Matrix Based Computation of Floating-Point Roundoff Noise

Abstract

A matrix based procedure is presented for computing the output roundoff noise power for filters implemented with floating-point arithmetic. The filter's computational structure is represented in terms of a product of matrices, known as a factored state variable description. The quantities needed to compute the output roundoff noise power are obtained from the factored state variable description via matrix manipulation. The expression for output roundoff noise power is shown to be of the same form as that for fixed-point arithmetic roundoff noise. Comparison indicates that, under very general conditions, fixed-point arithmetic provides better roundoff noise performance than floating point. Several examples are provided.