Filter Bank Structure Research Articles

Resonator based logarithmic filter banks

The paper provides a technique to design and approximate computationally efficient digital filter banks whose centre frequencies are spaced logarithmically. The design procedure consists of two steps: The design of ‘mother’ filter banks and the frequency windowing processing for the final filter banks. The resonator with the purely imaginary transfer function on the unit circle is treated as the basic element of the mother bank and the frequency interpolating filter bank structure is applied. Different pole-zero structures are studied and an infinite filter bank is explored from the theoretical point of view. The outputs of the mother filter banks are weighted and summed to produce the final banks with significantly improved responses. Linear programming is applied to find the optimal weighting coefficients, and the experiments for a variety of windows are made with a discussion of the results and some tradeoffs for window selection. The results show that these filter banks have good frequency response and allow control of crossover gain, and they are useful for voice and music analysis and tone receivers.

The discrete wavelet transform: wedding the a trous and Mallat algorithms

Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Low-complexity subband coding of still images and video

In many applications involving storage and transmission of digital images, there is an explicit need for data compression. Subband coding has emerged as one suitable technique for satisfying this need. Initially, image subband coders were based on FIR filter banks employing the quadrature mirror filters (QMF) of Johnston. To reduce the complexity associated with these subband coders, we have introduced image subband coders based on two types of IIR filter banks. The first is a tree structured filter bank, whereas the other is a fully parallel construction. The computational complexity ofthese filter banks is examined. The computational complexity of the llR-based structures is significantly lower than their FIR counterparts. Furthermore, we introduce multiplier-free IIR filter banks realizing even further complexity reductions. For the bit-efficient representation of the subband signals of both our still image and video coders, we propose a simple scheme similar to the ones employed for DCT-based coding in the CCITT H.261 recommendation and the emerging ISO/JPEG standard. In demonstrating the performance of our coders, we present simulation results at less than 0.5 bits per pel for still image coding and 64 to 200 kbps for coding of video. The performance of our low-complexity IIR structures is found to be comparable to structures based on FIR filters.

Resonator-based filter-banks for frequency-domain applications

The filter-bank structure proposed is based on a digital simulation of a singly terminated ladder filter. This filter bank can also be arrived at from a filter described by G Peceli (1989) and represents an extremely hardware efficient structure, having a complexity of O(N). The main application examined is adaptive line enhancement. The filter-bank-based line enhancer is shown to have the necessary conditions for global convergence and to yield uncorrelated sinusoidal enhanced outputs that are undistorted versions of the corresponding frequency components of the input. A number of additional possible applications for the filter-bank are described. These include the tracking of periodic signals, subband coding, frequency-domain adaptive noise-cancellation, and frequency-domain processing of signals from phased arrays.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of an efficient parallel IIR filter bank to image subband coding

The principle of subband coding has recently been successfully applied for the purpose of image data compression. The analysis/synthesis filter banks and the subband signal encoder/decoder are the main parts of a subband coder. Previously the filter banks in image subband coders have been designed with FIR filters organized in a tree structure. In this paper we propose a novel structure that deviates from previously reported structures in these respects: (1) The filter bank is organized as a parallel structure. (2) The filters employed are 1st order IIR allpass filters featuring very low computational complexity. (3) The resulting subbands are complex. (4) The filter bank features exact reconstruction in the absence of encoding/decoding. In the paper we give a detailed derivation of the filter bank structure. The computational complexity is evaluated and shown to be considerably less than that of existing structures. We have incorporated this filter bank structure into a complete image subband coder. Finally, coding results obtained by computer simulation are presented.

An LS algorithm based on a posteriori output sequences for IIR adaptive filtering

In this paper, we propose a modified least-squares (LS) algorithm that may be regarded as an improved version of the least-squares-based infinite impulse response (IIR) adaptive digital filter (ADF) algorithm. In the proposed algorithm, a posteriori output sequences and their filtered signals are used, and a weighting factor is utilized to increase the convergence speed for stationary input signals. To properly handle the instability problem of the IIR ADF, a filter-bank structure in the frequency-domain is also used. In addition, as an application of the proposed IIR ADF algorithm, modelling of a telephone channel is considered.

Classical sampling theorems in the context of multirate and polyphase digital filter bank structures

The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n) with a Fourier transform vanishes for mod omega mod >or=L pi /M, where L and M are integers with L<M, can in principle be represented by reducing the data rate by the amount M/L. The digital polyphase framework is used as a convenient tool for the derivation as well as mechanization of the sampling theorems.<<ETX>>

Block realization of multirate adaptive digital filters

In this paper, we study multirate transversal adaptive digital filters (ADF's) based on the block least-mean-square (BLMS) algorithms. These include an ADF with decimation (ADFD) and an ADF with interpolation (ADFI). We first formulate these filters based on the block mean-squared error (BMSE) criterion and derive BLMS multi-rate weight-adjustment algorithms, and then study efficient realization of those filters. It is shown that the BLMS ADFD can be realized efficiently in the direct form or in the filter-bank structure both using the fast Fourier transform (FFT) and an appropriate sectioning procedure. According to our analysis of computational complexity, the FFT realization of the BLMS ADFD in the filter-bank structure is more efficient than in the direct form, and the two structures using the FFT become more efficient in comparison to the LMS ADFD as the number of weights increases. Unlike the direct form realization, the filter-bank realization of the BLMS ADFD using the FFT becomes more efficient as the decimation ratio increases. Similar results have been obtained for the BLMS ADFI. Finally, we investigate by computer simulation the effects of different weight-adjustment algorithms and several system parameters on the performances of ADFD's. The results of simulation indicate that, as expected, the convergence speed of the BLMS ADFD can be significantly improved by self-orthogonalization of weight adjustment in the frequency domain. Furthermore, the convergence factor of the self-orthogonalizing BLMS ADFD can be chosen such that the steady-state performance of the new ADFD is the same as that of the existing LMS ADFD.