CA2264644A1 - Method and apparatus for sub-band modulation of signals for transmission and/or storage - Google Patents

Abstract

A method and apparatus for processing an input signal for transmission and/or storage, uses an analysis filter bank (21; 51) to decompose the signal into sub-band signals which are used to modulate a plurality of carriers. The carriers are combined into a single encoded signal for transmission/storage.
The encoder/decoder is especially applicable to telecommunications systems and recording systems. The analysis filter bank may comprise a multiresolution filter, such as an octave band filter bank (40A/B/C/D...43A/B/C/D) implementing Discrete Wavelet Transform. The modulation may comprise double-sideband, single-sideband, quadrature amplitude modulation, and so on. Where the input signal is analog, the carriers may be modulated directly by the sub-band signals. Where the input signal is digital, however, the sub-band signals are interpolated, all to the same rate, and then used to modulate the carriers. The corresponding decoder (13) extracts the modulated carrier signals, demodulates them, decimates them (if applicable) and then synthesizes them to reconstruct the original input signal. One or more of the sub-bands, especially at the higher frequencies, may be discarded. Discrete wavelet transformation is applied to segments of the digital signal.

Description

10202530CA 02264644 1999-02-261METHOD AND APPARATUS FOR SUB-BAND MODULATIONOF SIGNALS FOR TRANSMISSION AND/OR STORAGEBACKGROUND OF THE INVENTIONTECHNICAL FIELDThe invention relates to a method and apparatus for encoding digital signals fortransmission and/or storage. The invention is especially, but not exclusively, applicableto the encoding of digital signals for transmission via communications channels, such astwisted wire pair subscriber loops in telecommunications systems, or to storage of signalsin or on a storage medium, such as video signal recordings, audio recordings, datastorage in computer systems, and so on.BACKGROUND ARTEmbodiments of the invention are especially applicable to Asynchronous TransferMode (ATM) telecommunications systems. Such systems are now available to transmitmillions of data bits in a single second and are expected to turn futuristic interactiveconcepts into exciting realities within the next few years. However, deployment of ATMis hindered by expensive port cost and the cost of running an optical fiber from an ATMswitch 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 wouldreduce the cost considerably and render the connection of ATM to customer-premisesfeasible.The introduction of ATM signals in the existing twisted-pair subscriber loopsleads to a requirement for bit rates which are higher than can be achieved withconventional systems in which there is a tendency, when transmitting at high bit rates,to lose a portion of the signal, typically the higher frequency part, causing the signalquality to suffer significantly. This is particularly acute in two—wire subscriber loops,such as so-called twisted wire pairs. Using quadrature amplitude modulation (QAM),it is possible to meet the requirements for Asymmetric Digital Subscriber Loops (ADSL),involving rates as high as 1.5 megabits per second for loops up to 3 kilometers long withspecified error rates. It is envisaged that ADSL systems will allow rates up to about 8megabits per second over 1 kilometer loops. Nevertheless, these rates are stillconsidered to be too low, given that standards currently proposed for ATM basicAMENDED SHEETl0l5202530CA 02264644 1999-02-26v«-.2subscriber access involve rates of about 26 megabits per second.QAM systems tend to operate at the higher frequency bands of the channel, whichis particularly undesirable for two-wire subscriber loops where attenuation and cross-talkare worse at the higher frequencies. It has been proposed, therefore, to use frequencydivision modulation (FDM) to divide the transmission system into a set of frequency-indexed sub-channels. The input data is partitioned into temporal blocks, each of whichis independently modulated and transmitted in a respective one of the sub-channels. Onesuch system, known as discrete multi-tone transmission (DMT), is disclosed in UnitedStates patent specification No. 5,479,447 issued December 1995 and in an article entitled"Performance Evaluation of a Fast Computation Algorithm for the DMT in High-SpeedSubscriber Loop", IEEE Journal on Selected Areas in Communications, Vol. l3, No.9, December 1995 by 1. Lee et al. Specifically, US 5,479,447 discloses a method andapparatus for adaptive, variable bandwidth, high-speed data transmission of a multi-carrier signal over a digital subscriber loop. The data to be transmitted is divided intomultiple data streams which are used to modulate multiple carriers. These modulatedcarriers are converted to a single high speed signal by means of IFFT (Inverse FastFourier Transform) before transmission. At the receiver, Fast Fourier Transform (FFT)is used to split the received signal into modulated carriers which are demodulated toobtain the original multiple data streams.Such a DMT system is not entirely satisfactory for use in two-wire subscriberloops which are very susceptible to noise and other sources of degradation which couldresult in one or more sub-channels being lost. If only one sub—channel fails, perhapsbecause of transmission path noise, the total signal is corrupted and either lost or, iferror detection is employed, may be retransmitted. It has been proposed to remedy thisproblem by adaptively eliminating noisy sub-channels, but to do so would involve verycomplex circuitry.A further problem with DMT systems is poor separation between sub-channels.In United States patent specification No. 5,497,398 issued March 1996, M.A. Tzannesand M.C. Tzannes proposed ameliorating the problem of degradation due to sub—channelloss, and obtaining superior burst noise immunity, by replacing the Fast FourierTransform with a lapped transform, thereby increasing the difference between the mainlobe and side lobes of the filter response in each sub—channel. The lapped transform maycomprise wavelets, as disclosed by M.A. Tzannes, M.C. Tzannes and H.L. ResnikoffAMENDED SHEET1015202530CA 02264644 1999-02-263in an article "The DWMT: A Multicarrier Transceiver for ADSL using M-bandWavelets", ANSI Standard Committee TlE1.4 Contribution 93-067, Mar. 1993 and byS.D. Sandberg, M.A. Tzannes in an article "overlapped Discrete Multitone Modulation-for High Speed Copper Wire Communications", IEEE Journal on Selected Areas inComm., Vol. 13, No. 9, pp. 1571-1585, Dec. 1995, such systems being referred to as"Discrete Wavelet Multitone (DWMT).A disadvantage of both DMT and DWMT systems is that they typically use alarge number of sub-channels, for example 256 or 512, which leads to complex, costlyequipment and equalization and synchronization difficulties. These difficulties areexacerbated if, to take advantage of the better characteristics of the two-wire subscriberloop at lower frequencies, the number of bits transmitted at the lower frequencies isincreased and the number of bits transmitted at the higher frequencies reducedcorrespondingly.It is known to use sub-band filtering to process digital audio signals prior torecording on a storage medium, such as a compact disc. Thus, US patent specificationnumber 5,214,678 (Rault et al) discloses an arrangement for encoding audio signals andthe like into a set of sub-band signals using a commutator and a plurality of analysisfilters, which could be