Theory of roundoff noise in cascade realizations of finite impulse response digital filters

This paper presents a theoretical treatment of the roundoff noise problem for the special case of cascade realizations of Finite Impulse Response (FIR) digital filters.† Explicit relations for evaluating roundoff noise with the usual assumption of uncorrelated samples are presented. Useful scaling methods are stated and classified as to conditions when these methods are optimum. Important differences between use of these scaling procedures for Infinite Impulse Response (IIR) filters and FIR filters are pointed out. Finally, useful properties of linear phase FIR filters are discussed.