This application is a U.S. National Stage filing under 35 U.S.C. § 371 and 35 U.S.C § 119, based on and claiming priority to PCT/GB2016/054030 for “LOSSLESS BANDSPLITTING AND BANDJOINING USING ALLPASS FILTERS” filed Dec. 21, 2016 and claiming priority to GB Application No. 1225560.0 filed Dec. 21, 2015.
The invention relates to the processing of sampled signals, and particularly to lossless bandsplitting and bandjoining of such signals.
Many applications require a sampled signal to be split into two or more frequency bands to produce subband signals that can be processed or transmitted separately at a lower sampling rate, followed by recombination to produce signal at the full sampling rate. Polyphase filtering networks (including Quadrature Mirror Filters) to perform the splitting and joining have been the subject of extensive research. Signal artefacts potentially introduced by bandsplit methods include passband ripple and aliasing, but designs are known in which the ripple is zero and in which, for transmission applications where the subband signals are presented unmodified to a final bandjoining filter, alias products that exist in the subband signals are cancelled in the final recombination.
The term lossless' is often used in the communications literature to refer to such designs, but in such literature perfect arithmetic is assumed and the designs so labelled may or may not provide exact reconstruction in the presence of arithmetic rounding errors. In this document we shall adopt terminology of the audio literature, wherein ‘lossless’ implies exact bit-for-bit reconstruction of signals that are already quantised. Thus, a lossless decoder must reverse any arithmetic errors or quantisations that are produced by an encoder.
‘Lifting’ techniques have frequently been used to implement lossless processing, and bandsplitting/joining architectures that use lifting have been described by A. R. Calderbank, I. Daubechies, W. Sweldens, and B-L. Yeo, “Wavelet Transforms That Map Integers to Integers”, Applied And Computational Harmonic Analysis 5, 332-369 (1998) with particular reference to FIGS. 4 and 5 therein. For an encoder to split a sampled signal into a low frequency (LF) and a high frequency band (HF) and then for a corresponding decoder to join the bands, such architectures generally require that the encoder and the decoder each implement two finite impulse response (FIR) filters. The filters may be inconveniently long, each needing a number of taps inversely proportional to the width the transition between the LF and HF bands. Also, a 2-FIR design does not provide LF and HF responses that are mirror-images about the half-Nyquist frequency, as to achieve greater symmetry requires at least three FIR filters each in the encoder and decoder.
Another type of bandsplitting and joining in the communications literature uses IIR filtering. IIR filters can generally achieve higher slopes with a given number of arithmetic operations than can FIR filters, but the IIR band splitting and joining filters in the literature do not achieve lossless reconstruction. For example, in Kleinmann T and Lacroix A, “Efficient Design of Low Delay IIR QMF Banks for Speech Subband Coding” in Proceedings of EUSIPCO-96 Eighth European Signal Processing Conference Trieste, Italy, 10-13 Sep. 1996, the reconstructed amplitude response is flat but the group delay increases in the vicinity of the crossover frequency. This scheme would thus not be lossless even if implemented without quantisation errors.
What is needed therefore is an economical IIR architecture that provides lossless reconstruction. For applications where an encoder transmits the LF and HF bands separately to a consumer product, it is particularly desirable to minimise the computational complexity of the decoder.
The invention in a first aspect provides method of splitting an original stream of quantised signal samples having an original sample rate into two output substreams of quantised signal samples having half the original sample rate, the two output substreams representing higher frequency components and lower frequency components of the original stream respectively, the method comprising the steps of:
The feedback is used to create poles in the transfer function which allow good frequency discrimination with few coefficients. Making the poles maximum phase enhances the prior art of Kleinmann and Lacroix by allowing a casual bandjoiner to remove the phase distortions. Operating on the samples in reverse order allows filtering with maximum phase poles to be stably implemented.
Preferably, for any output substream, the transfer function from both intermediate substreams have the same DC gain magnitude. In this way the use of a sum and difference matrix ensures that the bandsplitter directs DC purely to one output and Nyquist frequencies purely to the other.
