Fixed point roundoff noise in frequency sampling filters

✍ Scribed by Peter A. Stubberud

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 833 KB
• Volume: 332
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(95)00048-8

✦ Synopsis

A frequency sampling filter which & 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 fnite length registers and finite precision arithmetic can prevent exaet pole zero cancellation makin 9 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 2frequency sampling filters is determinedas a function ofre#ister length, time and the value of r. An example demonstrates that for a fixed register lenyth and output noise level, a frequency sampling filter designed with 0 < r < 1 can approximate a linearphasefilter better than a frequency sampling filter designed with r = 1.