Topic
Remez algorithm
About: Remez algorithm is a research topic. Over the lifetime, 434 publications have been published within this topic receiving 6394 citations.
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Book•
13 May 2004
TL;DR: This book offers the first systematic, clear, and intuitive introduction to multirate signal processing for working engineers and system designers.
Abstract: Multirate Signal Processing for Communication Systems: Current Practice and Next Generation Techniques fredric j harrisMultirate signal processing can reduce costs and improve performance in applications ranging from laboratory instruments to cable modems, wireless systems, and consumer entertainment products. This book offers the first systematic, clear, and intuitive introduction to multirate signal processing for working engineers and system designers.The author uses extensive examples and figures to illuminate a wide range of multirate techniques, from basic resampling to leading-edge cascade and multiple-stage filter structures. Along the way, he draws on extensive research and consulting experience to introduce processing itricksi shown to maximize performance and efficiency.Coverage includes: Effective sampling and resampling in time and frequency domains Relationships between IIR Filter specifications and filter length (taps) Window design and equal-ripple (Remez) design techniques Square-Root Nyquist and Half Band Filters, including new design enhancements Polyphase IIR Filters: up-sampling, down-sampling, and cascade up-down sampling Polyphase interpolators and filters that perform arbitrary sample rate change Dyadic Half Band Filters, including quadrature mirror and IIR Filters Polyphase Channelizers, including M-path modulators, demodulator channel banks, simultaneous interpolation, and channel bank formation Comprehensive coverage of recursive all-pass filtersoa topic never before covered in this detail Comparisons with traditional DSP design techniques Extensive applications coverage throughout
537 citations
TL;DR: In this paper, a method for designing finite-duration impulse-response (FIR) linear-phase digital filters is presented in which the four possible cases for such filters are treated in a unified approach.
Abstract: A method for designing finite-duration impulse-response (FIR) linear-phase digital filters is presented in which the four possible cases for such filters are treated in a unified approach. It is shown how to reduce each case to the proper form so that the Remez exchange algorithm can be used to compute the best approximation to the desired frequency response. The result is that a very flexible and fast technique is available for FIR linear-phase filter design.
284 citations
TL;DR: In this article, the number of multipliers required in the implementation of interpolated FIR (Finite-impulse response) filters in the form H(Z)=F(z/sup L/)G(z) is studied.
Abstract: The number of multipliers required in the implementation of interpolated FIR (Finite-impulse response) filters in the form H(Z)=F(z/sup L/)G(z) is studied. Both single-stage and multistage implementations of G(z) are considered. Optimal decompositions requiring fewest number if multipliers are given for some representative low-pass cases. An efficient algorithm for designing these filters is described. It is based on iteratively designing F(z/sup L/) and G(z) using the Remez multiple-exchange algorithm until the difference between the successive stages is within the given tolerance limits. A novel implementation for G(z) based on the use of recursive running sums is given. The design of this class of filters is converted into another design problem to which the Remez algorithm is directly applicable. The results show that the proposed methods result in significant improvements over conventional multiplier efficient implementations of FIR digital filters. >
229 citations
TL;DR: The alternation theorem is extended from the real-only to the complex case, so that arbitrary magnitude and phase responses can be approximated and an efficient exchange algorithm is derived for designing complex FIR filters in the Chebyshev sense.
Abstract: The alternation theorem is at the core of efficient real Chebyshev approximation algorithms. In this paper, the alternation theorem is extended from the real-only to the complex case. The complex FIR filter design problem is reformulated so that it clearly satisfies the Haar condition of Chebyshev approximation. An efficient exchange algorithm is derived for designing complex FIR filters in the Chebyshev sense. By transforming the complex error function, the Remez exchange algorithm can be used to compute the optimal complex Chebyshev approximation. The algorithm converges to the optimal solution whenever the complex Chebyshev error alternates; in all other cases, the algorithm converges to the optimal Chebyshev approximation over a subset of the desired bands. The new algorithm is a generalization of the Parks-McClellan algorithm, so that arbitrary magnitude and phase responses can be approximated. Both causal and noncausal filters with complex or real-valued impulse responses can be designed. Numerical examples are presented to illustrate the performance of the proposed algorithm. >
192 citations
TL;DR: In this paper, a modified Remez exchange algorithm for the design of "wavelet" filters is derived in the spirit of the Parks-McClellan algorithm, which is greatly improved as compared to linear programming techniques, and optimum filters are generally obtained after 3 or 4 iterations.
Abstract: Compactly supported orthonormal wavelets are obtained from two-band paraunitary FIR filter bank solutions, with the additional "flatness" constraint that the low-pass filter should have K zeroes at half the sampling frequency. This constraint is set to obtain "regular" wavelets. However, it is somewhat in contradiction with the usual requirement for good frequency selectivity, since it is well known that maximally flat filters (yielding Daubechies wavelets) have poor frequency selectivity. An efficient procedure for designing maximally frequency selective filter banks under a given flatness constraint is described in this paper. Classical Remez exchange algorithms, based on the alternation theorem, can no longer be used in this case. Linear programming techniques are capable of setting up constraints of this type, but require high memory storage and computation time. First, a variation of the alternation theorem adapted to this new situation is derived. Then, a modified Remez exchange algorithm for the design of "wavelet" filters is derived in the spirit of the Parks-McClellan algorithm. The efficiency of the algorithm is greatly improved as compared to linear programming techniques, and optimum filters are generally obtained after 3 or 4 iterations. A MATLAB listing is provided. >
117 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 15 |
| 2020 | 4 |
| 2019 | 10 |
| 2018 | 11 |
| 2017 | 11 |