combined. Rault et al use recording means which record the sub-band signals as multiple, distinct tracks. This is not entirely satisfactory because eachsub-band signal would require its own recording head or, if applied to transmission, itsown transmission channel.It is also known to use sub-band filtering for compression of audio signals, asdisclosed by C. Heegard and T. Shamoon in "High-Fidelity Audio Compression:Fractional-Band Wavelet", 1992 IEEE Conference on Acoustics, Speech and SignalProcessing, 23-26 March 1992, New York.In an article entitled "Wavelet-Coded Image Transmission Over Land MobileRadio Channels, IEEE Global Telecommunications Conference, 6-9 Dec. 1992, NewYork, You—Jong Liu et al disclosed the use of two-dimensional wavelet decompositionto convert an image into sub-images. The sub-images were quantized to produce digitalnumeric representations which were transmitted.United States patent specification number 5,161,210 (Druyvesteyn) discloses asimilar analysis technique to that disclosed by Rault et al but, in this case, the sub-bandsignals are combined by means of a synthesis filter before recordal. The input audio.4-3‘JlEi‘lC-ED SHEET1015202530CA 02264644 1999-02-264signal first is analyzed, and an identification signal is mixed with each of the sub-bandThetechnique ensures that the identification signal cannot be removed simply by normalsignals. The sub-band signals then are recombined using a synthesis filter.filtering. The frequency spectrum of the recombined signal is substantially the same asthat of the input signal, so it would still be susceptible to corruption by loss of the higherfrequency components. The corresponding decoder also comprises an analysis filter anda synthesis filter. Consequently, the apparatus is very complex and would involve delayswhich would be detrimental in high speed transmission systems.It is desirable to combine the sub-band signals in such a way as to reduce the riskof corruption resulting from part of the signal being lost or corrupted during transmissionand/or storage.It should be noted that, although Rault et al use the term "analysis filter" in theirspecification, in this specification the term "analysis filter" will be used to denote adevice which decomposes a signal into a plurality of sub-band signals in such a way thatthe original signal can be reconstructed using a complementary synthesis filter.SUMMARY OF THE INVENTION:The present invention seeks to eliminate, or at least mitigate, the disadvantagesof these known systems and has for its object to provide an improved method andapparatus for encoding signals for transmission and/or storage.According to one aspect of the invention, apparatus for encoding an input signalfor transmission or storage and decoding such encoded signal to reconstruct the inputsignal, comprising an encoder (11) for encoding a digital input signal for transmissionor storage and a decoder (13) for decoding such encoded signal to reconstruct the inputsignal, the encoder comprising analysis filter bank means (2l;5 1) for analyzing the inputsignal into a plurality of sub-band signals, each sub-band centered at a respective one ofa corresponding plurality of frequencies and the decoder comprising synthesis filter bankmeans (33;67) complementary to said analysis filter bank means for producing a decodedsignal corresponding to the input signal, characterized in that:the encoder (11) comprises(i) interpolation means (52) for interpolating of the plurality of sub-band signals toprovide a plurality of interpolated signals each occupying the same frequencyband as the others; and..-ms.-*1£«?.~‘a SHEET1015202530CA 02264644 1999-02-265(ii) combining means (23;5 8) for combining the interpolated sub-band signals to formthe encoded signal for transmission or storage;and the decoder (13) comprises(iii) means (3l;610, 61,, 612) for extracting the interpolated sub-band signals from thereceived or recorded encoded signal;(iv) decimator means (66) for decimating each of the plurality of extractedinterpolated sub-band signals to remove the interpolated values and applying thedecimated signals to the synthesis filter bank means,the synthesis filter bank means processing the plurality of decimated sub-band signals toreconstruct said input signal.According to second and third aspects of the invention, there are provided theencoder per se and the decoder per se of the apparatus.The analysis filter means may be uniform, for example an M-band filter bank orShort-time Fast Fourier Transform unit; or non-uniform, for example a "multiresolution"filter bank such as an octave—band or dyadic filter bank implementing discrete wavelettransform (DWT) which will produce sub—bands having different bandwidths, typicallyeach half the width of its neighbour.The interpolation rate may be such that the resulting interpolated sub-band signalsall have the same rate.The interpolation rate will be chosen according to the requirements of a particulartransmission channel or storage means but typically will be of the order of 1:8 or more.The interpolation means may comprise an upsampler, for interpolating intervalsbetween actual values, and filter means, for example Raise Cosine filter means, fordetermining values between the actual samples and inserting them at the appropriateintervals.Usually, when used with digital signals, sub-band analysis filter banks create sub-band signals which occupy a wide spectrum as compared with the original signal, whichmakes modulation difficult. Interpolating and smoothing the sub-band signalsadvantageously band-limits the spectrum of the sub-band signals, permitting modulationby a variety of techniques, for example Double or Single Sideband AmplitudeModulation, Quadrature Amplitude Modulation (QAM), Carrier Amplitude/Phasemodulation (CAP), and so on.l0l5202530CA 02264644 1999-02-266According to a fourth aspect of the invention, there is provided a method ofencoding an input signal for transmission or storage and decoding such encoded signalto reconstruct the input signal, the encoding of the input signal comprising the steps ofusing analysis filter bank means to analyze the input signal into a plurality of sub-bandsignals, each sub-band centered at a respective one of a corresponding plurality offrequencies, characterized in that the encoding comprises the steps of:(i) interpolating each of the plurality of sub-band signals to provide a correspondingplurality of interpolated sub-band signals each occupying the same frequency bandas the others; and(ii) combining the interpolated sub-band signals to form the encoded signal fortransmission or storage;and the decoding of the encoded signal comprises the steps of:(iii) extracting the plurality of interpolated sub-band signals from the received orrecorded encoded signal;(iv) decimating each of the plurality of extracted interpolated sub-band signals toremove values interpolated during encoding; and(v) using synthesis filter bank means complementary to said analysis filter bankmeans, processing the plurality of decimated sub-band signals to produce a decodedsignal corresponding to the input signal.According to fifth and sixth aspects of the invention, there are provided themethod of encoding per se and the method of decoding per se.In embodiments of any of the above aspects of the invention which use DiscreteWavelet Transform, the digital input signal may be divided into segments and thediscrete wavelet transform used to transform successive segments of the digital signal.The foregoing and other objects, features, aspects and advantages of the presentinvention will become more apparent from the following detailed description of preferredembodiments of the invention which are described by way of example only withreference to the accompanying drawings.»'