The Mathematical Institute, University of Oxford, Eprints Archive

The Remez algorithm for trigonometric approximation of periodic functions

Javed, Mohsin and Trefethen, Lloyd N. (2015) The Remez algorithm for trigonometric approximation of periodic functions. Technical Report. Unspecified. (Submitted)

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Abstract

In this paper we present an implementation of the Remez algorithm for trigonometric minimax approximation of periodic functions. There are software packages which implement the Remez algorithm for even periodic functions. However, we believe that this paper describes the first implementation for the general periodic case. Our algorithm uses Chebfun to compute with periodic functions. For each iteration of the Remez algorithm, to construct the approximation, we use the second kind barycentric trigonometric interpolation formula instead of the first kind formula. To locate the maximum of the absolute error, instead of dense sampling of the error function, we use Chebfun’s eigenvalue based root finding method applied to the Chebyshev representation of the derivative of the underlying periodic function. Our algorithm has applications for designing FIR filters with real but asymmetric frequency responses.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1881
Deposited By: Helen Taylor
Deposited On:08 May 2015 07:59
Last Modified:29 May 2015 19:34

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