Decomposition of High-Order FIR Filters and Minimum-Phase Filter Design

In this study, the implementation of high-order FIR filter decomposition and minimum-phase filter design is investigated. One method is presented for decomposing arbitrary linear-phase FIR filters with distinct roots into the cascade of first-order, second-order and fourth-order subfilters. The other method is described for transforming nonrecursive filters with even-order, equal-ripple attenuation in the pass-band, stop-band and linear-phase into those with minimum-phase and half the degree, and again with equal-ripple attenuation in the pass-band and stop-band. The technique consists of quick and accurate polynomial root finding of the z -domain filter transfer function by searching a finite region in the complex z-plane, and separating the zeros in the complex z -domain. In FIR filter decomposition, the search of roots to determine the subfilter impulse response coefficients is restricted to distinct roots in four regions in the complex z -plane: on the real axis, on the unit circle, inside the unit circle and at (1, 0) or (-1, 0). In minimum-phase filter design, the search of roots is restricted in two categories: on the unit circle and inside the unit circle. In both methods, we used Lang’s root finding program to get the zeros of the FIR filter. Arbitrary FIR filters were designed and decomposed for all possible orders of subfilters. FIR filters with even-order, zero-phase and equal-ripple were designed and generated the half degree minimum-phase filters. Both methods have been tested on FIR filters with orders ranging to over 500 and have proven effective in decomposing filters to the cascade realization and designing minimum-phase filters

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices

A technique is developed for the design of analysis filters in an M-channel maximally decimated, perfect reconstruction, finite-impulse-response quadrature mirror filter (FIR QMF) bank that has a lossless polyphase-component matrix E(z). The aim is to optimize the parameters characterizing E(z) until the sum of the stopband energies of the analysis filters is minimized. There are four novel elements in the procedure reported here. The first is a technique for efficient initialization of one of the M analysis filters, as a spectral factor of an Mth band filter. The factorization itself is done in an efficient manner using the eigenfilters approach, without the need for root-finding techniques. The second element is the initialization of the internal parameters which characterize E(z), based on the above spectral factor. The third element is a modified characterization, mostly free from rotation angles, of the FIR E(z). The fourth is the incorporation of symmetry among the analysis filters, so as to minimize the number of unknown parameters being optimized. The resulting design procedure always gives better filter responses than earlier ones (for a given filter length) and converges much faste

A New Low Complexity Uniform Filter Bank Based on the Improved Coefficient Decimation Method

In this paper, we propose a new uniform filter bank (FB) based on the improved coefficient decimation method (ICDM). In the proposed FB’s design, the ICDM is used to obtain different multi-band frequency responses using a single lowpass prototype filter. The desired subbands are individually obtained from these multi-band frequency responses by using low order frequency response masking filters and their corresponding ICDM output frequency responses. We show that the proposed FB is a very low complexity alternative to the other FBs in literature, especially the widely used discrete Fourier transform based FB (DFTFB) and the CDM based FB (CDFB). The proposed FB can have a higher number of subbands with twice the center frequency resolution when compared with the CDFB and DFTFB. Design example and implementation results show that our FB achieves 86.59% and 58.84% reductions in resource utilizations and 76.95% and 47.09% reductions in power consumptions when compared with the DFTFB and CDFB respectively

Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

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