Thus within interpolator 52, the sub-band wavelet signals yO and Yl are upsampled by upsamplers 530 and 531, respectively, which insert zero value samples at intervals between actual samples. The upsampled signals then are filtered by two Raise-25 Cosinefilters 540 and 541, respectively, whichinsertateachupsampled "zero" pointasample calculated from actual values of previous samples. The Raise-Cosine filters are preferred so as to minimi~ intersymbol intelrerellce. The two interpolated sub-band wavelet signals yU0 and yul are supplied to quadrature amplitude modulator 55 which uses them to modulate in-phase and quadrature components fi and fQ of a carrier signal fO, 30 provided by oscillator 56, the quadrature component being derived by means of a phase shifter 57. The modulator 55 comprises multipliers 580 and 58l which multiply the carrier signal in-phase and quadrature components fi, and fQ by the two interpolated sub-band wavelet signals yO, and Y1, respectively. The resul~ing two modulated carrier signals y'0 and Y'l are added together by a summer 59 to form the encoded signal SO for 5 tr~n~mi~ion by way of port 24 (and bandpass filter 25 if provided) to tr~n~mi~ion medium 12.
At the co~spollding decoder 13' shown in Figure 6, the signal S'O received at port 30 is supplied to a QAM demodulator 61 which comprises multipliers 620 and 621, which multiply the signal S'O by in-phase and quadrature components fi and fQ of a 10 carrier signal fO from an oscillator 63, the quadrature signal fQ being derived by way of phase shifter 64. The resulting signals are passed through lowpass filters 650 and 651~
respectively, which extract the upsampled versions yU~0 and yu~1 which then are decimated by decimators 660 and 661, respectively, of decimator 67. The resulting recovered sub-band signals y~0 and Y~1 are each supplied directly to a corresponding one of two inputs 15 of a synthesis filter bank 68 which applies to them an Inverse Discrete Wavelet Transform (IDWT) as per Figure 4B to recover the signal S'i which corresponds to the input signal Si. The highpass sub-band wavelet signals Y2 and y3, which were nottransmitted, are replaced by a "zero" signal at the colle~nding "higher" frequency inputs 692 and 693 of the synthesis filter bank 68. The resulting output signal S'i from 20 the synthesis filter bank 68 is the decoder output signal supplied via output port 34, and is a close approximation to the input signal Si at the input to the encoder 11' of Figure 5.
If the higher sub-band signals are used, the DQAM and decimator would be duplicated as appropliate and a suitable synthesis filter used.
Figures 7A to 15 illustrate simplified signals at various points in the system during operation and, in some, the frequency spectrum. Figure 7A shows the frequency spectrum of a much-simplified input signal Si occupying a bandwidth BW centered at frequency fc~ As shown in Figure 7B, after analysis filtering and interpolation, the input signal Si has been partitioned into two interpolated sub-band signals, yU0 and yu1. It 30 should be noted that, for complex input signals, the sub-band signals yO and Y1 prior to interpolation have a very wide spectrum. After upsampling and filtering by the interpolator 52 (Figure 5), sub-band signals yO and Y1 each have a spectrum that is narrower than the frequency spectrum of the original signal Si Theoretically, their bandwidth BW' is substantially equal to one half of the bandwidth BW of the original signal.
As shown in Figure 7C, following modulation by the QAM means 55, the output signal from the QAM means 55 has a spectrum which has two lobes, one each side of 5 the carrier frequency fO used by the QAM means 55. The center frequency of the lower frequency lobe is equal to fO - ~, and the center frequency of the upper frequency lobe is equal to fO plus /~, where ~ prereldbly is equal to about one quarter of the bandwidth BW of the original input signal S;. However, /~ may vary depending upon the complexity of the input signal and the design of the analysis filter 51. The bandwidth 10 BW' is determined in dependence upon the sampling rate of the digital input signal S,.
In the aforementioned C~n~ n patent application number 2,184,541 and coll~s~onding PCT application, the sub-bands were mod~ t~ onto sepaldle carriers so their frequency spectrum lobes were separated by a guard band and each lobe contained information from its own sub-band only. By contrast, in the present invention, there is 15 no need for a guard band between the lobes in the output signal S0. (Figure 7C). It should be noted that each lobe contains information from both of the sub-band signals yO and Yl- Thus, as illustrated in Figures 7A and 7B, the information A contained in the input signal Si is split into lower-frequency colllponent L(A) in sub-band signal yO and higher-frequency component H(A) in sub-band signal y;. As shown in Figure 7C, after 20 quadrature amplitude modulation, each lobe of encoded signal SO contains some of components L(A) and H(A). Consequently, if one lobe is corrupted, perhaps because of noise or attenuation of higher frequencies, it may still be possible to reconstruct the original signal S;. Hence, the tr~n~mi~sion is more robust.
It should be appreciated that, if signal comp~ssion is desired, pelhaps because 25 bandwidth is limited, one of the lobes need not be tr~n~mitted. If the lower lobe were to be discarded, a high pass filter could be used to filter the output from encoder 11 in Figure 5. Conversely, if the higher lobe were to be discarded, a low pass filter could be used inst~fl In the embodiments shown in Figures 2 and 5, a bandpass filter 25 is shown (in broken lines) for removing the higher lobe. Use of a bandpass filter rather 30 than a low-pass filter allows the portion of the spectrum below and above the lower lobe to be used for other purposes.

