Derivation of the class of digital filters with all second-order modes equal

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1109/TSP.2011.2164403

Derivation of the class of digital filters with all second-order modes equal

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

This paper reveals the class of digital filters with all second-order modes equal. We first prove that if the second-order modes of a digital filter are all equal, the L₂-sensitivity minimization problem of the digital filter can be solved analytically. We derive a general expression of the transfer function of digital filters with all second-order modes equal. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter.

Original language	English
Article number	5982445
Pages (from-to)	5236-5242
Number of pages	7
Journal	IEEE Transactions on Signal Processing
Volume	59
Issue number	11
DOIs	https://doi.org/10.1109/TSP.2011.2164403
Publication status	Published - 2011 Nov

Keywords

Analytical solutions' L-sensitivity minimization
first-order FIR digital filters
frequency transformations
second-order modes
state-space digital filters

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2011.2164403

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AB - This paper reveals the class of digital filters with all second-order modes equal. We first prove that if the second-order modes of a digital filter are all equal, the L2-sensitivity minimization problem of the digital filter can be solved analytically. We derive a general expression of the transfer function of digital filters with all second-order modes equal. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter.

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KW - frequency transformations

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KW - state-space digital filters

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Derivation of the class of digital filters with all second-order modes equal

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Keywords

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