Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response

Masahiro OKUDA; Masaaki IKEHARA; Shin-ichi TAKAHASHI

Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response

Masahiro OKUDA, Masaaki IKEHARA, Shin-ichi TAKAHASHI

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In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase -squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.11 pp.1879-1885

Publication Date: 1996/11/25

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Type of Manuscript: PAPER

Category: Digital Signal Processing

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Masahiro OKUDA, Masaaki IKEHARA, Shin-ichi TAKAHASHI, "Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 11, pp. 1879-1885, November 1996, doi: .
Abstract: In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase -squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e79-a_11_1879/_p

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@ARTICLE{e79-a_11_1879,
author={Masahiro OKUDA, Masaaki IKEHARA, Shin-ichi TAKAHASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response},
year={1996},
volume={E79-A},
number={11},
pages={1879-1885},
abstract={In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase -squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Simultaneous Approximation for IIR Digital Filters with Log Magnitude and Phase Response
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1879
EP - 1885
AU - Masahiro OKUDA
AU - Masaaki IKEHARA
AU - Shin-ichi TAKAHASHI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1996
AB - In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase -squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.
ER -