Perfect reconstruction recursive QMF banks for image subband coding

The authors have experimented with a variety of analysis/synthesis systems in the presence of quantization. The systems were block discrete Fourier transform (DFT), block DFT with trapezoidal windowing, block discrete cosine transform, Hanning windowed short-time Fourier transform (STFT) oversampled by a factor of two, Kaiser windowed STFT oversampled by a factor of four, quadrature mirror filter (QMF) banks, perfect-reconstruction QMF banks, pseudo-QMF banks, and Princen-Bradley filter banks. All systems were evaluated for speech compression; a subset was evaluated for image compression. It is shown that for speech the more sophisticated systems (e.g., QMF) provide the best objective performance, but comparable subjective performance can be obtained at a fraction of the complexity using simpler systems (e.g. pseudo-QMF and Princen-Bradley filter banks). For images, a tree-structured QMF bank did not perform well for 16*16 frequency bands when compared to block-oriented analysis/synthesis systems. >

A proficient approach to the design of Quadrature Mirror Filter (QMF) Bank is studied and an algorithm is offered for straightforward accomplishment of QMF bank with near perfect reconstruction. Objective function is built upon perfect reconstruction condition. The cutoff frequency is repetitively varied to adjust the filter coefficients using the anticipated algorithm and reconstruction error is minimized. Using the optimal value of cutoff frequency the prototype filter is designed and other filters of the bank is considered from that single prototype filter. Kaiser and Dolph-Chebyshev window functions are used to investigate the betterment of the design method. The performance of the projected design method are evaluated in terms of computation time required i.e. CPU time, Perfect Reconstruction Error (PRE), Magnitude Square Error (MSE) and Number of Iterations (NOI). The proposed algorithm is simple, easy to implement, and linearly converges to optimal solution. Finally, the sub-band decomposition of an audio signal is done using the filter bank.

A review is presented first of the evolution of transmultiplexers since about 1966, in the context of a long progression of theoretical advances and developments leading to recent proposals to fundamentally improve OFDM type systems using principles of perfect reconstruction filter (PRF) banks. The equivalence of transmultiplexers to OFDM type multi-user systems is discussed. The desirable goals for performance and implementation of transmultiplexers or multiband, multiuser communication systems that are addressed and met in this paper using filter bank trees are set down. Then modifications and extensions are presented of the designs and architectures of wavelet packet based synthesis and analysis pairs of filter bank trees (Sablatash and Lodge in Digital Signal Process 13: 58–92, 2003) that can be used as transmultiplexers. These exhibit a number of advantages over the previous designs and address three shortcomings of the designs used to illustrate basic principles in Sablatash and Lodge (Digital Signal Process 13:58–92, 2003). The first of these is the asymmetry of the magnitude frequency responses of the multiplexer channels, which is addressed using a symmetric design for a lowpass and highpass quadrature mirror filter (QMF) pair described herein. The second is the problem of minimizing the total delay of the signal in passing through the analysis and synthesis filter banks. This is addressed using an architecture involving DFT polyphase synthesis filter banks to replace the wideband VSB filters at the roots of the two identical synthesis filter bank trees, but results in the multiplexer having fewer levels. In this way a tradeoff is effected of lower delay and complexity with fewer levels of bandwidth on demand. At the receiver matching DFT polyphase analysis filters and the other matching analysis filters are implemented. The third shortcoming is the difficulty in designing a synchronization scheme if the filters in the synthesis and analysis filter banks have non-linear phase. This is addressed by designing linear phase filters that do not affect the ISI to any significant degree for communication purposes, although exact perfect reconstruction is lost, but greatly ease and improve the design of the synchronization scheme. Relationships of this paper and its advantages over recent research studies and IEEE 802.22 standards proposals using PR filter banks for multi-user systems to greatly improve on OFDM systems are discussed.

An iterative approach for minimax design of multidimensional quadrature mirror filters

Describes a perfect-reconstruction two-channel QMF (quadrature mirror filter) bank, in which the analysis and synthesis filters have linear phases. First, a technique for designing filter banks is presented. Next, the results of two examples demonstrate that the method can lead to good filters although its procedure is very simple; also, this yields filters without multipliers such as the SSKF (symmetric short kernel filter) bank. >

Scene adaptive coders are constituted by the cascade of a linear transform, scalar quantization, entropy coding and a buffer controlled by a feedback loop for bit rate regulation. The main contribution of this paper is to derive an analytical criterion evaluating the performances of any perfect reconstruction linear transform in the frame of scene adaptive coding. This criterion is, thereafter, used in order to optimize linear multiresolution transforms. The optimization adapts the filters parameters to the codec features and to the statistics of the 2-D sources; so, the authors call these transforms adapted multiresolution transforms (AMTs). The transforms under study are implemented by a cascade of separable perfect-reconstruction (PR) FIR two-band filter banks that can change at each resolution level. Two types of filter banks are envisaged: the PR orthogonal quadrature mirror filter (QMF) bank, which allows to implement the orthogonal AMT and the PR linear-phase filter (LPF) bank, which implements the biorthogonal AMT. They perform the optimization of the filters in their factorized lattice form, taking the finite length of the multipliers into account. Their criterion also allows them to show the performances achieved by these two linear multiresolution transforms compared to other linear (multiresolution) transforms. >

This paper proposes the use of conjointly time-frequency well localized filters that constitute a perfect reconstruction quadrature mirror filterbank. The time-frequency measure to determine optimality is the product of a filter's time and frequency variances, which has already been proposed. An in depth analysis of parameter selection and novel use of polynomial fitting to ensure perfection reconstruction of the optimal quadrature mirror filterbank are provided in this paper. The output of the separably extended 2-D analysis filters of the optimized 1-D perfect reconstruction quadrature mirror filter-bank illustrates the best space-frequency localized decomposition of the original image.

