Design of nonuniformly spaced linear-phase FIR filters using mixed integer linear programming

Kim, Joon Tae; Oh, Woo Jin; Lee, Yong Hoon

doi:10.1109/78.482018

Cited by 23 publications

(3 citation statements)

References 9 publications

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“…We solve the problem in (14) by using the optimization method presented in [23]. The method referred to is able to solve a general SGP problem shown in (2). However, our problem is simpler because it does not contain equality constraints.…”

Section: Solving Of Sgp Problemmentioning

confidence: 99%

“…However, their implementation complexity is higher than the complexity of infinite-impulse-response filters with similar properties [1]. One technique for reducing the complexity is sparse-filter design [2]- [7].…”

Section: Introductionmentioning

confidence: 99%

“…However, several approximate methods have been developed. Many of them utilize l0-norm and estimate the positions of zero coefficients by using greedy algorithms [12], [13], integer programming [2], [14], iterative second order cone programming [15], iterative shrinkage/thresholding [16], and genetic algorithms [17]. If l0-norm in (1) is replaced by l1-norm, the filter is obtained with many small coefficients [5].…”

Section: Introductionmentioning

confidence: 99%

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Sparse FIR Filter Design Based on Signomial Programming

Bellotti

Vučić

2020

ELEKTRON ELEKTROTECH

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The goal of sparse FIR filter design is to minimize the number of nonzero filter coefficients, while keeping its frequency response within specified boundaries. Such a design can be formally expressed via minimization of l0-norm of filter’s impulse response. Unfortunately, the corresponding minimization problem has combinatorial complexity. Therefore, many design methods are developed, which solve the problem approximately, or which solve the approximate problem exactly. In this paper, we propose an approach, which is based on the approximation of the l0-norm by an lp-norm with 0 < p < 1. We minimize the lp-norm using recently developed method for signomial programming (SGP). Our design starts with forming a SGP problem that describes filter specifications. The optimum solution of the problem is then found by using iterative procedure, which solves a geometric program in each iteration. The filters whose magnitude responses are constrained in minimax sense are considered. The design examples are provided illustrating that the proposed method, in most cases, results in filters with higher sparsity than those of the filters obtained by recently published methods.

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Section: Solving Of Sgp Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sparse FIR Filter Design Based on Signomial Programming

Bellotti

Vučić

2020

ELEKTRON ELEKTROTECH

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Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

Fraser

2015

Circuits Syst Signal Process

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In this work, a greedy algorithm for the design of sparse linear-phase finite impulse response filters wherein the coefficients are successively fixed to zero individually is proposed. To meet the filter specifications, the coefficient for which the middle value of its feasible range is closest to zero is selected to be set to zero, whereas all the other unfixed coefficients are free to change. Design examples show that the proposed technique can design FIR filters with higher sparsity than that obtained by existing nonexhaustive algorithms for given specifications. To show the optimality of the algorithm, we design 100 filters, with results showing that the global optimal solution, i.e., the sparsest solution found by exhaustive search, can be achieved in most cases, but with much less computation time.

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Design of Sparse Filters by a Discrete Filled Function Technique

Feng

Yiu

2018

Circuits Syst Signal Process

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In this paper, we consider the sparse filter design problem where some of the coefficients can be reduced to zeroes in order to lower implementation complexity. The objective is to choose the fewest number of nonzero filter coefficients to meet a given performance requirement. We formulate a discrete optimization problem to minimize the number of nonzero terms and develop a discrete search method to find the minimal nonzero terms. In each step, we need to consider a subproblem to design the filter coefficients with a given set of nonzero terms. We formulate this subproblem as a linear programming problem and apply an exchange algorithm to find the optimal coefficients. For illustration, we compare the proposed algorithm with existing methods and show that the proposed method gives better results in all our test cases. KeywordsSparse filter design • filled function • discrete search method 1 Introduction Digital finite-impulse response (FIR) filters design have been widely studied in the literature. There are many optimization methods available to deal with this class of problems. In particular, Parks-McClellan method is recognized to

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Design of nonuniformly spaced linear-phase FIR filters using mixed integer linear programming

Cited by 23 publications

References 9 publications

Sparse FIR Filter Design Based on Signomial Programming

Sparse FIR Filter Design Based on Signomial Programming

Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

Design of Sparse Filters by a Discrete Filled Function Technique

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