.2.«i::s:z:i:;;3 3:45:-rt1015202530CA 02264644 1999-02-26BRIEF DESCRIPTION OF DRAWINGS:Figure 1 is a simplified schematic diagram illustrating a transmission systemincluding an encoder and decoder according to the invention; 4Figure 2 is a schematic block diagram of an encoder embodying the presentinvention;Figure 3 is a schematic block diagram of a corresponding decoder for signalsfrom the encoder of Figure 1;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—bandsignals of Figure 4A;Figure 5 is a block schematic diagram of an encoder using a sub-band analysisfilter and Double Sideband amplitude modulation with three sub-bands and correspondingcarriers;Figure 6 is a block schematic diagram of a decoder using three sub-bands andcarriers for use with the encoder of Figure 5;Figures 7A, 7B and 7C illustrate the frequency spectrums of an input signal, andthree sub-band signals before and after multi-carrier SSB modulation;Figure 8 illustrates, as an example, a very simple input signal S; applied to theencoder of Figure 5;Figures 9A, 9B, 9C and 9D illustrate the sub-band wavelet signals yo, y,, y; andy, produced by analysis filtering of the input signal S; of Figure 8;Figures 10A, 10B and 10C illustrate modulated carrier signals y’.,, y’, and y’,modulated by sub-band wavelet signals yo, y, and yz, respectively;Figure 11 illustrates the encoded/transmitted signal S,;Figure 12 illustrates the power spectrum of the transmitted signal So;Figures 13A, 13B and 13C illustrate the recovered wavelet modulated carriers,y"o, Y": and y”;Figure 14A, 14B and 14C illustrate the recovered wavelet signals y'.,, y‘, and y'z;andFigure 15 illustrates the reconstructed signal.WENDED SHEET1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/006088DESCRIPTION OF THE PREFERRED EMBODIMENTSA transmission system embodying the present invention is illustrated in Figure1. The system comprises digital input signal source 10, an encoder 11, transmissionmedium 12, decoder 13 and signal destination 14. Input signal S, from signal source 10is applied to the encoder 11 which encodes it using sub-band filtering and multi-carriermodulation and supplies the resulting encoded signal S, to transmission medium 12,which is represented by a transmission channel 15, noise source 16 and summer 17, thelatter combining noise with the signal in the transmission channel 15 before it reachesthe decoder 13. Although a transmission medium 12 is illustrated, it could be ananalogous storage medium instead. The output of the decoder 13 is supplied to thesignal destination 14. The usable bandwidth of channel 15 dictates the maximumallowable 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.The input signal S, is applied via an input port 20 to analysis filter bank 21 whichdecomposes it into sub-bands to generate/extract a lowpass sub-band signal yo, bandpasssub-band signals y, - yN_2 and a highpass sub-band signal y,.,_,. The sub-band signals y, -y,.,_, are supplied to a multi-carrier modulator 22 which uses each sub-band signal tomodulate a respective carrier of a selected frequency, as will be explained later. Thelowpass sub-band signal yo contains more low frequency components than the other sub-band signal, and is used to modulate a low frequency carrier fo; The bandpass sub-bandsignals y, - ym and highpass sub-band signal yN_, have more high frequency componentsthan the lowpass wavelet signal yo and are therefore used to modulate higher frequencycarrier signals f, - fN_,, respectively, of which the frequencies increase from f, to f,.,_,.The modulated carrier signals y'0 - y’N_, are combined by summer 23 to form theencoded output signal S, which is transmitted via output port 24 to transmission medium12 for transmission to decoder 13 (Figure l).A suitable decoder 13, for decoding the encoded output signal, will now bedescribed with reference to Figure 3. After passing through the transmission medium12, the transmitted signal S, may be attenuated and contain noise. Hence, as receivedby the decoder at port 30 it is identified as received signal S’, (the prime signifying thatit is not identical to enclosed signal S,,) and supplied to a filter array 31. Each of thefilters in the array 31 corresponds to one of the frequencies fa - f,.,_, of the multi-carriermodulator 22 (Figure 2) andrecovers the corresponding modulated carrier signals. The1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/006089recovered modulated carrier signals y”., - y",.,_, separated by the array then aredemodulated by a multi—carrier demodulator 32 to recover the lowpass, bandpass andhighpass sub-band signals y'., - y'N_, corresponding to sub-band signals yo - y(N_,,,respectively, in the encoder 11. The recovered sub-band signals are supplied to synthesisfilter bank 33 which, operating in a complementary and inverse manner to analysis filterbank 21, produces an output signal S’, which should closely resemble the input signal S,in Figure 2, and supplies it to signal destination 14 via output port 34. Usually, therecovered signal S’, will be equalized using an adaptive equalizer to compensate fordistortion and noise introduced by the channel 12.It should be noted that the highpass sub-band signal y,.,_, and some of sub-bandsignals yo - y,,,, in Figure 2 may not need to be transmitted, if they contain littletransmission power as compared with other sub-band signals. When these sub-bandsignals are not transmitted, the synthesis filter bank 33 shown in Figure 3 will insertzeros in place of the missing sub-band signals. The reconstructed signal S’, would thenbe only a close approximation to the original input signal Si. Generally, the more sub-bands used, the better the approximation.Preferably, analysis filter 21 is a multiresolution filter bank which implements aDiscrete Wavelet Transform (DWT). In order to facilitate a better understanding of theembodiments which use DWT, a brief introduction to discrete wavelet transforms (DWT)will first be given. DWT represents an arbitrary square integrable function as thesuperposition of a family of basis functions called wavelets. A family of wavelet basisfunctions can be generated by translating and dilating the mother wavelet correspondingto the family. The DWT coefficients can be obtained by taking the inner productbetween the input signal and the wavelet functions. Since the basis functions aretranslated and dilated versions of each other, a simpler algorithm, known as Mallat’s treealgorithm or pyramid algorithm, has been proposed by S. G. Mallat in "A theory ofmultiresolution signal decomposition: the wavelet representation", IEEE Trans. onPattern Recognition and Machine Intelligence, Vol. 11, No. 7, July 1989. In thisalgorithm, the DWT coefficients of one stage can be calculated from the DWTcoefficients of the previous stage, which is expressed as follows:W,_(n,j) = 2 WL(m._7'-l)h(m—2n) (la)1015202530CA 02264644 1999-02-26W0 98/092583 PCT/CA97/0060810w,,(n,j) = 2 WL(m,j—1)g(m-2n) (lb)mwhere W(p,q) is the p-th wavelet coefficient at the q-th stage, and hm) and g(n) are thedilation 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 represents the DWT coefficients of a high resolution stage. Equations laand lb can then be used for obtaining DWT coefficients of subsequent stages. Inpractice, this decomposition is performed only for a few stages. It should be noted thatthe dilation