Subband Filter Banks Research Articles

Audio codec using adaptive sparse vector quantization with subband vector classification

An audio coder/decoder ("codec") that is suitable for real-time applications due to reduced computational complexity, and a novel adaptive sparse vector quantization (ASVQ) scheme and algorithms for general purpose data quantization. The codec provides low bit-rate compression for music and speech, while being applicable to higher bit-rate audio compression. The codec includes an in-path implementation of psychoacoustic spectral masking, and frequency domain quantization using the novel ASVQ scheme and algorithms specific to audio compression. More particularly, the inventive audio codec employs frequency domain quantization with critically sampled subband filter banks to maintain time domain continuity across frame boundaries. The input audio signal is transformed into the frequency domain in which in-path spectral masking can be directly applied. This in-path spectral masking usually results in sparse vectors. The ASVQ scheme is a vector quantization algorithm that is particularly effective for quantizing sparse signal vectors. In the preferred embodiment, ASVQ adaptively classifies signal vectors into six different types of sparse vector quantization, and performs quantization accordingly. The ASVQ technique applies to general purpose data quantization as well as to quantization in the context of audio compression. The invention also includes a "soft clipping" algorithm in the decoder as a post-processing stage. The soft clipping algorithm preserves the waveform shapes of the reconstructed time domain audio signal in a frame- or block-oriented stateless manner while maintaining continuity across frame or block boundaries. The invention includes related methods, apparatus, and computer programs.

A pitch extraction method using the wavelet transform

One of the reasons why pitch extraction from speech has been difficult is that pitch is nonstationary and changes over a wide range. In most of the conventional methods, it is assumed that speech remains stationary in an analysis frame of fixed width. This essentially produces an extraction error. In order to remedy this point, there have been attempts to apply the wavelet transform to the pitch extraction, where the resolution can be adjusted dynamically on the time–frequency plane [5, 6]. This paper proposes an implementation of pitch extraction based on discrete wavelet transform, which can execute the computation efficiently by a subband filter bank for pitch filtering. Since the subband filter bank contains internal down-sampling, aliasing in the pitch filtering is a problem. In the proposed method, aliasing is avoided by scaling of the input signal. A computer simulation is tried for the test signal and actual speech. The synthesized test signal includes the first three harmonic components, and the pitch frequency is increased exponentially so that the time variation is faster for higher frequencies. It is verified that the pitch can be extracted with an error rate of about ±2% for any pitch frequency. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(6):36–45, 1999

Method and system for adaptive filtering of speech signals using signal-to-noise ratio to choose subband filter bank

A method and system for adaptively filtering a speech signal. The method includes decomposing the signal into subbands, which may include performing a discrete Fourier transform on the signal to provide approximately orthogonal components. The method also includes determining a speech quality indicator for each subband, which may include estimating a signal-to-noise ratio for each subband. The method also includes selecting a filter for filtering each subband depending on the speech quality indicator, which may include estimating parameters for the filter based on a clean speech signal. The method further includes determining an overall average error for the filtered subbands, which may include calculating a mean-squared error. The method still further includes identifying at least one filtered subband which, if excluded from the filtered speech signal, would reduce the overall average error determined, and combining, with exception of the filtered subbands identified, the filtered subbands to provide an estimated filtered speech signal. The system includes filters and software for performing the method.

Optimal construction of subband coders using Lloyd-Max quantizers

A new method is presented for the analysis of the effects of Lloyd-Max quantization in subband filterbanks and for the optimal design of such filterbanks. A rigorous statistical model of a vector Lloyd-Max quantizer is established first, consisting of a linear time-invariant filter followed by additive noise uncorrelated/with the input. On the basis of this model, an expression for this variance of the error of a subband coder using Lloyd-Max quantizers is explicitly determined. Given analysis filters that statistically separate the subbands, it is shown that this variance is minimized if the synthesis filters are chosen, which mould achieve perfect reconstruction in lossless coding. The globally optimum of such a filterbank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. An alternative design method is also evaluated and optimized. In this, the errors correlated with the signal are set to zero, leaving a random error residue uncorrelated with the signal. This design method is optimized by choosing the analysis filters so as to minimize the random error variance. The results are evaluated experimentally in the realistic setting of a logarithmically split subband image coding scheme.

