Frequency interval model reduction of complex fir digital filters

Ahmad Jazlan; Umair Zulfiqar; Victor Sreeram; Deepak Kumar; Roberto Togneri; Hasan Firdaus Mohd Zaki

doi:10.3934/naco.2019021

Article Contents

2019, Volume 9, Issue 3: 319-326. Doi: 10.3934/naco.2019021

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Frequency interval model reduction of complex fir digital filters

1.
Department of Mechatronics Engineering, Kulliyah of Engineering, International Islamic University Malaysia, 53100 Jalan Gombak, Malaysia
2.
School of Electrical and Electronics Engineering, University of Western Australia, 35 Stirling Highway, WA 6009, Australia
3.
Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad, 211004, India

^* Corresponding author: ahmadjazlan@iium.edu.my
^* Corresponding author: ahmadjazlan@iium.edu.my

Received: May 2018

Revised: April 2019

Published: May 2019

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Abstract

In this paper, a model reduction method for FIR filters with complex coefficients based on frequency interval impulse response Gramians is developed. The advantage of the proposed method is that only one Lyapunov equation needs to be solved in order to obtain the information regarding the frequency interval controllability and observability of the system. In addition this method overcomes the limitations of using cross Gramians which are not applicable for filters with complex coefficients. The effectiveness of the proposed method is demonstrated by a numerical example.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Magnitude Response of 35^th order IIR Filter

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Figure 2. Magnitude Response of 30^th order IIR Filter

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Figure 3. Magnitude Response of 23^rd order IIR Filter

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