coefficients h(n) represent a lowpass filter, whereas the coefficients g(n)represent a highpass filter. Hence, DWT extracts information from the signal atdifferent scales. The first stage of wavelet decomposition extracts the details of thesignal (high frequency components) while the second and all subsequent stages of waveletdecompositions extract progressively coarser information (lower frequency components).It should be noted that compactly supported wavelets can be generated by a perfect-reconstruction two-channel filter banks with a so-called octave—band tree-structuredarchitecture. Orthogonal and biorthogonal filter banks can be used to generate waveletsin these system. A three stage octave-band tree structure for Discrete WaveletTransformation will now be described with reference to Figures 4A and 4B, in which thesame components in the different stages have the same reference number but with thesuffix 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 inseries 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-offfrequency of the associated highpass filter 40. In each stage, the cut-off frequency isequal 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 highpassfilter 40A and lowpass filter 42A. The corresponding high frequency samples fromhighpass filter 40A are downsampled by a factor of 2 by downsampler 41A and theresulting N/2 samples supplied to the output as the highpass wavelet y3. The N lowfrequency samples from lowpass filter 42A are downsampled by a factor of 2 bydownsampler 43A and the resulting N/2 samples supplied to stage B where the same10152025CA 02264644 1999-02-26WO 98/09383 PCT/CA97/0060811procedure is repeated. In stage B, the N/2 higher frequency samples from highpass filter40B are downsampled by downsampler 41B and the resulting N/4 samples supplied tothe output as bandpass wavelet y,. The other N/2 samples from lowpass filter 42B aredownsampled by downsampler 43B and the resulting N/4 samples are supplied to thethird stage C, in which highpass filter 40C and downsampler 41C process them in likemanner to provide at the output N/8 samples as bandpass wavelet y,. The other N/4samples from lowpass filter 42C are downsampled by downsampler 43C to give N/8samples and supplies them to the output as low-pass wavelet yo.It should be noted that, if the input signal segment comprises, for example, 1024samples or data points, wavelets yo and y, comprise only 128 samples, wavelet yzcomprises 256 samples and wavelet y, comprises 512 samples.Instead of the octave—band structure of Figure 4A, a set of one lowpass, twobandpass filters and one highpass filter could be used, in parallel, with differentdownsampling rates.Referring now to Figure 4B, in order to reconstruct the original input signal, theDWT wavelet signals are upsampled and passed through another set of lowpass andhighpass filters, the operation being expressed as:WL(n,j) = ; WL(k,j+1)h’(n—2k) ii: W,,(l,j+1) g’(n~2l) (2)where h'(n) and g'(n) are, respectively, the lowpass and highpass synthesis filterscorresponding to the mother wavelet. It is observed from equation 2 that j—th level DWTwavelet signals can be obtained from (i + l)—th level DWT coefficients.Compactly supported wavelets are generally used in various applications. TableI lists a few orthonormal wavelet filter coefficients h(n) that are popular in variousapplications as disclosed by I. Daubechies, in "Orthonormal bases of compactlysupported wavelets", Comm. Pure Appl. Math, Vol. 41, pp. 906-966, 1988. Thesewavelets have the property of having the maximum number of vanishing moments fora given order, and are known as "Daubechies wavelets".1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/0060812If WaveletsCoefficients Daub_6 Daub_8h(0) 0.332671 0.230378h(1) 0.806892 0.714847h(2) 0.459878 0.630881“ M3) -0. 135011 —0.027984, h(4) —0.08544l -0. 187035h(5) 0.035226 0.030841h(6) 0.032883h(7) -0.010597Table 1An embodiment of the invention in which the higher sub-bands are nottransmitted, and which uses discrete wavelet transforms for encoding a digital signal,will now be described with reference to Figure 5. In the transmitter/encoder 11' ofFigure 5, the input signal S, is supplied to an input port 20 of analysis filter meanscomprising an octave-band filter bank 51 for applying Discrete Wavelet Transform asillustrated in Figure 4A to the signal S, to generate lowpass sub-band wavelet signal yo,two bandpass sub-band wavelet signals, y, and y,, and the highpass sub-band waveletsignal y3. In this implementation, only sub-band wavelet signals y,,, y, and y, will beprocessed. Highpass sub-band wavelet signal y, is discarded. Interpolator means 52interpolates sub-band wavelet signals yo, y, and y, by factors 2M, 2M and M,respectively, where M is an integer, typically 8 to 24, such that the three sub-bandwavelet signals (yo, y, and y,) have equal sample rates. Thus, within interpolator 52,the sub-band wavelet signals y.,, y, and y, are upsampled by upsamplers 530, 53, and 532,respectively, which insert zero value samples at intervals between actual samples. Theupsampled signals then are filtered by three Raise—Cosine filters 540, 54, and 542,respectively, which insert at each upsampled "zero" point a sample calculated fromactual values of previous samples. The Raise-Cosine filters are preferred so as tominimize intersymbol interference. The three interpolated sub-band wavelet signals aresupplied to double side-band (DSB) multi-carrier modulator 55 which uses them to1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/0060813modulate three separate carrier signals f,,, f, and f,, where f,, < f, < f, provided bycarrier generator 56. The modulator 55 comprises multipliers 570, 57, and 57, whichmultiply the carrier signals f,,, f, and f, by the three interpolated wavelet signals y",,, y“,and y“,, respectively. The resulting three modulated carrier signals y',,, y’, and y’, areadded together by a summer 58 to form the encoded signal S, for transmission by wayof port 24 to transmission medium 12.At the corresponding decoder 13’ shown in Figure 6, the signal S’, received atport 30 is supplied to each of three bandpass filters 610, 61, and 61, which recover themodulated carrier signals y",,, y", and y",. The recovered modulated carrier signals y",,,y", and y", are demodulated using multi-carrier double sideband (DSB) demodulator 62.A carrier generator 63 generates carrier signals having frequencies f,,, f, and f2, whichare supplied to multipliers 64,, 64, and 64, within the demodulator 62 and whichmultiply the carrier signals f,,, f, and f, by the recovered modulated carrier signals y",.,y", and y",, respectively. The DSB demodulator 62 comprises lowpass filters 65,, 65,,and 65, for filtering the outputs of the multipliers 640, 64, and 64,, respectively, as isusual in a DSB demodulator.The demodulated signals from the filters 65,, 65, and 65, are decimated by 2M,2M and M, respectively, by decimators 66,, 66, and 66, of a decimator unit 66 and theresulting recovered sub-band signals y',,, y’, and y’, each supplied to a corresponding oneof four inputs of a synthesis filter bank 67 which applies to them an Inverse DiscreteWavelet Transform (IDWT) as illustrated in Figure 4B to recover the signal S’, whichcorresponds to the input signal S,. The highpass sub-band wavelet signal y,, which wasnot transmitted, is replaced by a "zero" signal at the corresponding "highest" frequencyinput 68 of the synthesis filter bank 67. The resulting output signal S’, from thesynthesis filter bank 67 is the decoder output signal supplied via output