The design of two channel linear phase quadrature mirror filter (QMF) banks is considered with constraints on the peaks of the reconstruction error and that of the subband filter ripple sizes. We further considered the design specification without explicitly specified transition band for the subband filters. An iterative algorithm is proposed to design QMF banks that can incorporate with various design constraints. We have suggested the possible design tradeoff between transition band bandwidth and the ripple size of the subband subband filter and/or the reconstruction error. Various design examples are presented to illustrate the versatility of the digital QMF banks obtained by the proposed design method. The algorithm is proved to converge and was found to converge efficiently in all the simulations.

The design process is reduced to designing the filter bank to satisfy a set of conditions and it is known that the reconstructed signal always possesses some alias and distortion. It is the present objective to find the necessary and sufficient conditions on the filters so that the resulting QMF (quadrature mirror filter) bank cancels most alias components. Having found these conditions, the author suggests an algorithm to design the PAC (partial alias cancellation) QMF bank. Examples are given to demonstrate the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The perfect reconstruction cosine/sine-modulated filter banks belonging to the class of modulated filter banks have been studied extensively due to their attractive features (simple structure, analysis and synthesis filters are of equal length, low computational complexity), and consequently, they have received a great interest in audio coding applications. In fact, they are employed in the international speech and audio coding standards and proprietary audio compression algorithms. The oddly and evenly stacked modified discrete cosine transform (MDCT) and the corresponding modified discrete sine transform (MDST), the modulated lapped transform (MLT), the extended lapped transforms (ELTs), and their biorthogonal versions are real-valued cosine/sine-modulated filter banks satisfying the perfect reconstruction property. The modulated complex lapped transform (MCLT) is the complex-valued filter bank whose real part is the MLT or equivalently, the oddly stacked MDCT, and the imaginary part is the oddly stacked MDST. In this chapter, definitions, general properties, and matrix representations of the MDCT/MDST, MLT, ELT, and MCLT filter banks are presented. In order to an analysis/synthesis filter bank be perfect reconstruction, the necessary and sufficient conditions imposed on the analysis and synthesis windowing functions play an important role. Therefore, additionally the windowing procedure and perfect reconstruction (biorthogonal) conditions in the case of identical and (nonidentical) analysis and synthesis windowing functions, design of a windowing function including definitions of commonly windowing functions used in audio coding applications, adaptive switching of transform block sizes and windowing functions, and general perfect reconstruction conditions for the ELT filter bank with multiple overlapping factor both for the orthogonal and biorthogonal cases are derived and/or discussed in detail.

A new approach to the design of M-channel pseudo quadrature mirror filter (QMF) banks is presented. The analysis and synthesis filters are cosine-modulated versions of the prototype filters. The prototype filter is constrained to be a linear-phase spectral-factor of a 2M/sup th/ band filter. As a result, the reconstructed signal has no amplitude nor phase distortions. The only error at the output is aliasing, which is comparable to the stopband attenuation of the prototype filter. Using this approach, it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of 100 dB. Consequently, the resulting reconstruction error is also on the order of -100 dB. An example is included to demonstrate the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper describes a two channel linear phase quadrature mirror filter bank using Kekre's matrix. It has been derived mathematically that the rows of the Kekre's second order matrix satisfies the conditions for perfect reconstruction. The filters obtained from the Kekre's matrix satisfies the aliasing cancellation conditions and the distortion transfer function is a all pass filter with linear phase response. It is shown that when a sampled speech signal is passed through the filter the signal experiences a one sample delay without any change in amplitude.

The relationship between block digital filtering and quadrature mirror filter (QMF) banks is explored. Necessary and sufficient conditions for alias cancellation in QMF banks are expressed in terms of an associated matrix, derived from the polyphase components of the analysis and synthesis filters. These conditions, called the pseudocirculant conditions, make it possible to unite QMF banks with the framework of block digital filtering directly. Absence of amplitude distortion in an alias-free QMF bank translates into the 'losslessness' property of the pseudocirculant matrix involved. >

A new designing method for uniform filter banks using all-pass filters is presented. This method is based on the two-stage filter bank structure using all-pass filters. By using this method, the authors realized a continuous soft-band property for polyphase filters and analysis filter banks. Moreover, the realization of synthesis filter banks is given. which in cascade with analysis filter banks eliminates aliasing and amplitude distortions of the whole system. An example is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A structure for analog-to-digital (A/D) conversion capable of attaining high resolution and high speed using lower-resolution, lower-speed A/D converters is presented. The structure is based on quadrature mirror filter (QMF) banks, except that the analysis filter bank is a switched-capacitor circuit whereas the synthesis bank is a digital filter circuit. The structure incorporates the advantages of subband coding, and considerably reduces the effect of mismatches among the low-resolution A/D converters. An illustrative example and experimental results verifying the good performance of the proposed approach are included. >