In some embodiments, the step of matrix filtering comprises
In this way, the bandsplitter according to the invention can process the audio in overall forwards order, whilst operating locally on time reversed blocks. The overlap and discard allows for transients caused when processing of each block starts to have dissipated before reaching the section that affects the bandsplitter outputs.
Preferably, the two output substreams together contain the information required to allow the original quantised stream to be recovered exactly by a suitably initialised bandjoiner.
In this way, the operation can be exactly inverted allowing a system involving bandsplit, lossless transmission of each band, bandjoin to be lossless overall.
It is preferred that no two distinct input streams produce both the same output substreams and residual state in the filters.
In this way, no information about the signal samples is lost in the operation of the bandsplitter because each possible set of outputs is produced by at most one stream of input. Consequently, the bandsplitter can be described as lossless. Filter state needs including in the comparison because filtering spreads the effect of the input in time.
In some embodiments, the step of filtering and matrixing comprises:
In this way, an implementation can use two filtering operations with simple matrixing for greater implementation efficiency. The tradeoff may sometimes run the other way however with low order allpass filters.
Preferably, the matrixing is performed using a sum and difference matrix.
Preferably, the output substreams are derived from the quantised signal by invertible linear processing with no further quantisation.
In this way, the bandsplitter can operate with only one quantisation in the signal path with lower quantisation noise on the bandsplitter outputs.
Since the feedback is derived from the quantisation, if follows that a subsequent process may unambiguously determine the quantised signal, and hence the feedback, from the output substreams. Knowledge of the feedback is important in order that state variables in a bandjoiner can accurately track those in a bandsplitter.
The invention in a second aspect provides a bandsplitter adapted to perform the method of the first aspect.
The invention in a third aspect provides a recorded medium containing data derived in dependence on a high frequency output and on a low frequency output of a bandsplitter according to the second aspect.
In this way, the recorded medium can cater both for consumers who use the bandjoiner to reconstruct a replica of the full bandwidth audio and consumers who do not who enjoy the reduced bandwidth audio.
The invention in a fourth aspect provides a method of joining two subband streams of quantised signal samples each having a subband sample rate, the method furnishing an output stream of quantised signal samples having twice the subband sample rate, the output stream having higher frequency components and lower frequency components represented by the two subband streams respectively, the method comprising the steps of:
In this way, the operation of prior art Kleinmann and Lacroix's bandjoiner is enhanced to ensure it can exactly invert the operation of a bandsplitter according to the invention. Firstly the phase distortion of their prior art bandsplitter bandjoiner combination is removed. Secondly, subband streams produced by a bandsplitter according to the invention inevitably contain quantisation noise but appropriate quantisation within the bandjoining method cancels the noise introduced by the bandsplitting quantisation instead of adding further noise.
Preferably, for any subband stream, the transfer function to both intermediate streams has the same DC gain magnitude. In this way the use of a sum and difference matrix ensures that DC in the output comes purely from one input and Nyquist frequencies purely from the other.
For clarity, we note that if the operation of a bandjoiner can be inverted by a subsequent bandsplitter then the operation of the bandsplitter will also be inverted by the same bandjoiner placed subsequently to the bandsplitter.
In some embodiments the step of matrixing and filtering the two subband streams comprises:
In this way, an implementation can use simple matrixing and two filtering operations for greater implementation efficiency. The tradeoff may sometimes run the other way however with low order allpass filters.
In some embodiments the step of matrixing incorporates quantisation. This operates to invert less preferred bandsplitter embodiments where the matrixing is performed after filtering and incorporates further quantisation.
Preferably, the quantisation included within the signal processing loop is performed by a vector quantiser.
In this way, the bandjoiner can losslessly invert the operation of the preferable bandsplitter embodiments whose output substreams are derived from the quantised signal with no further quantisation.
Preferably, the steps of filtering are characterised by two different allpass responses.
In this way, the bandsplitter discrimination is derived from the extent to which the two allpasses exhibit a differential phase shift of 90 degrees. This leads to effective discrimination with few coefficients.
