Fixed Point Roundoff noise in Frequency Sampling Filters

Document Type

Article

Publication Date

5-1995

Publication Title

The Journal of the Franklin Institute

Volume

332

Issue

3

First page number:

337

Last page number:

360

Abstract

A frequency sampling filter which is a finite impulse response digital filter uses a recursive structure that requires exact pole zero cancellation on the unit circle. When implemented with digital technology, errors due to finite length registers and finite precision arithmetic can prevent exact pole zero cancellation making the filter unstable. To guarantee stability, the poles and zeros on the unit circle are moved to a circle of radius r where 0 < r < 1. Most frequency sampling filter design techniques determine optimal frequency responses for r = 1 and then chose a value of r, 0 < r < 1, near to 1 so that the filter's frequency response does not differ significantly. Recently, other techniques have been presented that determine optimal frequency responses for 0 < r < 1. In this paper, the fixed point roundoff noise of Type 1 and Type 2 frequency sampling filters is determined as a function of register length, time and the value of r. An example demonstrates that for a fixed register length and output noise level, a frequency sampling filter designed with 0 < r < 1 can approximate a linear phase filter better than a frequency sampling filter designed with r = 1.

Keywords

Digital filters (Mathematics); Electric distortion; Electric filters; Electric filters; Digital; Electric noise; Frequency response (Electrical engineering); Frequency sampling filter

Permissions

Use Find in Your Library, contact the author, or use interlibrary loan to garner a copy of the article. Publisher copyright policy allows author to archive post-print (author’s final manuscript). When post-print is available or publisher policy changes, the article will be deposited

UNLV article access

Search your library

Share

COinS