Closed-form design of all-pass fractional delay filters
Journal
IEEE Signal Processing Letters
Journal Volume
11
Journal Issue
10
Pages
788-791
Date Issued
2004
Author(s)
Wang, Peng-Hua
Abstract
In this letter, we propose a novel all-pass (AP) fractional delay filter whose denominator polynomial is obtained by truncating the power series of a certain function. This function is derived from the frequency response of the denominator whose magnitude response is related to the desired phase response through the Hilbert transform since the denominator of a stable AP filter is of minimum phase. The target function and corresponding power series are calculated analytically and expressed in closed form. The closed-form expressions facilitate the analysis of stability. According to the properties for the coefficients of the denominator polynomial, we show that the proposed AP filter is stable for positive delay. Numerical examples indicate that the phase delays of the proposed filters are flat around DC. © 2004 IEEE.
Other Subjects
FIR filters; Frequency response; Mathematical transformations; Poles and zeros; Polynomials; Theorem proving; Transfer functions; Allpass filter; Fractional delay filter; Hilbert transform; Minimum phase; Phase delay; Signal filtering and prediction
Type
journal article
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