Reduced Complexity Approximation and Design of Gaussian Impulse Response Filters and Wavelets

A systematic method for realizing filters with a Gaussian impulse response is introduced in this work. For this purpose, the Laplace transform is used to obtain the transfer function which corresponds to the Gaussian impulse response. Since this transfer function has an exponential term, a rational integer-order approximating transfer function is derived by employing a curve-fitting based method applied on both gain and phase responses of the original transfer function. This concept is also applied on the derivatives of the Gaussian impulse response, leading to wavelet filter transfer functions. The findings in this work are supported by both simulation and experimental results using the Cadence IC design suite as well as a Field Programmable Analog Array (FPAA) platform.