In some embodiments a first allpass response has coefficients of 1.0 and within 2−15 of 0.527864045 and a second allpass response has coefficients of 1.0 and within 2−15 of 0.105572809.
In some embodiments a first allpass response has coefficients of 1.0, within 2−15 of 0.3644245374 and within 2−15 of 0.01036373471 and a second allpass response has coefficients of 1.0, within 2−15 of 0.8365625224 and within 20.15 of 0.09327361235.
In these ways, bandsplitter transfer functions without ripple are achieved from first or second order allpasses, appropriate for applications where the bandsplit audio will be listened to. Actual implementations will need to round the non-unit coefficients, a tolerance of 2−15 corresponds to rounding to a common coefficient size of 16 signed bits.
The invention in a fifth aspect provides a bandsplitter comprising:
In this way, operation by taking sums and differences of allpass filters allows good discrimination to be achieved with few coefficients. The reverse time order operation allows allpass filters with maximum phase poles to be stably implemented. These can be inverted by a casual allpass filter with minimum phase poles in a corresponding bandjoiner so that no phase or amplitude errors arise from splitting into bands.
In some embodiments the bandsplitter comprises also a quantiser wherein each allpass filter is adapted to furnish an output sample equal to the quantised sum of a previously received sample of the input stream and a linear combination of previously furnished output samples and samples of the input stream received subsequently to said previously sample of the input stream up to and including the current sample.
Preferably, each allpass filter has a second input adapted to receive feedback derived from the outputs of the sum-and-difference unit, the sum-and-difference unit thereby being integrated within the filter.
In this way, the bandsplitter can operate with only one quantisation in the signal path, allowing for the bandsplitter outputs to be lower noise approximations to the high and low frequency components of the original signal respectively.
Preferably, the bandsplitter comprises also a quantiser wherein each allpass filter is adapted to furnish an output sample equal to the quantised sum of a previously received sample of the input stream and a linear combination of feedback samples previously received by the second input of the allpass filter and samples of the input stream received subsequently to said previously received sample of the input stream up to and including the current sample.
In some embodiments one of the two filters is characterised by an infinite impulse response ‘IIR’ response having coefficients 340/32768 and 11941/32768 and the other allpass filter is characterised by an IIR response having coefficients 3056/32768 and 27412/32768.
In this way, coefficients are used for second order allpasses that approximate bandsplitter transfer functions without ripple. These values are rounded for fixed point implementation with 16 bit coefficients.
In a preferred embodiment, the bandsplitter comprises:
In this way, each block of samples is processed in reverse time allowing the maximum phase poles to be stably implemented. However successive blocks can be processed in normal order, allowing the bandsplit to proceed with finite lookahead. The overlap and discard gives time for transients caused as the bandsplitter starts up on each block to disperse before processing samples which contribute to the output. Due to the reverse time processing these transients occur at the end of each block.
The invention in a sixth aspect provides a bandjoiner comprising:
In this way, the lossless characteristic enhances the operation of Kleinmann and Lacroix's bandjoiner by allowing a system consisting of a bandjoiner according to the invention and bandsplitter according to the invention to exactly replicate the input to the bandjoiner. Thus not only is the phase distortion of Kleinmann and Lacroix removed but also the noise introduced by the bandsplitter's quantisations is removed by the bandjoiner's quantisations.
In some embodiments, the sum-and-difference scales one of its inputs by a factor 2 before taking the sum and difference.
In this way the sum and difference matrix can accommodate a factor of two difference in gain on the two inputs, arising from a bandsplitter using a unit determinant sum and difference unit.
Preferably, the bandjoiner comprises also a quantiser wherein each allpass filter is adapted to furnish an output equal to a quantised sum of a sample previously received by the first input and a linear combination of previously furnished output samples and input samples received subsequently to said previously received sample up to and including the current sample.
Preferably, the quantiser is a vector quantiser adapted to jointly quantise signals within both allpass filters.
