Restricted range approximation and its application to digital filter design
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The multiple exchange algorithm for restricted range approximation is discussed and efficient formulas are derived for the numerical implementation of the method.Abstract:
The multiple exchange algorithm for restricted range approximation is discussed. Efficient formulas are derived for the numerical implementation of the method. Discretization effects are analyzed mathematically. The method is applied to a certain problem arising in digital filter design.read more
Citations
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Journal ArticleDOI
Associate fractal functions in Lp-spaces and in one-sided uniform approximation
TL;DR: In this article, a fractal interpolation function defined with the aid of iterated function system can be employed to show that any continuous real-valued function defined on a compact interval is a special case of a class of fractal functions (self-referential functions).
Journal ArticleDOI
Fractal trigonometric polynomials for restricted range approximation
TL;DR: One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it.
Journal ArticleDOI
Bernstein Fractal Rational Approximants with no Condition on Scaling Vectors
TL;DR: Fractal functions defined through iterated function system have been successfully used to approximate any continuous real-valued function defined on a compact interval as mentioned in this paper, where the fractal dimension is a q.
Journal ArticleDOI
The discrete linear restricted Chebyshev approximation
TL;DR: A numerically stable simplex algorithm for calculating the restricted Chebyshev solution of overdetermined systems of linear equations is described and a new way of implementing a triangular decomposition method to the basis matrix is used.
Book ChapterDOI
An Application of a Restricted Range Version of the Differential Correction Algorithm to the Design of Digital Systems
TL;DR: The application of a restricted range version of the differential correction algorithm of Cheney and Loeb to the design of digital filters will be considered, with a discussion of numerical results and such topics as continuity of the best approximation operator and degeneracy.
References
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Book
Introduction to approximation theory
TL;DR: In this paper, Tchebycheff polynomials and other linear families have been used for approximating least-squares approximations to systems of equations with one unknown solution.
Journal ArticleDOI
Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase
T. Parks,J. McClellan +1 more
TL;DR: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented, which obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands.
Journal ArticleDOI
Approximation of Functions
TL;DR: Theory of Approximation of functions of a real variable as mentioned in this paper was proposed by A. F. Timan, translated by J. Cossar and J. Berry.