On the properties and design of stable IIR transfer functions generated using Fibonnaci numbers

C. S. Gargour; V. Ramachandran; Ravi Ramachandran

doi:10.1109/APCCAS.2006.342384

On the properties and design of stable IIR transfer functions generated using Fibonnaci numbers

C. S. Gargour, V. Ramachandran, Ravi Ramachandran

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper considers z-domain transfer functions whose denominator polynomial possesses the property that the coefficient of zⁱ is greater than the coefficient of z^i-1. Such transfer functions can be shown to be always stable and their denominator polynomials can be formed as a finite length time reversed Fibonacci sequence of numbers. Appropriate numerator polynomials can be configured to design lowpass, highpass, bandpass, band-elimination and allpass IIR filters. It is observed that the phase response closely approximates a linear behavior. This study is on the design of IIR filters using Fibonacci numbers. The advantages are that frequency selective filters with an approximately linear phase characteristic can be obtained with neither a stability test nor an analog prototype,

Original language	English (US)
Title of host publication	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Pages	1228-1231
Number of pages	4
DOIs	https://doi.org/10.1109/APCCAS.2006.342384
State	Published - Dec 1 2006
Event	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems - , Singapore Duration: Dec 4 2006 → Dec 6 2006

Other

Other	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Country	Singapore
Period	12/4/06 → 12/6/06

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/APCCAS.2006.342384

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Gargour, C. S., Ramachandran, V., & Ramachandran, R. (2006). On the properties and design of stable IIR transfer functions generated using Fibonnaci numbers. In APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems (pp. 1228-1231). [4145621] https://doi.org/10.1109/APCCAS.2006.342384

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title = "On the properties and design of stable IIR transfer functions generated using Fibonnaci numbers",

abstract = "This paper considers z-domain transfer functions whose denominator polynomial possesses the property that the coefficient of zi is greater than the coefficient of zi-1. Such transfer functions can be shown to be always stable and their denominator polynomials can be formed as a finite length time reversed Fibonacci sequence of numbers. Appropriate numerator polynomials can be configured to design lowpass, highpass, bandpass, band-elimination and allpass IIR filters. It is observed that the phase response closely approximates a linear behavior. This study is on the design of IIR filters using Fibonacci numbers. The advantages are that frequency selective filters with an approximately linear phase characteristic can be obtained with neither a stability test nor an analog prototype,",

author = "Gargour, {C. S.} and V. Ramachandran and Ravi Ramachandran",

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Gargour, CS, Ramachandran, V & Ramachandran, R 2006, On the properties and design of stable IIR transfer functions generated using Fibonnaci numbers. in APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems., 4145621, pp. 1228-1231, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems, Singapore, 12/4/06. https://doi.org/10.1109/APCCAS.2006.342384

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AU - Gargour, C. S.

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N2 - This paper considers z-domain transfer functions whose denominator polynomial possesses the property that the coefficient of zi is greater than the coefficient of zi-1. Such transfer functions can be shown to be always stable and their denominator polynomials can be formed as a finite length time reversed Fibonacci sequence of numbers. Appropriate numerator polynomials can be configured to design lowpass, highpass, bandpass, band-elimination and allpass IIR filters. It is observed that the phase response closely approximates a linear behavior. This study is on the design of IIR filters using Fibonacci numbers. The advantages are that frequency selective filters with an approximately linear phase characteristic can be obtained with neither a stability test nor an analog prototype,

AB - This paper considers z-domain transfer functions whose denominator polynomial possesses the property that the coefficient of zi is greater than the coefficient of zi-1. Such transfer functions can be shown to be always stable and their denominator polynomials can be formed as a finite length time reversed Fibonacci sequence of numbers. Appropriate numerator polynomials can be configured to design lowpass, highpass, bandpass, band-elimination and allpass IIR filters. It is observed that the phase response closely approximates a linear behavior. This study is on the design of IIR filters using Fibonacci numbers. The advantages are that frequency selective filters with an approximately linear phase characteristic can be obtained with neither a stability test nor an analog prototype,

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