Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided

Design of FIR paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition

The problem of paraunitary filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), paraunitary filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimisation scheme that maximises the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infiniteorder principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios

A novel insight to the SBR2 algorithm for diagonalising Para-Hermitian matrices

The second order sequential best rotation (SBR2) algorithm was originally developed for achieving the strong decorrelation of convolutively mixed sensor array signals. It was observed that the algorithm always seems to produce spectrally majorized output signals, but this property has not previously been proven. In this work, we have taken a fresh look at the SBR2 algorithm in terms of its potential for optimizing the subband coding gain. It is demonstrated how every iteration of the SBR2 algorithm must lead to an increase in the subband coding gain until it comes arbitrarily close to its maximum possible value. Since the algorithm achieves both strong decorrelation and optimal subband coding, it follows that it must also produce spectral majorisation. A new quantity $\gamma$ associated with the coding gain optimization is introduced, and its monotonic behaviour brings a new insight to the convergence of the SBR2 algorithm

Cyclic-by-row approximation of iterative polynomial EVD algorithms

A recent class of sequential matrix diagonalisation (SMD) algorithms have been demonstrated to provide a fast converging solution to iteratively approximating the polynomial eigenvalue decomposition of a parahermitian matrix. However, the calculation of an EVD, and the application of a full unitary matrix to every time lag of the parahermitian matrix in the SMD algorithm results in a high numerical cost. In this paper, we replace the EVD with a limited number of Givens rotations forming a cyclic-by-row Jacobi sweep. Simulations indicate that a considerable reduction in computational complexity compared to SMD can be achieved with a negligible sacrifice in diagonalisation performance, such that the benefits in applying the SMD are maintained

A novel insight to the SBR2 algorithm for diagonalising Para-Hermitian matrices

The second order sequential best rotation (SBR2) algorithm was originally developed for achieving the strong decorrelation of convolutively mixed sensor array signals. It was observed that the algorithm always seems to produce spectrally majorized output signals, but this property has not previously been proven. In this work, we have taken a fresh look at the SBR2 algorithm in terms of its potential for optimizing the subband coding gain. It is demonstrated how every iteration of the SBR2 algorithm must lead to an increase in the subband coding gain until it comes arbitrarily close to its maximum possible value. Since the algorithm achieves both strong decorrelation and optimal subband coding, it follows that it must also produce spectral majorisation. A new quantity $\gamma$ associated with the coding gain optimization is introduced, and its monotonic behaviour brings a new insight to the convergence of the SBR2 algorithm

Polynomial eigenvalue decomposition for multichannel broadband signal processing

This article is devoted to the polynomial eigenvalue decomposition (PEVD) and its applications in broadband multichannel signal processing, motivated by the optimum solutions provided by the eigenvalue decomposition (EVD) for the narrow-band case [1], [2]. In general, the successful techniques from narrowband problems can also be applied to broadband ones, leading to improved solutions. Multichannel broadband signals arise at the core of many essential commercial applications such as telecommunications, speech processing, healthcare monitoring, astronomy and seismic surveillance, and military technologies like radar, sonar and communications [3]. The success of these applications often depends on the performance of signal processing tasks, including data compression [4], source localization [5], channel coding [6], signal enhancement [7], beamforming [8], and source separation [9]. In most cases and for narrowband signals, performing an EVD is the key to the signal processing algorithm. Therefore, this paper aims to introduce PEVD as a novel mathematical technique suitable for many broadband signal processing applications

Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"

In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R (z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow the notation in Weiss (2018)

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Application of symmetric orthogonal multiwavelets and prefilter technique for image compression

Multiwavelets are new addition to the body of wavelet theory. There are many types of symmetric multiwavelets such as Geronimo-Hardin-Massopust (GHM) and Chui-Lian (CL) multiwavelets. However, the matrix filter generating the GHM system multiwavelets does not satisfy the symmetric property. For this reason, this paper presents a new method to construct the symmetric orthogonal matrix filter, which leads to the symmetric orthogonal multiwavelets (SOM). Moreover, we analyze the prefilter technique, corresponding to the symmetric orthogonal matrix filter, to get a good combining frequency response. To prove the good property of SOM in image compression application, we compared the compression effect with other writers' work, which was in published literature.Facultad de Informátic

Cyclic-by-Row Approximation of Iterative Polynomial EVD Algorithms

Abstract-A recent class of sequential matrix diagonalisation (SMD) algorithms has been demonstrated to provide a fast converging solution to iteratively approximating the polynomial eigenvalue decomposition of a parahermitian matrix. However, the calculation of an EVD, and the application of a full unitary matrix to every time lag of the parahermitian matrix in the SMD algorithm results in a high numerical cost. In this paper, we replace the EVD with a limited number of Givens rotations forming a cyclic-by-row Jacobi sweep. Simulations indicate that a considerable reduction in computational complexity compared to SMD can be achieved with a negligible sacrifice in diagonalisation performance, such that the benefits in applying the SMD are maintained