Chebyshev approximation for two-dimensional nonrecursive digital filters

Kamp, Y.; Thiran, J. P.

doi:10.1109/tcs.1975.1084025

Cited by 88 publications

(29 citation statements)

References 11 publications

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“…An example of engineering applications is the design of two dimensional nonrecursive digital filters [24]. In a recent study [25], the authors applied the Chebyshev approximation method to a two-degrees-of-freedom mechanism for the first time.…”

Section: Introductionmentioning

confidence: 99%

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

Kiper

Bilgincan

2015

Mechanism and Machine Theory

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The Chebyshev approximation is well known to be applicable for the approximation of single input-single output functions by means of a function generator mechanism. The approximation method may be also applied to multi-input functions, although until recently, it was not used for function generation with multi-degrees-of-freedom mechanisms. In a recent study, the authors applied the approximation method to a two-degrees-of-freedom mechanism for the first time, however the selection and iteration of the design points at which the errors were minimized was not satisfactory. In this study, an alternative method of selection and iteration for these design points is introduced and the corresponding spacing is called the "regional spacing". As a case study for the application of the approximation of multi-input functions, a spherical 5R mechanism is used to generate a two input-single-output function. The input joints of the mechanism are selected as one of the fixed joints and the moving mid-joint, whereas the remaining fixed joint represents the output. The synthesis problem is analytically formulated and presented in polynomial form for five and six unknown parameters. The synthesis problem for five unknown parameters is illustrated as a numerical example. Regional spacing is used for the selection and iteration of design points for the synthesis. The Chebyshev approximation along with the Remez algorithm is utilized to find the unknown construction parameters and the error of the function. The design points and the coefficients of the approximation polynomial are determined by numerical iteration using six moving points. At each iteration step, the design points are relocated at the extremum error points in their respective regions. Iterations are repeated until the magnitudes of the extremum point errors are approximately equal. Finally, the construction parameters of the mechanism are determined and the variation of the percentage error between the desired and generated function values is obtained.

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Section: Introductionmentioning

confidence: 99%

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

Kiper

Bilgincan

2015

Mechanism and Machine Theory

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“…Many methods have been presented for the minimax design of 2-D linear-phase FIR [2][3][4][5][6][7]. Several exchange-type design techniques were developed based on the Remez exchange algorithm in [4,5].…”

Section: Introductionmentioning

confidence: 99%

Least Total Squared Error Design of 2-D MINIMAX FIR Filters

Che

Lai

2008

2008 International Conference on Intelligent Computation Technology and Automation (ICICTA)

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The minimax Design of 2-D (two-dimensional) FIRFilters is not necessarily unique since the Haar condition is not generally satisfied. In order to obtain a unique solution, we introduce some additional constraints to the minimax design. This paper presents least total squared error design of 2-D minimax FIR Filters which is always unique. This unique minimax solution can be obtained by using a quadratic programming with the primal-dual algorithm. Design examples and comparison with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed method. The resulted filter is not only a minimax filter but also has least total squared error among minimax filters .

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“…This procedure has been chosen in [14] for two-dimensional digital filter design and in [7] for bivariate polynomial approximation. Recently, Brannigan described in [3], an ascent exchange algorithm for the strict Chebyshev solution to an overdetermined system of linear equations and extended it in [4] and [5] to include linear constraints on the solution.…”

Section: Introductionmentioning

confidence: 99%

Strict Chebyshev approximation for general systems of linear equations

Thiran

Thiry

1987

Numer. Math.

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Summary. An ascent exchange algorithm for computing the strict Chebyshev solution to general systems of linear equations is presented. It uses generalized exchange rules to ensure convergence and splits up the entire system into subsystems by means of a canonical decomposition of a matrix obtained by Gaussian elimination methods. All updating procedures are developed and several numerical examples illustrate the efficiency of the algorithm.

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Chebyshev approximation for two-dimensional nonrecursive digital filters

Cited by 88 publications

References 11 publications

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

Function generation synthesis of spherical 5R mechanism with regional spacing and Chebyshev approximation

Least Total Squared Error Design of 2-D MINIMAX FIR Filters

Strict Chebyshev approximation for general systems of linear equations

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