WLS design of variable frequency response FIR filters

Tarczyński, Andrzej; Cain, G.D.; Hermanowicz, E.; Rojewski, M.

doi:10.1109/iscas.1997.612768

Cited by 62 publications

(75 citation statements)

References 5 publications

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“…The obtained maximum absolute error and the root mean square error are presented in Table 1; for comparison purpose the results obtained by using the approaches in [18][19][20][21]24] are also presented.…”

Section: Obtained Resultsmentioning

confidence: 99%

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Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Díaz-Carmona

Dolecek

Ramirez-Agundis

2010

International Journal of Digital Multimedia Broadcasting

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A frequency-designed fractional delay FIR structure, which is suitable for software radio applications, is presented. The design method is based on frequency optimization of a combination of modified Farrow and mutirate structures. As a result the optimization frequency range is made only in half of desired total bandwidth. According to the obtained results the proposed fractional delay structure allows online desired fractional delay update, with a high fractional delay value resolution.

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Section: Obtained Resultsmentioning

confidence: 99%

“…Several design methods have been proposed such as, for example, [18], where the FD filter is implemented in a modified Farrow structure and a Taylor approximation is achieved. Similarly in [19][20][21] the implementation is made using an original Farrow structure and a weighted least square optimization is accomplished.…”

Section: Introductionmentioning

confidence: 99%

Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Díaz-Carmona

Dolecek

Ramirez-Agundis

2010

International Journal of Digital Multimedia Broadcasting

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“…Therefore, the variable 2-D transfer function (2) can be expressed as (14) whose frequency response is given by (15) where Defining the complex-valued error (16) our objective here is to find the optimal coefficient matrices and such that the total weighted squared-error (17) is minimized, where is a nonnegative fourdimensional weighting function. In this paper, we assume that the weighting function is separable, i.e., (18) and the 1-D functions are piecewise constant. For example, for the frequencies in the range we first divide the interval into the union of several small intervals (sub-intervals) as (19) where Then, the sub-weighting function is chosen to be constant in each sub-interval, i.e., for (20) where are constants for In addition, we assume that the sub-weighting function for is symmetric with respect to Likely, is defined as for (21) where As for the sub-weighting function the interval [0, 1] is divided into the union of sub-intervals as (22) where For each sub-interval, the corresponding sub-weighting function is constant, i.e., for…”

Section: Problem Formulation and Objective Functionmentioning

confidence: 99%

“…Paper [17] examines some methods of FIR designs including the Lagrangian interpolation method. Recently, weighted least-squares methods with and without discretizing parameters have been proposed to improve the design accuracy with reduced computational complexity [18], [19]. Paper [15] ) and 2-D fractional delays ( ).…”

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confidence: 99%

Weighted least-squares method for designing variable fractional delay 2-D FIR digital filters

Deng

2000

IEEE Trans. Circuits Syst. II

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Abstract-This paper proposes a closed-form weighted least-squares solution for designing variable two-dimensional (2-D) finite-impulse response (FIR) digital filters with continuously variable 2-D fractional delay responses. First, the coefficients of the variable 2-D transfer function are represented by using the polynomials of a pair of fractional delays ( 1 2 ). Then the weighted squared-error function of the variable 2-D frequency response is derived without sampling the two frequencies ( 1 2 ) and two fractional delays ( 1 2 ), which leads to a significant reduction in computational complexity. With the assumption that the overall weighting function is separable and stepwise, the design problem is reduced to the minimization of the weighted squared-error function. Based on the error function, the closed-form optimal solutions for the coefficient matrices of the variable 2-D transfer function can be determined through solving a pair of matrix equations. In addition, Cholesky decomposition is applied to the final closed-form expressions in order to avoid some numerical instability problem. An example is given to illustrate the effectiveness of the proposed design method.Index Terms-Two-dimensional digital filters, variable digital filters, variable fractional delay filters, weighted least-squares design.

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“…The optimization of adjustable filters was typically performed using a least-squares criterion, see e.g. [3,4]. Minimax optimization was employed in [2], using linear programming, and in [5], using semidefinite programming (SDP).…”

Section: Introductionmentioning

confidence: 99%

Minimax design of adjustable FIR filters using 2D polynomial methods

Dumitrescu

Sicleru

Stefan

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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The problem under study here is the minimax design of linearphase lowpass FIR filters having variable passband width and implemented through a Farrow structure. We have two main contributions. The first is the design of adjustable FIR filters without discretization, using 2D positive trigonometric polynomials, an approach leading to semidefinite programming (SDP) formulation of the design problem. The second is to modify the design problem by a special choice for the passband and stopband edges of the variable FIR filter. The advantage is a lower implementation complexity. The new problem is solved using positive hybrid real-trigonometric polynomials and their SDP parameterization. Design examples prove the viability of our methods.

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WLS design of variable frequency response FIR filters

Cited by 62 publications

References 5 publications

Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Weighted least-squares method for designing variable fractional delay 2-D FIR digital filters

Minimax design of adjustable FIR filters using 2D polynomial methods

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