On the Properties And Design of Stable IIR Transfer Functions Generated Using Fibonnaci Numbers

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