Theory of Roundoff Noise in Cascade Realizations of Finite Impulse Response Digital Filters

In recent years, many techniques have been developed for the design of Finite Impulse Response (FIR) digital filters. 2-8 It is now possible to readily design filters with arbitrary frequency or time response characteristics using the windowing, 2 - 3 frequency sampling, 4 or optimal design 5 - 8 methods. While both the windowing and frequency sampling techniques jrield suboptimal filters, they are useful because of their simplicity and ease of design. The optimal design technique is of special importance because the filters it generates can be proved to be optimum in a certain sense, 7 and because efficient algorithms exist for its implementation. 7 , 8 As a result of these important developments, the F I R type of digital filter is becoming increasingly attractive as an alternative to the I I R (Infinite Impulse Response) type of filter for practical applications. A major advantage of F I R filters over I I R filters is that an F I R filter f This paper is based on a thesis' submitted in partial fulfillment of the requirements for the degrees of Bachelor of Science and Master of Science in the Department of Electrical Engineering at the Massachusetts Institute of Technology in September 1972.