An Approximation to Gaussian Wavelet Suitable for Analog Filter Implementations

Abstract

This paper presents a novel fourth order approximation function to 1st Gaussian wavelet using time domain analysis of linear time-invariant (LTI) systems and the conditions for the transfer functions of realizable analog filters. Fourth order approximation is used for compact circuit implementations which might use a cascade of only two biquads. Transfer function for a realizable filter and the related Simulink model are also supplied in the paper with numerical results.