Analysis of Wavelet Transform Design via Filter Bank Technique

The technique of filter banks has been extensively applied in signal processing in the last three decades. It provides a very efficient way of signal decomposition, characterization, and analysis. It is also the main driving idea in almost all frequency division multiplexing technologies. With the advent of wavelets and subsequent realization of its wide area of application, filter banks became even more important as it has been proven to be the most efficient way a wavelet system can be implemented. In this chapter, we present an analysis of the design of a wavelet transform using the filter bank technique. The analysis covers the different sections which make up a filter bank, i.e., analysis filters and synthesis filters, and also the upsamplers and downsamplers. We also investigate the mathematical properties of wavelets, which make them particularly suitable in the design of wavelets. The chapter then focuses attention to the particular role the analysis and the synthesis filters play in the design of a wavelet transform using filter banks. The precise procedure by which the design of a wavelet using filter banks can be achieved is presented in the last section of this chapter, and it includes the mathematical techniques involved in the design of wavelets

Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filter banks

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A new multichannel spectral factorisation algorithm for parahermitian polynomial matrices

A novel multichannel spectral factorization algorithm is illustrated in this paper. This new algorithm is based on an iterative method for polynomial eigenvalue decomposition (PEVD) called the second order sequential best rotation (SBR2) algorithm [1]. By using the SBR2 algorithm, multichannel spectral factorization problems are simply broken down to a set of single channel problems which can be solved by means of existing one dimensional spectral factorization algorithms. In effect, it transforms the multichannel spectral factorization problem into one which is much easier to solve. The proposed algorithm can be used to calculate the approximate spectral factor of any parahermitian polynomial matrix. Two worked examples are presented in order to demonstrate its ability to find a valid spectral factor, and indicate the level of accuracy which can be achieved

Low Delay Filter Banks with Perfect Reconstruction

The design of modulated filter banks with a low system delay and with perfect reconstruction will be shown. The filter lengths K can be chosen arbitrarily. The well known orthogonal filter banks have a system delay of K - 1 samples. The proposed filter banks can reduce this delay to N - 1 samples, where N is the number of bands. The design method uses a decomposition or factorization of the polyphase matrix into cascades of simple matrices. Several factorizations with different properties will be shown. A factorization will be introduced which is more general and needs fewer multiplications than previous approaches (K/2 + N). The resulting filter banks can have analysis and synthesis frequency responses that can be made different from each other, leading to biorthogonal filter banks. An optimization algorithm for the frequency response of the resulting filter banks will be given. Examples show the feasibility of designing even big filter banks with many bands with low system delay and high stopband attenuation