Divide-and-conquer 2-D phase retrieval using subband decomposition and filter banks

The two-dimensional (2-D) discrete phase-retrieval problem is to reconstruct a discrete-time signal whose support is known and compact from the magnitude of its discrete Fourier transform. We show how a subband decomposition of this problem can be performed using filter banks. The result is a series of smaller 2-D phase-retrieval problems whose solutions are the phases of the original problem in different frequency bands. The 2-D phase-retrieval problem is first mapped to a one-dimensional (1-D) phase-retrieval problem, and the subband decomposition is applied to this problem to decompose it into smaller 1-D problems, each of which can be viewed as a smaller 2-D problem. This is more flexible than performing the decomposition directly in 2-D. The filter must have finite support, zero phase, and be approximately halfband. While these results can also perform subband decomposition of any 1-D phase-retrieval problem, the general lack of uniqueness for 1-D phase retrieval creates problems in reassembling the solutions to the smaller 1-D problems.

The fast Haar transform

Wavelet theory and its relatives (subband coding, filter banks and multiresolution analysis) have become hot this last decade. Like the sinusoids in Fourier analysis, wavelets form bases that can decompose (analyze) and reconstruct (synthesize) signals and images. As a by-product, we obtain the accompanying processing (filtering, compression, denoising, etc.). But unlike the sinusoids, there seems to be an inexhaustible variety of different wavelet types: orthogonal, biorthogonal, spline, smooth, rough, short, long and so forth. We construct the simplest wavelet algorithm possible, called the fast Haar transform (FHT). We then indicate how this may be generalized to other fast wavelet algorithms.

Optimal construction of filter banks for subband coding of quantised signals

A new general method is presented for the analysis of the effects of quantisation and transmission noise in subband filter bank coders. Using general statistical noise characterisation, the filter banks are obtained, which are optimal in the sense of minimising the variance of the difference of the reconstructed signal from the original. It is shown that these are not identical to those achieving perfect reconstruction in lossless coding. A general method is described for the optimal selection of the synthesis filters if the analysis filters and quantisers are given. Assumming the use of these optimal synthesis filters, a method is developed for the determination of the optimal analysis filters and the optimal bit allocation to the subbands. The effects of quantisation on perfect reconstruction filter banks are analysed next, and an explicit expression is determined for the quantiser noise-to-signal ratio for such banks. Given arbitrary quantisers, the analysis filters which are optimal in the sense of minimising the output noise power are obtained. Finally, the jointly optimal selection is determined for the analysis filters and the bit allocations of the subbands. It is seen that this selection is identical to that determined for the theoretically optimal filter banks.

Layered blind deconvolution using subband filter banks

A blind deconvolution method using the concept of subband filter banks has been proposed. This method makes possible the speedy convergence of solution, due to estimation of supports of the reconstructed images by a deconvolution in the lower layer. We apply the method to blind deconvolution by a simulated annealing algorithm and confirm its usefulness.

A novel MPEG-2 audio decoder with efficient data arrangement and memory configuration

The paper describes a novel MPEG-2 audio decoder with a new modified scheme. In the techniques of intelligent data arrangement, the complexity of the multichannel decoding can be largely reduced. In the modified decoding scheme, the bottleneck computation module can be reduced to a quarter of the size of the original. Also, the major memory storage only requires half the size of the standard synthesis subband filterbank.

Analytical optimization of CQF filter banks

The optimization of subband filter banks for signal and image coding is normally dealt with by numerical means. It is shown that this optimization can be done analytically in the case of the prototype four-tap causal conjugate quadrature filter (CQF). The coding gain and aliasing energy are considered in the optimization. Using parametrizations of the prototype filter coefficients, it was found that the optimal filter is the regular Daubechies D/sub 2/ wavelet filter.

Scalable implementation scheme for multirate FIR filters and its application in efficient design of subband filter banks

A scalable implementation scheme for multirate finite impulse response (FIR) filters is presented in this paper. The implementation scheme can reduce the time and area cost of a multirate FIR filter simultaneously. According to the throughput requirement, the proposed scheme achieves a minimum-area design with specified speed. Furthermore, by employing the scalable implementation scheme, we also propose an efficient design technique for subband filter banks.

Optimal PR-QMF Design for Subband Image Coding

A multivariable optimization problem is set to design 2-band PR-QMFs. The energy compaction, aliasing energy, unit step response, zero-mean high-pass filter, uncorrelated subband signals, constrained nonlinearity of the phase-response, and the given input statistics are simultaneously considered in the proposed optimal filter design technique. A set of optimal PR-QMF solutions and the optimization criteria along with their objective performance is given for comparison. This PR-QMF design approach leads to an input driven adaptive subband filter bank structure. It is shown that the optimal filters objectively outperform the well known fixed PR-QMFs in the literature. The proposed PR-QMF design technique provides the mathematical tools for subjective performance improvements in subband image and video coding applications.