port 34, and isa close approximation of the input signal S, supplied to the encoder 11' of Figure 5.The bandwidth of the transmitted signal S, is wider than that of the original signalS, because each sub-band has upper and lower sidebands. A bandwidth reduction canbe achieved by using Single Sideband (SSB) modulation. To do so, the encoder 11’ ofFigure 5 would be modified by replacing each of the multipliers 570, 57, and 572 by aSSB modulator. Figures 7A, 7B and 7C illustrate operation of the encoder using verysimplified signals and, for convenience of illustration, SSB modulation.Figure 7A shows theifrequency spectrum of a much-simplified input signal S,1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/0060814occupying a bandwidth BW centered at frequency f,_.. As shown in Figure 7B, afteranalysis filtering and interpolation, the input signal Sihas been partitioned into threeinterpolated sub-band signals, y“o, y“, and y"2. It should be noted that, for complex inputsignals, the sub-band signals yo, y, and y, prior to interpolation have a very widespectrum. After upsampling and filtering by the interpolator 52 (Figure 5), sub-bandsignals y“o, y“, and y“, each have a frequency spectrum that is much narrower than thefrequency spectrum of the original signal Si.Following modulation by the DSB mu1ti—carrier modulation means 55, thebandwidths BW,,, BW,, and BW2 of the corresponding modulated carriers y’.,, y’. andy’, are determined by the sampling rate of the input signal Si. The total bandwidth BW,,+ BW, + BW, + 2G may be greater than the bandwidth BW if all sub—bands are used,but may be less if only two are used. The output signal So from the summing means 58has a spectrum which, as shown in Figure 7C, has three lobes, namely a lower frequencylobe centered at frequency f.,, a middle frequency lobe centered at frequency f, and anupper frequency lobe centered at frequency f,. The three lobes are separated from eachother by two guard bands G to avoid interference and ensure that each carriesinformation for its own sub-band only.Simplified versions of the input signal Si, sub-band wavelet signals y,,, y,, y, andy3, sub-band wavelet modulated carriers y’.,, y’, and y’,, and the transmitted signal So,which are similar in the encoders of Figures 2 and 5, are shown in Figures 8 — 10.Figure 8 shows the simplified input signal S,,, (which is not the same as that illustratedin Figure 7A). Figures 9A, 9B, 9C and 9D illustrate the sub-band wavelet signals yo,y,, y, and y3 obtained by DWT processing of the input signal Si. Figures 10A, 10B and10C illustrate the corresponding modulated carrier signals y’,,, y’, and y’, obtained bymodulating the carrier signals f,,, f, and f2 with the sub-band wavelet signals yo, y, andy2, respectively. Because the waveform of the simplified input signal is so smooth, thewavelet signal y, is interpolated by a factor of 2 only, and the wavelet signal yo and y,by a factor of 4 only. This is, of course, for illustration only; in practice the interpolatormay typically range from 1:8 to 1:24. Figure 11 shows the encoded signal S, and Figure12 shows its frequency spectrum which comprises the spectrum components of y’,,, y’,and y’, centered at frequencies of 1000 Hertz, 3000 Hertz and 5000 Hertz, respectively.for a message rate of 750 Hertz. The asymmetric distribution of transmission powerbetween the lower-and high frequency carriers should be noted. It should be appreciated1015202530CA 02264644 1999-02-26WO 98/09383 PCT/CA97/0060815that these simplified signals are for illustration only and that real signals would be muchmore complex.Figures 13A, 13B and 13C illustrate the recovered modulated carrier signals y",,,y”,, and y",, and Figures 14A, 14B and 14C illustrate the recovered sub—band waveletsignals y‘.,, y',, and y‘,. Finally, Figure 15 illustrates the reconstructed signal S’, whichcan be seen to be a close approximation of the input signal S, shown in Figure 8.In the above-described embodiment, the highpass sub-band signal y, is not used,on the grounds that it probably contains negligible energy. If it has significant energy,however, it could be used, and the encoder and decoder modified appropriately.While similar implementations using more than two sub-bands and carriers arepossible, and might be desirable in some circumstances, for most applications, andespecially communication of digital signals via twisted wire subscriber loops, they wouldbe considered complex without significant improvement in performance.It should be appreciated that other kinds of modulation might be used to modulatethe sub-band signals, for example, narrow-band frequency modulation, and so on.It should also be appreciated that the signal source 10 and encoder 11 could beparts of a transmitter having other signal processing means. Likewise, the decoder 13and signal destination 14 could be parts of a corresponding receiver.Although the above—described embodiments of the invention use three or more ofthe sub-band signals, it is envisaged that other applications, such as deep spacecommunications, might use only one or two of the wavelets.INDUSTRIAL APPLICABILITYAn advantage of embodiments of the present invention, which use sub—bandsignals to modulate carriers, is that transmission is reliable because the impairment ofone sub—band in the system would cause the transmission system to degrade only gently.Also, the decoder bandpass filters can be easily designed because there are only a fewfrequency bands used. Moreover, in applications involving data transmission, datasynchronization and clock recovery can be easily achieved in the decoder.It should be noted that the present invention is not limited to transmission systemsbut could be used for other purposes to maintain signal integrity despite noise andattenuation. For example, it might be used in recording of the signal on a compact discor other storage medium. The storage medium can therefore be equated with the20CA 02264644 1999-02-2616transmission medium 12 in Figure 1. It should be appreciated that the encoders anddecoders described herein would probably be implemented by a suitably programmeddigital signal processor or as a custom integrated circuit. 9 ’Although embodiments of the invention have been described and illustratedin detail, it is to be clearly understood that the same are by way of illustration andexample only and not to be taken by way of the limitation, the scope of the presentinvention being limited only by the appended claims.References[Mallat 1989] S. G. Mallat, “A theory of multiresolution signal decomposition: thewavelet representation,” IEEE Trans. on Pattern Recognition and Machine Intelligence,Vol. 11, No. 7, July 1989.[Daubechies 1988] I. Daubechies, “Orthonorma1 bases of compactly supportedwavelets,” Comm. Pure Appl. Math, Vol. 41, pp. 906-966, 1988[Bingham 1990] J.A.C. Bingham, "Multicarrier Modulation for Data Transmission: AnIdea Whose Time Has Come", IEEE Comm. Magazine, Vol. 28, Apr. 1990.[Chow 1991] J.S. Chow, J.C. Tu, and J.M. Cioffi, "A Discrete Multitone TransceiverSystem for I-IDSL Applications", IEEE J. on Selected Areas in Comm., Vol. 9, No. 6,pp. 895-908, Aug. 1991.[Tzannes 1993] M.A. Tzannes, M.C. Tzannes and H.L. Resnikoff, "The DWMT: AMulticarrier Transceiver for ADSL using M-band Wavelets ", ANSI Standard CommitteeTIE1.4 Contribution 93-067, Mar. 1993.[Sandberg 1995] S.D. Sandberg, M.A. Tzannes, "Over1apped Discrete MultitoneModulation for High Speed Copper Wire Communications ", IEEE J. on Selected Areasin Comm., Vol. 13, No. 9, pp. 1571-1585, Dec. 1995.AMENDED SHEET