In this way, the bandjoiner can invert the operation of a bandjoiner operating in the preferable lower noise mode with a single quantisation instead of separate quantisations in the matrixing and filtering.
Preferably, the bandjoiner comprises a vector quantiser having two inputs and two and two outputs,
Preferably, the bandjoiner comprises also a quantiser wherein each allpass filter is adapted to furnish an output equal to a quantised sum of a sample previously received by the first input and a linear combination of previously furnished samples of the feedback and input samples received subsequently to said previously received sample up to and including the current sample.
Preferably, the bandjoiner is configured to process pairs of signals produced by a bandsplitter such that the output of the bandjoiner is a lossless replica of a stream of signal samples that was received by the bandsplitter.
In this way, the lossless operation of the bandjoiner is evident providing the advantages of no phase distortion and no net quantisation noise outlined above.
Preferably, the bandjoiner contains allpass filters having state variables such that if the bandjoiner is operated twice to furnish a first output stream and a second output stream, with identical initialisation of the state variables but with a difference in the input streams received on the two occasions, then either there will be a difference between the first output stream and the second output stream or there will be a difference between the states of the filters after each operation.
In this way, it is established that the bandjoiner does not lose information since distinct inputs are still distinguishable after operation and thus is lossless.
In some embodiments a first allpass filter is characterised by an IIR response having coefficients 340/32768 and 11941/32768 and a second allpass filter is characterised by an IIR response having coefficients 3056/32768 and 27412/32768.
In this way, coefficients are used for second order allpasses that approximate bandsplitter transfer functions without ripple. These values are rounded for fixed point implementation with 16 bit coefficients.
The invention in a seventh aspect provides a transmission system comprising an encoder comprising a lossless bandsplitter and a decoder comprising a lossless bandjoiner,
In this way, the quantisations in the bandsplitter benefit from the use of dither whilst the synchronisation preserves the lossless behaviour of the combined system. Those quantisations are audible if the bandsplit signal is listened to directly.
As will be appreciated by those skilled in the art, the present invention provides techniques and devices for lossless bandsplitting and bandjoining of sampled signals that provide for lossless reconstruction. Further variations and embellishments will become apparent to the skilled person in light of this disclosure.
Examples of the present invention will be described in detail with reference to the accompanying drawings, in which:
AlIpass with Time-Reverse
The prior-art structure of
We note that the sum-and-difference unit 3 inverts the effect of sum-and-difference unit 2, save for an overall scaling by a factor 2. Units 2 and 3 could be identical. The operation of
Thus, the even samples from the de-interleaving unit have been filtered by E0 then by E1 while the odd samples have been filtered by E1 then by E0. Since filtering is commutative it is evident that the effect of
If filters 5 and 6 were straight-through paths, i.e. if E0=1 and E1=1, then signal 10 would have zero response to zero-frequency signal components of the input 11 and similarly signal 9 would have zero response to original signal components at the Nyquist frequency, i.e. half the sampling frequency of the signal 11. Thus very low and very high frequencies would have been separated. Other frequencies are incompletely separated because of the frequency dependent phase shift produced by the “z−1” delay within the de-interleaving unit. It is the purpose of the filters 5 and 6 to compensate approximately this phase shift so that good discrimination between high and low frequencies is maintained over a significant bandwidth.
Thus the response E0 should provide at low frequencies a phase shift relative to that of E1 that approximates a delay of one sample period of the signal 11. Because E0 and E1 are implemented at half the original sample frequency, they must therefore be designed as a pair of allpass filters whose phase difference approximates one half sample period at the local sampling frequency. We shall exhibit suitable designs shortly but firstly we need to address the problem that the combination of bandsplitter and bandjoiner shown in
Conceptually, the unwanted transfer function (E0·E1) can be corrected using an inverse filter (E0·E1)−1. Ignoring for the moment the significant practical difficulty that this inverse filter is acausal, in
Design procedures suitable for generating pairs of allpass filters whose sums and differences provide Butterworth, Chebyshev or elliptic responses are given in: P. P. Vaidyanathan, S. K. Mitra and Y. Neuvo, “A New Approach to the Realization of Low Sensitivity IIR Digital Filters”, IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-34, no. 2, pp. 350-361, April 1986.