A generalized structural subband decomposition of FIR filters and its application in efficient FIR filter design and implementation

It is shown that any FIR (finite-impulse-response) transfer function can be realized as a parallel connection of interpolated FIR (IFIR) sections consisting of a cascade of a subfilter with a sparse impulse response and an FIR interpolator which fills in the missing samples of the corresponding subfilter. The set of interpolators can be realized as a subband filter bank, and as a result, each IFIR section contributes to the overall frequency response essentially within a given band of frequencies. The proposed decomposition can be considered as a generalization of the polyphase decomposition. It results in a computationally efficient structure in sampling rate alteration applications and also leads to faster FIR filter design algorithms. Examples are included to demonstrate the improvements in the speed of least-squares and minimax design algorithms based on the suggested structure. >

Time-frequency localization in transforms, subbands, and wavelets: a critical review

In many still-image and video processing applications, the time-frequency localization properties of the decomposition technique are an important consideration. While bandwidth compression of the image requires operators with good localization in frequency, spatial features such as edge preservation demand a high degree of localization in time (or the spatial variable). These requirements compete with each other and one is secured at the expense of the other. The classical "uncertainty" principle in the continuous-time domain provides the back drop for this trade-off. Our purpose is to review recent extensions of this principle to the discrete-time case and to develop optimum wave forms. We review common features of block transforms, subband filter banks, and wavelets, and demonstrate how the discrete uncertainty can be used to evaluate these decomposition methods. In particular, we evaluate the trade-off between localization in time and in frequency for several proposed signal decomposition structures.

Performance evaluation of subband coding and optimization of its filter coefficients

In this paper, two analytical methods for evaluating the coding efficiency of subband coding are proposed, and optimization of filter coefficients of the perfect reconstruction FIR filter banks is considered, based on a new performance measure called unified coding gain. First, matrix representation of the subband coding in the time domain is considered, and conventional subband filter banks are classified into orthogonal ones such as the QMF and nonorthogonal ones such as the SSKF. For the orthogonal filter banks, the coding gain shown by Jayant and Noll is introduced, and their theoretical performance evaluation is carried out. However, this first method cannot be applied to nonorthogonal filter banks any longer because the coding gain is defined on the assumption of filter orthogonality. Therefore, an optimum bit allocation problem for subband coding is considered, and the unified coding gain, which can be applied to arbitrary subband filter banks, is derived as a new performance measure to take the place of the coding gain. This second method enables us to estimate the coding efficiency of arbitrary transform techniques as well as the subband approaches, and its result suggests that the SSKF(5 × 3) outperforms the QMF as long as the number of subbands is not too large, even though its filter length is much shorter. This result encourages us to find filter coefficients that maximize the unified coding gain according to filter length. In addition, new perfect reconstruction FIR filter banks which have not only low computational complexity but also good energy compaction properties are presented.

Design of HDTV subband filterbanks considering VLSI implementation constraints

The design of a subband filter bank for encoding high-definition television (HDTV) signals at 140 Mb/s is presented. Considering filter reconstruction errors, quantization errors, signal statistics, and VLSI implementation constraints in the filter design, quadrature mirror filters (QMFs) are found to be most appropriate. As a result, two-dimensional QMFs with 10 coefficients for vertical and 14 coefficients for horizontal filtering are proposed. A compact VLSI implementation is possible by filter architectures utilizing the special features of QMFs. The timing constraints can be relaxed by the use of polyphase filter structures for decimation and interpolation. Utilization of the symmetry property of QMFs reduces the arithmetic hardware expense approximately by a factor of two. By taking advantage of the special VLSI architecture and optimization of the circuit technique, a one-chip realization for each, the analysis and synthesis filter bank of the luminance components can be achieved in a 1- mu m CMOS technology. A second pair of filter-bank chips is required for the two chrominance components.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Video subband VQ coding at 64 kbit/s using short-kernel filter banks with an improved motion estimation technique

A motion compensated interframe prediction (MCIP) coder incorporating short-kernel subband filter-banks with an improved motion estimation technique is described. The coder is based on two-dimensional subband decomposition of the error image obtained after motion compensated interframe prediction. The luminance and chrominance subbands, generated after the decomposition process, form image vectors which are then quantized using vector quantization. The block matching method works well with low velocities and low noise content in the image frames. For a motion compensation estimation algorithm to cope with higher activity image frames, it is important that rapid movements, having high-amplitude motion vectors, are effectively recognized. It is also essential that the motion estimation performance does not degrade due to noise in the previously decoded frame. To achieve this, a combination of phase correlation and block search methods is applied sequentially to a hierarchy of low-pass filtered and subsampled images, while the motion vectors are progressively refined at each step of the process. Details of the proposed coding algorithm and simulation results operating at 64 kbits/s are presented.