Laguerre discrete-time filter design

The design of discrete-time ideal filters by finite impulse response (FIR) method requires long FIR filter structures.This is due to the infinite impulse response characteristics of the ideal filters. Optimum Laguerre filter structures with smaller length can be used instead of FIR filters to reduce the order of the filters.In this paper the method of designing optimum Laguerre ideal low-pass, band-pass, high-pass, and band-reject filters is introduced. The optimization is performed by evaluating the Laguerre parameter and coefficients when the mean-square-error between the frequency response of the desired filter and its corresponding Laguerre network frequency response is minimum. The problem with the Laguerre filter design is the complexity of computations for evaluating the optimum Laguerre parameter. This complexity is reduced to one half by introducing a lemma.Both, analytical and numerical solutions are presented and the results are illustrated via some examples. The corresponding results yield a reduced filter order, and appropriate linear phase, with lower ripples in stop-band and pass-band compared to the conventional FIR filters.