Nonlinear phase FIR filter design according to the L2 norm with constraints for the complex error

Lang, Markus; Bamberger, Joachim

doi:10.1016/0165-1684(94)90145-7

Cited by 18 publications

(5 citation statements)

References 11 publications

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“…In general, the filter coefficients obtained as a solution to (5) has non-linear phase response [12], [23], [32]. Filters with linear phase responses can also be obtained by constraining filter coefficients to be symmetric in (5).…”

Section: Herementioning

confidence: 99%

FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm

Dedeoğlu

Kemal

Arıkan

2016

IEEE Trans. Signal Process.

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The advances in convex optimization techniques have offered new formulations of design with improved control over the performance of FIR filters. By using lifting techniques, the design of a length-FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an matrix that must be rank-1. Although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter, convex solvers implementing interior point methods almost never provide a rank-1 solution matrix. To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem. The semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations. Analytically it is shown that the DIRR iterations provide monotonic improvement, and the global optimum is a fixed point of the iterations. Over a set of design examples it is illustrated that the DIRR requires only a few iterations to converge to an approximately rank-1 solution matrix. The effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints, the constraints on the phase and group delay of filter are placed on the designed filter. Index Terms-Finite impulse response (FIR) filter design, spectral mask, convex optimization, semidefinite programming, semidefinite relaxation, iterative rank refinement. I. INTRODUCTION D IGITAL FINITE IMPULSE RESPONSE (FIR) filters have always been one of the prominent building blocks in digital signal processing because of their assured stability and efficient implementations based on the Fast Fourier Transform (FFT) [1]-[3]. A diverse class of FIR filter design techniques have been proposed in the literature including the Parks-McClellan algorithm [2], [4], optimization based techniques like METEOR [5] and peak-constrained least squares (PCLS)

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Section: Herementioning

confidence: 99%

FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm

Dedeoğlu

Kemal

Arıkan

2016

IEEE Trans. Signal Process.

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“…Based on the above analysis, all the FIR filters design problems presented in refs. [5][6][7][8][9][10][11][12] can be solved by our SOCP approach, which shows good flexibility of SOCP.…”

Section: Design Of Fir Filtersmentioning

confidence: 99%

“…Minimax design [5,6] was used, where the peak errors were more important than the total squared errors, and least-squares design [7,8] was used, where the total squared errors were more important. When single norm approximation criterion is not appropriate in many applications, the mix-norm criterion is used, in which some constraints are imposed on the passbands or/and stopbands, e.g., the peak constrained weighted least square error (PCWLSE) FIR filters design [9,10] , equiripple passbands and peak-constrained least-squares stopbands design [11] , the mean-square stopbands (passbands) constrained least square passbands (stopbands) design [12] , and so on. However, most of these approaches are ad hoc techniques.…”

Section: Introductionmentioning

confidence: 99%

Optimal design and verification of temporal and spatial filters using second-order cone programming approach

Yan

2006

SCI CHINA SER F

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Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming (SOCP) and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach.

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“…are the coe cients, a = (a0; : : : ; am) t , and the multipliers, = ( 1; : : : ; L) t . In eq (cos 2 kfdf(4) di = siD(fi) + T(fi)…”

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confidence: 99%

Constrained least square design of FIR filters without specified transition bands

Selesnick

Lang

Burrus

1996

IEEE Trans. Signal Process.

112

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We consider the design of digital lters and discuss the inclusion of explicitly speci ed transition bands in the frequency domain design of FIR lters. We put forth the notion that explicitly speci ed transition bands have been introduced in the lter design literature as an indirect and often inadequate approach for dealing with discontinuities in the desired frequency response.We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR lters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR lters and gives the best L2 lter and a continuum of Chebyshev lters as special cases.

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Nonlinear phase FIR filter design according to the L2 norm with constraints for the complex error

Cited by 18 publications

References 11 publications

FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm

FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm

Optimal design and verification of temporal and spatial filters using second-order cone programming approach

Constrained least square design of FIR filters without specified transition bands

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