For audio applications in which zero ripple is desirable and in which sharp corners are undesirable, we have found the following filters suitable:
First order:
Second order:
Here and subsequently within this document, z−1 represents a delay of one sample at the sub-band sample rate: this is appropriate for implementation but different from the convention used by Kleinmann and Lacroix.
Inserting a scale factor of ½, the lowpass and highpass responses are given by:
lopass=(E1−1+E0−1)/2 hipass=(E1−1−E0−1)/2
It is well known that the time-reverse of an allpass filter is also its inverse. This can be verified for example by substituting z for z−1 in the expression for E0 above, which has the same effect as interchanging numerator and denominator.
We note that reverse-time processing is not necessarily impractical. In some consumer applications, an encoder separates an audio signal into LF and HF components, these being conveyed separately and combined in the consumer's decoder. Pre-encoding of an audio track is normally performed as a file-to-file process, so reverse-time processing is not conceptually more difficult than forwards processing. Hence the acausal allpass filters E1−1 and E0−1 can be implemented as causal filters in reverse time:
lopass=Rev(E1+E0)/2 hipass=Rev(E1−E0)/2
The resulting lowpass and hipass responses are shown in
With suitable initialisation, the above prescription would provide for exact reconstruction by a bandjoiner of a signal presented to a bandsplitter, assuming exact arithmetic throughout. We now review how filtering can be made lossless when using quantised arithmetic.
Lossless Minimum-Phase IIR Filtering
The popular “Direct form I” implementation of a minimum-phase IIR filter is easily made lossless, as was indicated in WO 96/37048 “Lossless Coding Method for Waveform Data”.
The input to
The operation of
Reverse-Time Implementation of Acausal IIR Filters
We now show in more detail how the first order allpass filter E0 and its inverse E0−1 may be implemented, where:
or more compactly:
where k=0.527864045 and in particular |k|<1, which ensures that the denominator of E0 is minimum-phase and E0 is thereby a stable and causal filter that can be implemented by standard means.
We consider the LF path of an encoding-decoding application in which an input sequence of sample values {xi} is presented to E0−1 in an encoder to produce a transmitted sequence {yi}, which in turn is presented to E0 in a decoder. We require that the output of E0 be the identical input sequence {xi}, as expressed in the recurrence relation:
xi=yi-1+yik−xi-1k, i=1 . . . n
To deduce the operation of the E0−1 filter in the encoder, we solve for yi-1:
yi-1=xi−yik+xi-1k, i=n . . . 1
Causality requires the computation of the values {yi} to be performed in order of decreasing i, as indicated by the notation i=n . . . 1 and reflecting the reverse time implementation of filter E0−1. To initialise the computations the encoder needs a value for yn as well as the given signal values {xi, i=1 . . . n}. yn may be chosen arbitrarily, for example zero. The decoder also needs initialisation, a convenient method being for the encoder to transmit the original value x1 along with the filtered values {yi, i=1 . . . n}. The decoder then uses x1 directly as its first output value as well as using it as state initialisation for the remaining computations which run from i=2 onwards.
Given such initialisation the decoder is then able to reconstruct exactly the original signal {xi}, subject only to arithmetic rounding errors and any wordlength truncation in transmission. An exactly similar procedure with k=0.1055728090 may be used to implement E1 and E1−1.
Lossless Reverse-Time Processing
For lossless processing we assume a quantised input sequence {xi} and the results of multiplications by fractional coefficients must be quantised. The recurrence relations above are now replaced by:
xi=yi-1+Qi(yik−xi-1k), i=1 . . . n
where Qi represents quantisation with the same step size as the input sequence {xi}. The transmitted sequence {yi} then also contains values quantised to the same step size. The suffix “i” in “Qi” highlights that the quantisation Q may be different from one sample to another, as for example in a dithered quantiser. However in an encoder-decoder pair, each Qi in the encoder must be identical to the corresponding Qi in the decoder, which in the case of dither would normally be achieved by identical pseudorandom sequence generators, synchronised between encoder and decoder.