Claims (60)

1. Apparatus comprising an encoder (11) for encoding a digital input signal for transmission or storage and a decoder (13) for decoding such encoded signal to reconstruct the input signal, the encoder comprising analysis filter bank means (21;51) for analyzing the input signal into a plurality of sub-band signals, each sub-band centered at a respective one of a corresponding plurality of frequencies and the decoder comprising synthesis filter bank means (33;67) complementary to said analysis filter bank means for producing a decoded signal corresponding to the input signal, characterized in that:
the encoder (11) comprises interpolation means (52) interpolating the plurality of sub-band signals to provide a corresponding plurality of interpolated sub-band signals each occupying the same frequency band as the others; and combining means (22,23,25;55,56,58) for combining the interpolated sub-band signals to form the encoded signal for transmission or storage;
and the decoder (13) comprises means (31;61 0, 61 1, 61 2) for extracting the interpolated sub-band signals from the received or recorded encoded signal;
decimator means (66) for decimating each of the plurality of extracted interpolated sub-band signals to remove the interpolated values and applying thedecimated signals to the synthesis filter bank means, the synthesis filter bank means processing the plurality of decimated sub-band signals to reconstruct said input signal.

2. Apparatus as claimed in claim 1 characterized in that the interpolation means (52) comprises a plurality of upsamplers (53 0, 53 1, 53 2) each for upsampling intervals between actual values of a respective one of the sub-band signals and a plurality of filter means (54 0, 54 1, 54 2) for determining values between the actual samples of a respective one of the upsampled sub-band signals and inserting such determined values at the appropriate upsampled intervals.

3. Apparatus as claimed in claim 2, characterized in that the plurality of filter means (54 0, 54 1, 54 2) each comprise a lowpass filter.

4. Apparatus as claimed in claim 3, characterized in that each lowpass filter means (54 0, 54 1 54 2) comprises a Raise Cosine filter.

5. Apparatus as claimed in claim 1, 2, 3 or 4, characterized in that, in the encoder (11), the combining means (22,23,25;55,56,58) frequency-shifts one or more of the interpolated sub-band signals so that the interpolated sub-band signals occupy different frequency bands in the encoded signal.

6. Apparatus as claimed in any preceding claim, characterized in that, in the encoder, the means for combining the sub-band signals to form the encoded signalcomprises:
means (25;56) for providing a plurality of carrier signals;
modulation means (22;55) for using at least some of the interpolated sub-band signals each to modulate a respective one of the plurality of carrier signals;
the decoder further comprises:
means (35;63) for providing a plurality of carrier signals corresponding to those of said encoder;
and the means for extracting the interpolated sub-band signals from the received signal comprises:
means (61 0, 61 1, 61 2) for detecting the modulated carrier signals in the received signal; and demodulation means (32;62) for using at least some of the carrier signals to demodulate the extracted modulated carrier signals to extract a plurality of demodulated sub-band signals corresponding to the plurality of sub-band signals.

7. Apparatus as claimed in claim 6, characterized in that the plurality of carrier signals provided in the encoder (11) have different frequencies, the carrier signals provided in the decoder (13) having the same different frequencies.

8. Apparatus as claimed in any preceding claim, characterized in that the analysis filter bank means (21) comprises a uniform filter bank for producing sub-band signals each having the same bandwidth and the synthesis filter bank means (33) comprises a corresponding uniform filter bank.

9. Apparatus as claimed in any one of claims 1 to 7, characterized in that the analysis filter bank means (51) comprises a multiresolution filter bank for providing sub-bands signals having different bandwidths, the interpolation rates are such that the resulting interpolated sub-band signals all have the same rate, the synthesis filter bank means (67) comprises a corresponding multiresolution filter bank, and the decimator (66) decimates non-uniformly and complementarily to the interpolator means.

10. Apparatus as claimed in claim 9, characterized in that the multiresolution filter bank (51) comprises an octave band filter bank (40A/B/C/D, 41A/B/C/D, 42A/B/C/D,43A/B/C/D) implementing Discrete Wavelet Transform (DWT) to produce a plurality of wavelets as said plurality of sub-band signals, and the synthesis filter bank means (67) comprises an octave band filter bank (Fig. 4B) implementing a corresponding Inverse Discrete Wavelet Transform.

11. Apparatus as claimed in any preceding claim, characterized in that, in the encoder (11), the combining means (23;58) combines a selection of the plurality of interpolated sub-band signals and, in the decoder (13), the synthesis filter bank means (33;67) substitutes zero-level signals for the sub-band signals not selected.

12. An encoder for use in the apparatus according to claim 1, and for encoding an input signal for transmission or storage, comprises analysis filter bank means (21;51) for analyzing the input signal into a plurality of sub-band signals, each sub-band centered at a respective one of a corresponding plurality of frequencies, characterized by:
interpolation means (52) for interpolating the plurality of sub-band signals to provide a corresponding plurality of interpolated sub-band signals each occupying the same frequency band as the others; and combining means (23;58) for combining the interpolated sub-band signals to form the encoded signal for transmission or storage.

