Fixed Point Roundoff Effects in Frequency Sampling Filters

Under certain conditions, frequency sampling filters can implement linear phase filters more efficiently than direct convolution filters. Unlike a direct convolution filter, a frequency sampling filter uses a recursive structure which requires exact pole zero cancellation on the unit circle. When implemented with special purpose digital hardware or as a program on a digital computer, errors due to finite length registers and finite precision arithmetic prevent exact pole zero cancellation making the filter unstable. To stabilize the filter, the poles and zeros on the unit circle are moved to a circle of radius r where 0 r 1. The errors due to finite length registers and finite precision arithmetic also degrade the performance of frequency sampling filters. In this chapter, the effects that finite precision fixed point arithmetic have on frequency sampling filters are analyzed. These effects, represented as output noise levels, are determined as a function of register length, time and the value of r.