It is not required that the quantised values be integer multiples of a step size: sometimes it is advantageous to use a quantiser with a random offset as explained in co-pending patent application PCT/GB2015/050910. Other generalizations include that the signals {xi} and {yi} may be vector-valued, the Qi being vector quantisers.
Blockwise Reverse-Time Encoder Processing
In both the unquantised case and the lossless case, exact reconstruction of the complete output sequence {xn} requires initialisation of the decoder's state eg by the value x1.
With unquantised processing using exact arithmetic, failure to provide correct initialisation causes a transient error proportional to the impulse response of E0, which when E0 is first order will be a decaying exponential and more generally a linear combination including damped sinewaves. This transient error will reduce rapidly as i increases and will normally become insignificant after a few samples or a few tens of samples.
With lossless' quantised processing, incorrect initialisation will cause a similar initial transient error. Once the transient has died down the error becomes noiselike unless and until the states of the decoding filter E0 become synchronised with the states of the encoding. With filter of high order this state synchronisation may never happen, but for the filters E0 of order 2 considered in this document and using appropriate dithered quantisers we have estimated there is a probability of less than 10−12 that synchronisation will not have been achieved after 120 sample periods from the time when the initial transient has died down and the error has become noiselike. For the second-order filters discussed here, an initial transient takes about 30 samples to decay by 96 dB or 45 samples to decay by 144 dB. It follows that these filters settle to a state independent of the initialisation after 165 sample periods with almost complete certainty.
This reasoning may now be applied to reverse-time filtering. If a block of 1165 samples taken from the start of a longer file is filtered in reverse time, the first 1000 filtered samples will thereby be the same, with almost complete certainty, as the first 1000 samples of the whole file when filtered in reverse time. It follows therefore that reverse-time filtering of the whole file is unnecessary: the file may be processed in blocks that overlap by at least 165 samples. The blocks may be processed in any order, in particular in forwards order or in parallel, reverse-time filtering being used within each block and the final 165 samples of each block being discarded. This principle also makes possible the live processing of a stream of samples, subject to a delay introduced by the block processing and overlap.
The estimates of 165 sample is based on an extrapolation of
Second Order Recurrence Relations
For reference the recurrence relations presented previously are extended to second order filtering. Taking E0 as an example, the numeric expression:
can be expressed as:
where k1=0.3644245374 and k2=0.01036373471.
The decoding and encoding equations are now:
xi=yi-2+Qi(k1yi-1+k2yi−k1xi-1−k2xi-2), i=1 . . . n
yi-2=−Qi(k1yi-1+k2yi−k1xi-1−k2xi-2)+xi, i=n . . . 1
corresponding to the conceptual filters E0 and E0−1, respectively. The initialisation conditions for the encoder are that any convenient value, such as zero, may be used for the quantities yn-1 and yn, which are referred to but not computed. The encoder can initialise the decoder by transmitting the original values xi and x2 along with the filtered values {yi, i=1 . . . n}. The decoder then uses x1 and x2 directly as its first two output values as well as using them as state initialisation for the remaining computations which run from i=3 onwards.
Initialisation may alternatively be omitted if correct reconstruction is not required for the first few tens of decoded samples.
Lossless Sum and Difference
In the above discussion of implementing acausual filters we were content for the composition of units 2 and 3 to introduce a scaling of 2. When we move onto lossless operation however, this factor of 2 becomes awkward because we need the inputs to filters 7 and 8 to be exact lossless replicas of the outputs from filters 5′ and 6′. We present a number of ways of dealing with this issue.
The most straightforward approach is to incorporate a scaling by 2 into unit 3 so that it is indeed an exact inverse of unit 2.
Thus unit 2 computes:
and unit 3 computes:
which is a duplicate of unit 2 combined with a scaling by 0.5.
