Design of FIR Digital Differentiators Using Maximal Linearity Constraints

Ishtiaq Rasool KHAN; Masahiro OKUDA; Ryoji OHBA

Design of FIR Digital Differentiators Using Maximal Linearity Constraints

Ishtiaq Rasool KHAN, Masahiro OKUDA, Ryoji OHBA

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Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.8 pp.2010-2017

Publication Date: 2004/08/01

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Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)

Category: Filter Design

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Ishtiaq Rasool KHAN, Masahiro OKUDA, Ryoji OHBA, "Design of FIR Digital Differentiators Using Maximal Linearity Constraints" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 8, pp. 2010-2017, August 2004, doi: .
Abstract: Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e87-a_8_2010/_p

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@ARTICLE{e87-a_8_2010,
author={Ishtiaq Rasool KHAN, Masahiro OKUDA, Ryoji OHBA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Design of FIR Digital Differentiators Using Maximal Linearity Constraints},
year={2004},
volume={E87-A},
number={8},
pages={2010-2017},
abstract={Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Design of FIR Digital Differentiators Using Maximal Linearity Constraints
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2010
EP - 2017
AU - Ishtiaq Rasool KHAN
AU - Masahiro OKUDA
AU - Ryoji OHBA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2004
AB - Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.
ER -