Chebyshev optimization of sparse FIR filters using linear programming with an application to beamforming

Webb, J.L.H.; Munson, D.C.

doi:10.1109/78.533712

Cited by 20 publications

(26 citation statements)

References 24 publications

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“…, n} in (2). There are two reasons for using a fixed denominator in our design: First, from (3a)-(3e) it follows that a fixed b(z) leads to a fixed set of basis functions {w k (ω)}, hence a linear representation of frequency response H(e jω ) in terms of {w k (ω)} as seen in (2). This linear representation is the foundation on which the new design method is developed, see the rest of the section for details.…”

Section: A Linear Representation Of H(e Jω )mentioning

confidence: 99%

New algorithm for minimax design of sparse IIR filters

Hinamoto

2013

2013 IEEE International Symposium on Circuits and Systems (ISCAS2013)

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Abstract-Sparse digital filters are of importance as they offer improved implementation efficiency relative to their nonsparse counterparts. This paper examines the design of minimax sparse IIR filters from a sparse representation point of view. The result is a new algorithm that accomplishes a design with three phasesidentification of the whereabouts of zero coefficients; optimal design subject to the sparsity constraint; and performance enhancement by further dimension reduction of the working subspace. A design example is presented for illustrating the new algorithm. To date, most of the work in this area has been focused on sparse FIR filters, except that of [9]. This paper presents a new algorithm for minimax design of stable sparse IIR filters. The method is different from that of [9] in several ways. First, the new algorithm is built on a linear sparse representation framework. This linear representation is made possible due to the fact that the poles of a sparse IIR filter are very close to those of a nonsparse IIR counterpart as long as both filters approximate the same frequency response, which is in a certain sense similar to an observation made in [16]. Second, here we adopt a constrained formulation to avoid the use of a regularization parameter as in [9]. In this way, the filter's sparsity is explicitly related to the minimax error of the filter, which in turn makes sparsity tuning easier and more intuitive. Third, the new algorithm includes an additional phase to enhance performance by further reduction of the working subspace's dimension and re-optimization. A design example is presented to illustrate the new algorithm. I. INTRODUCTION

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Section: A Linear Representation Of H(e Jω )mentioning

confidence: 99%

New algorithm for minimax design of sparse IIR filters

Hinamoto

2013

2013 IEEE International Symposium on Circuits and Systems (ISCAS2013)

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“…Cascade structures however are not applicable to arrays. Sparse direct-form designs for approximately nth-band filters were developed in [7] utilizing the property of nth-band filters of having every nth impulse response coefficient equal to zero except for the central coefficient. The second approach is more general and attempts to optimize the locations of zerovalued coefficients so as to maximize their number subject to frequency response constraints.…”

Section: Introductionmentioning

confidence: 99%

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

Wei

Sestok

Oppenheim

2013

IEEE Trans. Signal Process.

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Abstract-This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signalto-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.

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“…The design of sparse lters under a Chebyshev error criterion in the frequency domain has been examined from a variety of perspectives, including integer programming [1] and heuristic approaches [2][3][4]. In comparison, the case of a weighted least-squares criterion has not received much attention.…”

Section: Introductionmentioning

confidence: 99%

Sparsity maximization under a quadratic constraint with applications in filter design

Wei

Oppenheim

2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

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This paper considers two problems in sparse lter design, the rst involving a least-squares constraint on the frequency response, and the second a constraint on signal-to-noise ratio relevant to signal detection. It is shown that both problems can be recast as the minimization of the number of non-zero elements in a vector subject to a quadratic constraint. A solution is obtained for the case in which the matrix in the quadratic constraint is diagonal. For the more dif cult nondiagonal case, a relaxation based on the substitution of a diagonal matrix is developed. Numerical simulations show that this diagonal relaxation is tighter than a linear relaxation under a wide range of conditions. The diagonal relaxation is therefore a promising candidate for inclusion in branch-and-bound algorithms.

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Chebyshev optimization of sparse FIR filters using linear programming with an application to beamforming

Cited by 20 publications

References 24 publications

New algorithm for minimax design of sparse IIR filters

New algorithm for minimax design of sparse IIR filters

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

Sparsity maximization under a quadratic constraint with applications in filter design

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