However this implementation is awkward to use as part of a system involving lossless compression of the Lf and Hf signals because when E and O are independently auantised values, L and H are not. Due to the transfer function
having determinant −2, there is mutual information in the L and H outputs (they have a common Isb), and any lossless compression would be inefficient if it did not exploit this redundancy. Yet having to exploit this curious redundancy is an onerous requirement to impose.
To avoid this issue, the sum and difference unit 2 preferably has determinant ±1, a sensible choice being sum and half difference, as follows:
And so unit 3 computes:
The computation of 0.5(O−E) needs quantising, which introduces extra noise into the Hf output of the bandsplitter, but can be done in a lossless manner by:
L=E+O
H=O−Q(0.5L)
And the inverse operation for unit 3 is:
O=H+Q(0.5L)
E=L−O
Integration of Allpass with Lossless Sum and Difference
It is further possible to reduce the amount of quantisation noise in the Lf output by integrating the allpass filtering with the sum and differencing operations. This is particularly beneficial in a system such as described in WO2013186561 where the Lf output of the bandsplitter may be listened to by those who do not have access to bandwidth extension data. It also avoids the need for the extra quantisation in the Hf audio path.
This is illustrated in
And the inverse sum and difference operations 3, 13 and 15 are intended to implement:
In contrast to the last section, these may now be performed with exact arithmetic.
but the quantisation is deferred till after the sum and difference operation 2 and feedback is taken from after an extra inverse sum and difference operation 15. Likewise, filter 17 replaces 6′. The net effect of this is that a vector quantisation is performed inside both allpasses, so that the Lf and Hf signals are separately quantised.
We now consider what conditions need to be satisfied for quantisers 31 to have the negated quantisation error of quantisers 30.
Firstly, consideration needs to be given to situations where two output values are equidistant from an input value. If the quantisers 30 round a tie towards −∞ then quantisers 31 must round a tie towards +∞. (This differs from the situation in
Secondly, supposing the inputs and outputs of
If E and O are both an even multiple of Δ or both an odd multiple of Δ then L will be an even multiple of Δ and H will be a multiple of Δ. But if E and O are have opposite parity, then L will be an odd multiple of Δ and H will be an odd multiple of Δ/2.
So the bandjoiner of
One way of doing this is to add half the quantised value of L before using a quantiser which quantises to integer values of Δ for QH and then subtract it again afterwards. This expansion of operation 31 is shown in
The operation in 13 of adding 0.5L cancels the operation in H of subtracting it and the combined operation simplifies as shown in
An alternative perspective illustrated in
Arithmetic Variations
It will be appreciated that there are numerous ways to rearrange the arithmetic without affecting the essence of the invention.
For example.
This multiplies out to
2 filters with sum and difference operations, have been transformed into 4 filters with related coefficients on all 4 paths between L/H and QLin/QHin. Clearly the essence of the invention is unchanged by such transformations.
Number | Date | Country | Kind |
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1522560.0 | Dec 2015 | GB | national |
Filing Document | Filing Date | Country | Kind |
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PCT/GB2016/054030 | 12/21/2016 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
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WO2017/109495 | 6/29/2017 | WO | A |
Number | Name | Date | Kind |
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20070016417 | Sung | Jan 2007 | A1 |
20080154584 | Andersen | Jun 2008 | A1 |
20100318349 | Kovesi | Dec 2010 | A1 |
20150255078 | Beack | Sep 2015 | A1 |
20150279378 | Craven | Oct 2015 | A1 |
20160042744 | Klejsa | Feb 2016 | A1 |
Number | Date | Country |
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2503110 | Dec 2013 | GB |
9637048 | Nov 1996 | WO |
2014096236 | Jun 2014 | WO |
Entry |
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Kleinmann, Thomas et al., Efficient design of low delay IIR QMF Banks for speech subband coding, 1996 8th European Signal Processing Conference (EUSIPCO 1996), IEEE, Sep. 10, 1996, pp. 1-4 Previously cited in an IDS filed on Jun. 21, 2018. |
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Number | Date | Country | |
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20190013032 A1 | Jan 2019 | US |