Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Iterative reweighted l1 design of sparse FIR filters

Sparse FIR filters have lower implementation complexity than full filters, while keeping a good performance level. This paper describes a new method for designing 1D and 2D sparse filters in the minimax sense using a mixture of reweighted l1 minimization and greedy iterations. The combination proves to be quite efficient; after the reweighted l1 minimization stage introduces zero coefficients in bulk, a small number of greedy iterations serve to eliminate a few extra coefficients. Experimental results and a comparison with the latest methods show that the proposed method performs very well both in the running speed and in the quality of the solutions obtained

A new iterative WLS Chebyshev approximation method for the design of two-dimensional FIR digital filters

[[abstract]]In this paper, based on Chi-Chiou's weighted least-squares (WLS) Chebyshev approximation method which is for the design of one-dimensional (1-D) FIR digital filters with arbitrary complex frequency response, we propose a new iterative WLS Chebyshev approximation method for the design of two-dimensional (2-D) FIR digital filters with arbitrary complex frequency response. Several design examples are provided to justify the good performance of the proposed approximation method.[[fileno]]2030157030004[[department]]電機工程學

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach

Iterative greedy algorithm for solving the FIR paraunitary approximation problem

In this paper, a method for approximating a multi-input multi-output (MIMO) transfer function by a causal finite-impulse response (FIR) paraunitary (PU) system in a weighted least-squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase-type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmultiplexers

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