It should be noted that this is not the same as single sideband tr~n~mi~ion where, although each sideband contains the same information, it is derived from a single source via a single modulated carrier.
Figure 8 illustrates, in the time domain, a very simple input signal Si comprising 5 two sinusoidal signals, of 400 Hz and 1200 Hz, respectively. Figure 9 illustrates the corresponding frequency spectrum of this two-tone input signal S;.
Figures lOA, lOB, lOC and lOD illustrate the coll~onding four sub-band signals yO~ Yl, Y2 and y3, respectively, obtained by analysis filtering the input signal. It should be noted that bandpass sub-band signal Y2 has little energy compared with signals 10 yO and Yl and the energy content of highp~s sub-band signal y3is negligible. Hence sub-band signals Y2 and y3 are not used in encoding the encoded signal SO which is illustrated in Figure 11. As shown in Figure 12, the frequency spectrum of the encoded signal SO
comprises two lobes, with respective peaks at 1600 Hz and 2400 Hz, i.e. at an offset ~
of 400 Hz either side of a center frequency of 2000 Hz. Some bandpass filt~ring was 15 applied to remove harmonics.
Figure 13 illustrates the colle~onding decoded signal S'i and shows that the twotones of the original input signal S; have been recovered, but without the portion corresponding to omitted sub-band signal Y2. It will be appreciated that, with suitable adaptive equalisation, the original digital signal can be recovered despite a portion of the 20 signal (sub-band signal Y2) not being tr~n~mi~ted.
As mentioned previously, a further reduction in bandwidth can be achieved by tr~n~mitting only one lobe of the encoded signal, predicated upon the fact that each lobe contains information from both sub-bands. Thus, Figure 14 illustrates the frequency spectrum of the encoded signal S"O when filtered by bandpass filter 25 to remove the 25 higher-frequency lobe. Figure 15 illustrates the collc;~onding decoded signal S'; and shows that, despite the fact that one lobe was not tr~n~mitted, the two tones have been recovered by the decoder.
Embodiments of the invention which allow higher frequency components and lower frequency components to be intermixed and compressed into a narrower bandwidth 30 than the original signal are especially useful for use with two-wire subscriber loops of telecommunications systems since such loops tend to attenuate higher frequenciesdisplopol lionately.

It should be noted that the sub-band signal bandwidths could be greater than onehalf of the original signal bandwidth BW, though still less. This would allow a less expensive analysis filter to be used.
It should be appreciated that, where the analysis filter 21 implements DWT, the 5 synthesis filter 33 will implement inverse DWT.
It should be appreciated that the quadrature amplitude modulation means S5 couldcomprise a C~rrierless Amplitude/Phase (CAP) modulation means which would comprise an in-phase filter means and a quadrature filter means each of which integrates the interpolation of the corresponding sub-band signal with the multiplier function, in essence lO combining interpolator S2 and QAM 55 (Figure 5).
While similar implementations using more than two pairs of sub-bands and carriers are possible, and might be desirable in some circum~t~nces, for most applications, and especially communication of digital signals via twisted wire subscriber loops, they would be considered complex without significant improvement in 15 performance.
It is envisaged that, instead of bandpass filter 25, other means could be used to elimin~te one of the lobes of the encoded signal before tr~n~mis~ionlstorage. For example, filter 2S could be replaced by a Fast Fourier Transform device, a phase shifting and cancellation circuit, or other suitable means.
Although a multiresolution filter, specifically one implementing DWT is c;relled, other forms of analysis filter could be used inst~-l If more sub-band signal pairs were to be used, an interpolator 52 and QAM 5S
would be provided for each additional pair, which would also be interpolated at such a rate that all of the mocl~ t~d carriers had the same bit rate. For a large number of sub-25 bands, it might then be preferable to use a uni~rlll analysis filter bank rather than a multiresolution analysis filter bank.

