A simple design of linear-phase, low-pass,recursive digital filters

Abstract

A simple technique for designing low-pass recursive digital filters with nearly linear phase characteristic is presented. The linearity of phase is obtained by placing the poles in the neighbourhood of the passband at equal intervals on a circle of radius r, inside the unit circle on the z-plane. The zeros are placed in the stopband on another circle of radius 1/r. The phase characteristics of these filters are shown to be linear with a maximum periodic error of r^m radian, where m is the sum of the number of poles and zeros of the filter. This error can be made small by suitably choosing m and r. Stop-band transmission characteristics of these filters are also examined and an upper bound obtained for the asymptotic db-loss.