13. An encoder as claimed in claim 1, for use in the apparatus of claim 2 and characterized in that the interpolation means (52) comprises a plurality of upsamplers (53 0, 53 1, 53 2), each for interpolating intervals between actual values of a respective one of the sub-band signals and a plurality of filter means (54 0, 54 1, 54 2) each for determining values between the actual samples of a respective one of the upsampled sub-band signals and inserting such determined values at the appropriate intervals.

14. An encoder as claimed in claim 13, characterized in that the plurality of filter means (54 0, 54 1, 54 2) each comprise a lowpass filter means.

15. An encoder as claimed in claim 14, for use in the apparatus of claim 3 and characterized in that each lowpass filter means (54 0, 54 1, 54 2) comprises a Raise Cosine filter.

16. An encoder as claimed in claim 12, 13, 14 or 15, characterized in that the combining means (22,23,25;55,56,58) frequency-shifts one or more of the interpolated sub-band signals so that the interpolated sub-band signals occupy different frequency bands in the encoded signal.

17. An encoder as claimed in any one of claims 12 to 16, characterized in that the means for combining the sub-band signals to form the encoded signal comprises:
means (25;56) for providing a plurality of carrier signals; and modulation means (22;55) for using at least some of the interpolated sub-band signals each to modulate a respective one of the plurality of carrier signals.

18. An encoder as claimed in claim 17, characterized in that the plurality of carrier signals have different frequencies.

19. An encoder as claimed in any one of claims 12 to 18, for use in the apparatus of claim 8 and characterized in that the analysis filter bank means (21) comprises a uniform filter bank for producing sub-bands each having the same bandwidth.

20. An encoder as claimed in any one of claims 12 to 18, for use in the apparatus of claim 9 and characterized in that the analysis filter bank means comprises a multiresolution filter bank (51) for providing sub-bands having different bandwidths, and the interpolation rate is such that the resulting interpolated sub-band signals all have the same rate.

21. An encoder as claimed in claim 20, for use in the apparatus of claim 10 and characterized in that the multiresolution filter bank (51) comprises an octave band filter bank (40A/B/C/D, 41A/B/C/D, 42A/B/C/D, 43A/B/C/D) implementing Discrete Wavelet Transform (DWT) to produce a plurality of wavelets as said plurality of sub-band signals.

22. An encoder as claimed in any one of claims 12 to 21, for use in the apparatus of claim 11 and characterized in that the combining means (23;58) combines a selection of the plurality of interpolated sub-band signals.

23. A decoder (13) for decoding an encoded signal encoded by an encoder (11) according to claim 12, the decoder comprising synthesis filter bank means for providing a decoded signal corresponding to the input signal, the decoder being characterized by:
means (31,32;61 0, 61 1, 61 2,62) for extracting interpolated sub-band signals from the received or recorded encoded signal; and decimator means (66) for decimating the plurality of extracted interpolated sub-band signals to remove interpolated values and applying the resulting plurality of decimated sub-band signals to the synthesis filter bank means, the synthesis filter bank means processing the plurality of decimated sub-band signals to reconstruct said input signal.

24. A decoder as claimed in claim 23, for use with the encoder of claim 16, to decode an encoded signal in which the interpolated signals so that the interpolated sub-band signals occupy different frequency bands in the encoded signal;
characterized in that in the extracting means comprises means (61 0, 61 1, 61 2) for detecting the different frequency bands.

25. A decoder as claimed in claim 23 or 24, characterized in that the extractingmeans comprises:-means (35;63) for providing a plurality of carrier signals corresponding to those of said encoder;
and the means for extracting the interpolated sub-band signals from the received signal comprises:
demodulation means (32;62) for using at least some of the carrier signals to demodulate the extracted modulated carrier signals to extract a plurality of demodulated sub-band signals corresponding to the plurality of sub-band signals.

26. A decoder as claimed in claim 25, for use with the encoder of claim 18, characterized in that the plurality of carrier signals have the same different frequencies as the carrier signals in the encoder.

27. A decoder as claimed in any one of claims 23 to 26, for decoding a signal encoded by the encoder (11) of claim 19, and characterized in that the synthesis filter bank means comprises a uniform filter bank for producing sub-bands each having the same bandwidth.

28. A decoder as claimed in any one of claims 23 to 26, for decoding a signal encoded by the encoder of claim 20, characterized in that the synthesis filter bank means (33;67) comprises a multiresolution filter bank and the decimator means (66) decimates the extracted sub-band signals non-uniformly and complementarily to the interpolation.

29. A decoder as claimed in claim 28, for decoding a signal encoded by the encoder of claim 21, and characterized in that the multiresolution filter bank (67) comprises an octave band filter bank (g', h' Fig. 4B) implementing Inverse Discrete Wavelet Transform (DWT) to process a plurality of wavelets as said plurality of sub-band signals.

30. A decoder as claimed in any one of claims 23 to 29, for decoding an encoded signal encoded by the encoder of claim 22 using fewer than the total number of interpolated sub-band signals generated by the analysis filter bank means, characterized in that the synthesis filter bank means (33;67) substitutes zero-level signals for the unused sub-band signals.

31. A method of encoding an input signal for transmission or storage and decoding such encoded signal to reconstruct the input signal, the encoding of the input signal comprising the steps of using analysis filter bank means to analyze the input signal into a plurality of sub-band signals, each sub-band centered at a respective one of acorresponding plurality of frequencies, characterized in that the encoding comprises the steps of:
interpolating the plurality of sub-band signal to provide a corresponding plurality of interpolated sub-band signals each occupying the same frequency band as the others; and combining the interpolated sub-band signals to form the encoded signal for transmission or storage;
and the decoding of the encoded signal comprises the steps of:
extracting the plurality of interpolated sub-band signals from the received or recorded encoded signal;
decimating each of the plurality of extracted interpolated sub-band signals to remove the interpolated values; and using synthesis filter bank means complementary to said analysis filter bank means, processing the plurality of decimated sub-band signals to produce a decoded signal corresponding to the input signal.

32. A method as claimed in claim 31, characterized in that the interpolation step includes the step of upsampling intervals between actual samples of each of the plurality of sub-band signals and filtering each of the upsampled sub-band signals to determine values between actual values of the upsampled sub-band signals and insert the determined values or the appropriate intervals.

33. A method as claimed in claim 31, characterized in that the filtering is lowpass filtering.

34. A method as claimed in claim 33, characterized in that the filtering uses a Raise-Cosine filter.

35. A method as claimed in claim 31, 32, 33 or 34, characterized in that the step of combining the interpolated sub-band signals comprises the step of shifting one or more of the interpolated sub-band signals so that the interpolated sub-band signals occupy different frequency bands in the encoded signal.