INDUSTRIAL APPLICABILITY
It should be appreciated that the signal source 10 and the encoder 11 could be 30 parts of a tr~n~mitter having other signal processing circuitry. Likewise, the decoder 13 and signal destination 14 could be parts of a cc,lresponding receiver.
It should be noted that the present invention is not limited to tr~n~mis~iQn systems but could be used for other purposes to m~int~in signal integrity despite noise and attenuation. For example, it might be used in recording of the signal on a compact disc or other storage medium. The storage medium can therefore be equated with the tr~n~mi~sion medium 12 in Figure 1. It should be appreciated that the encoders and decoders described herein would probably be implemented by a suitably programmed5 digital signal processor or as a custom inlegldted circuit.
Although embo~iment~ of the invention have been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and not to be taken by way of the limitation, the spirit and scope of the present invention being limited only by the appended claims.

Claims (28)

1. Apparatus for encoding an input signal for transmission or storage and decoding such encoded signal to reconstruct the input signal, comprising:
an encoder comprising (i) analysis filter means for analyzing the input signal (Si) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and (ii) means for combining a pair of said sub-band signals to provide a said encoded signal having two spectral lobes each comprising information from both sub-bands of said pair;
and a decoder comprising (iii) means for extracting said pair of sub-band signals from a received encodedsignal; and (iv) synthesis filter means complementary and substantially inverse to said analysis filter means for processing the extracted pair of sub-band signals to produce a decoded signal corresponding to the input signal.

2. Apparatus as claimed in claim 1, wherein the combining means comprises modulation means for using said pair of sub-band signals each to provide a respective one of a first modulated signal and a second modulated signal, the first modulated signal and the second modulated signal having the same frequency but phase displaced by 90 degrees one relative to the other, and combining the modulated signals to provide said encoded signal;
and the decoder comprises demodulation means for extracting the sub-band signals from the received encoded signal.

3. Apparatus as claimed in claim 2, wherein the modulation means comprises interpolation means for interpolating the sub-band signals, and quadrature amplitude modulation means for using each of the interpolated sub-band signals to modulate a respective one of an in-phase carrier signal and a quadrature carrier signal, the in-phase carrier signal and the quadrature carrier signal having the same frequency but phase-displaced by 90 degrees one relative to the other, and the demodulation means comprises means for demodulating the received encoded signal using in-phase and quadraturecarrier signals having the same frequency as those used to encode the encoded signal.

4. Apparatus as claimed in claim 1, wherein the analysis filter generates a plurality of pairs of sub-band signals and the modulation means modulates a selection of said pairs, the synthesis filter compensating for the unused sub-band signals by substituting zero level signals.

5. Apparatus as claimed in any one of claims 1 to 4, further comprising means for removing one of said spectral lobes from the encoded signal and providing the remaining one of said spectral lobes as said encoded signal.

6. An encoder for encoding an input signal for transmission or storage comprising:
(i) analysis filter means for analyzing the input signal (Si) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and (ii) means for combining at least one pair of said sub-band signals to provide a said encoded signal comprising two spectral lobes each comprising information from both sub-bands.

7. An encoder as claimed in claim 6, wherein the combining means comprises modulation means for using said pair of sub-band signals each to provide a respective one of a first modulated signal and a second modulated signal, the first modulated signal and the second modulated signal having the same frequency but phase displaced by 90 degrees one relative to the other, and combining the modulated signals to provide said encoded signal.

8. An encoder as claimed in claim 7, wherein the modulation means comprises interpolation means for interpolating the sub-band signals, and quadrature amplitude modulation means for using each of the interpolated sub-band signals to modulate a respective one of an in-phase carrier signal and a quadrature carrier signal, the in-phase carrier signal and the quadrature carrier signal having the same frequency but phase-displaced by 90 degrees one relative to the other,

9. An encoder as claimed in claim 6, wherein the analysis filter generates a plurality of pairs of sub-band signals and the modulation means modulates a selection of said pairs.

10. An encoder as claimed in any one of claims 6 to 9, further comprising means for removing one of said spectral lobes from the encoded signal and providing the remaining one of said spectral lobes as said encoded signal.

11. A decoder for decoding an encoded signal encoded by the encoder of claim 6, comprising:
(iii) means for extracting said pair of sub-band signals from a received encoded signal; and (iv) synthesis filter means complementary and substantially inverse to said analysis filter means for processing the extracted pair of sub-band signals to produce a decoded signal corresponding to the input signal.

12. A decoder as claimed in claim 11, for decoding an encoded signal encoded by the encoder of claim 7 and further comprising demodulation means for extracting the sub-band signals from the received encoded signal.

13. A decoder as claimed in claim 12, for decoding an encoded signal encoded by the encoder of claim 8, and wherein the demodulation means comprises means for demodulating the received encoded signal using in-phase and quadrature carrier signals having the same frequency as those used to encode the encoded signal.

14. A decoder as claimed in claim 13, for decoding an encoded signal encoded by the encoder of claim 9, and wherein the synthesis filter is arranged to compensate for the unused sub-band signals by substituting zero level signals.

15. A method of encoding an input signal for transmission or storage and decoding such encoded signal to reconstruct the input signal, comprising the steps of:
at an encoder (i) using analysis filter means to analyze the input signal (Si) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and (ii) combining at least one pair of said sub-band signals to provide a said encoded signal comprising two spectral lobes each comprising information from both sub-bands;
and at decoder, the steps of (iii) extracting said pair of sub-band signals from a received encoded signal; and (iv) using synthesis filter means complementary and substantially inverse to said analysis filter means, processing the extracted pair of sub-band signals to produce a decoded signal corresponding to the input signal.

16. A method as claimed in claim 15, wherein the combining step comprises using said pair of sub-band signals each to provide a respective one of a first modulated signal and a second modulated signal, the first modulated signal and the second modulated signal having the same frequency but phase-displaced by 90 degrees one relative to the other, and combining the modulated signals to provide said encoded signal;
and the demodulation at the decoder comprises the step of extracting the sub-band signals from the received encoded signal.

17. A method as claimed in claim 6, wherein the modulation comprises the step ofinterpolating the sub-band signals, and using quadrature amplitude modulation means for using each of the interpolated sub-band signals to modulate a respective one of an in-phase carrier signal and a quadrature carrier signal, the in-phase carrier signal and the quadrature carrier signal having the same frequency but phase-displaced by 90 degrees one relative to the other, and the demodulation step at the decoder comprises the step of demodulating the received encoded signal using in-phase and quadrature carrier signals having the same frequency as those used to encode the encoded signal.

18. A method as claimed in claim 15, wherein a plurality of pairs of sub-band signals are generated but only a selection of said pairs modulated, and the processing by the synthesis filter means compensates for the unused sub-band signals by substituting zero level signals.

19. A method as claimed in any one of claims 15 to 18, further comprising the step of removing one of said spectral lobes from the encoded signal and providing theremaining one of said spectral lobes as said encoded signal.

20. A method of encoding an input signal for transmission or storage comprising the steps of:
(i) using analysis filter means to analyze the input signal (Si) into a plurality of sub-band signals (y), each sub-band centered at a respective one of a corresponding plurality of frequencies (f); and (ii) combining at least one pair of said sub-band signals to provide a said encoded signal comprising two spectral lobes each comprising information from both sub-bands.

21. An encoding method as claimed in claim 20, wherein the combining step comprises the step of using said pair of sub-band signals each to provide a respective one of a first modulated signal and a second modulated signal, the first modulated signal and the second modulated signal having the same frequency but phase displaced by 90 degrees one relative to the other, and combining the modulated signals to provide said encoded signal.

22. An encoding method as claimed in claim 21, wherein the modulation comprises the step of interpolating the sub-band signals, and using each of the interpolated sub-band signals for quadrature amplitude modulation means of a respective one of an in-phase carrier signal and a quadrature carrier signal, the in-phase carrier signal and the quadrature carrier signal having the same frequency but phase-displaced by 90 degrees one relative to the other.

23. An encoding method as claimed in claim 20, wherein a plurality of pairs of sub-band signals are generated using the analysis filter means but only a selection of said pairs modulated.

24. An encoding method as claimed in any one of claims 20 to 23, further comprising the step of removing one of said spectral lobes from the encoded signal and providing the remaining one of said spectral lobes as said encoded signal.

25. A method of decoding an encoded signal encoded by the encoder of claim 20, comprising the steps of:
(iii) extracting said pair of sub-band signals from a received encoded signal; and (iv) using synthesis filter means complementary and substantially inverse to said analysis filter means, processing the extracted pair of sub-band signals to produce a decoded signal corresponding to the input signal.

26. A decoding method as claimed in claim 25, for decoding an encoded signal encoded by the encoding method of claim 21 and further comprising the step of demodulating the received signal to extract the sub-band signals.

27. A decoding method as claimed in claim 26, for decoding an encoded signal encoded by the encoding method of claim 22, and wherein the demodulating of the received encoded signal uses in-phase and quadrature carrier signals having the same frequency as those used to encode the encoded signal.

28. A decoding method as claimed in claim 25, for decoding an encoded signal encoded by the encoder of claim 23, and wherein the processing using the synthesis filter is arranged to compensate for the unused sub-band signals by substituting zero level signals.