36. A method as claimed in any one of claims 31 to 35, characterized in that thecombining of the interpolated sub-band signals comprises the steps of providing a plurality of carrier signals and using at least some of the interpolated sub-band signals each to modulate a respective one of the plurality of carrier signals, and the extracting of the plurality of interpolated sub-band signals comprises the steps of detecting the modulated carrier signals in the received signal and using a corresponding plurality of carrier signals to demodulate extracted modulated carrier signals.

37. A method as claimed in claim 36, characterized in that the plurality of carrier signals have different frequencies.

38. A method as claimed in any one of claims 31 to 37, characterized in that theanalyzing of the input signal uses a uniform filter bank to produce sub-band signals each having the same bandwidth, and the decoding uses a corresponding uniform filter bank as the synthesis filter bank means.

39. A method as claimed in any one of claims 31 to 37, characterized in that theanalyzing of the input signal uses a multiresolution filter bank to provide sub-band signals having different bandwidths, the interpolation rates are such that the resulting interpolated sub-band signals all have the same rate, the decimation of non-uniform and complementary to the interpolation, and the processing of the decimated sub-band signals uses a corresponding multiresolution filter bank as the synthesis filter bank means.

40. A method as claimed in claim 39, characterized in that the analyzing of the input signal uses an octave band filter bank implementing Discrete Wavelet Transform (DWT) to produce a plurality of wavelets as said plurality of sub-band signals, and the processing of the decimated sub-band signals uses an octave band filter bank implementing a corresponding Inverse Discrete Wavelet Transform.

41. A method as claimed in any one of claims 31 to 40, characterized in that thecombining step combines a selection of the plurality of interpolated sub-band signals and the decoding includes the step of supplying zero-level signals to the synthesis filter bank means to substitute for the omitted sub-band signals.

42. A method of encoding an input signal for transmission or storage comprising the steps of using analysis filter bank means to analyze the input signal into a plurality of sub-band signals, each sub-band centered at a respective one of a corresponding plurality of frequencies, characterized by the steps of:
interpolating the plurality of sub-band signals to provide a corresponding plurality of interpolated sub-band signals each occupying the same frequency band as the others; and combining the interpolated sub-band signals to form the encoded signal for transmission or storage.

43. An encoding method as claimed in claim 42, characterized in that the interpolation comprises the step of upsampling intervals between actual samples of each of the plurality of sub-band signals and filtering each of the upsampled sub-band signals to determine values between actual values of the upsampled sub-band signal and insert the determined values at the appropriate interval.

44. An encoding method as claimed in claim 43, characterized in that the filtering is lowpass filtering.

45. An encoding method as claimed in claim 44, characterized in that the lowpassfiltering uses Raise Cosine filtering.

46. An encoding method as claimed in claim 42, 43, 44 or 45 characterized in that the step of combining the interpolated sub-band signals comprises the step of frequency-shifting one or more of the interpolated sub-band signals so that the interpolated sub-band signals occupy different frequency bands in the encoded signal.

47. An encoding method as claimed in any one of claims 42 to 46, characterized in that the combining step comprises the steps of providing a plurality of carrier signals and using at least some of the interpolated sub-band signals each to modulate a respective one of the plurality of carrier signals, and the decoding step comprises the steps of detecting the modulated carrier signals in the received signal and using a corresponding plurality of carrier signals to demodulate the extracted modulated carrier signals and produce the plurality of sub-band signals for decimation.

48. An encoding method as claimed in claim 47, characterized in that the plurality of carrier signals have different frequencies.

49. An encoding method as claimed in any one of claims 42 to 48, characterized in that the analyzing of the input signal uses a uniform filter bank for producing sub-bands having the same bandwidth.

50. An encoding method as claimed in any one of claims 42 to 48, characterized in that the analyzing of the input signal uses a multiresolution filter bank for providing sub-bands having different bandwidths, and the interpolation rate is such that the resulting interpolated sub-band signals all have the same rate.

51. An encoding method as claimed in claim 50, characterized in that the analyzing of the input signal uses an octave band filter bank implementing Discrete Wavelet Transform (DWT) to produce a plurality of wavelets as said plurality of sub-bandsignals.

52. An encoding method as claimed in any one of claims 42 to 51, characterized in that the combining step combines a selection of the plurality of interpolated sub-band signals.

53. A method of decoding an encoded signal encoded by the method of claim 42 andcomprising a plurality of interpolated sub-band signals, characterized by the steps of:
extracting the plurality of interpolated sub-band signals from the received or recorded encoded signal;
decimating each of the plurality of extracted interpolated sub-band signals to remove interpolated values; and using synthesis filter bank means complementary to an analysis filter bank means used to produce the interpolated sub-band signal, processing the plurality of decimated sub-band signals to produce a decoded signal corresponding to the input signal.

54. A decoding method as claimed in claim 53, for decoding a signal encoded by the method of claim 46, and characterized in that the extraction step comprises the steps of detecting the different frequency bands.

55. A decoding method as claimed in claim 53 or 54, for use in decoding an encoded signal encoded according to the method of claim 47, characterized in that the extraction step comprises the steps of providing a plurality of carrier signals corresponding to those used during encoding, and using at least some of the carrier signals to demodulate extracted modulated carrier signals and provide the plurality of demodulated sub-band signals.

56. A decoding method as claimed in claim 55, for use in decoding an encoded signal encoded by the method of claim 48, characterized in that the plurality of carrier signals have the same different frequencies as the carrier signals used in the encoding of the encoded signal.

57. A decoding method as claimed in any one of claims 53 to 56, for use in decoding a signal encoded according to the method of claim 49, characterized in that the processing step uses a uniform filter bank for producing sub-bands having the same bandwidth.

58. A decoding method as claimed in any one of claims 53 to 56, for decoding a signal encoded according to the method of claim 50 and characterized in that theprocessing uses a multiresolution filter bank to process the sub-band signals having different bandwidths, and the extracted sub-band signals are decimated non-uniformly and at rates corresponding to those used to interpolate the corresponding sub-band signals.

59. A decoding method as claimed in claim 58, for decoding a signal encoded according to the method of claim 51 and characterized in that the processing step uses an octave band filter bank (g', h') implementing an Inverse Discrete Wavelet Transform (DWT) to produce the decoded signal from the plurality of wavelets constituting said plurality of sub-band signals.

60. A decoding method as claimed in any one of claims 53 to 59, for decoding a signal encoded according to the method of claim 52, and characterized in that zero-level signals are applied to the synthesis filter bank means to substitute for the sub-band signals omitted during encoding.