Analysis of roundoff noise in floating point digital filters

A systematic approach for the analysis of roundoff noise in floating point digital filters is presented. The analysis is based on a high level model developed to deal with the errors in the inner product operation. The model consists of an efficient procedure to keep track of the addition scheme is used in the inner product, and to compute the statistics of the errors. The tractability of the analysis is demonstrated by deriving general expressions for the roundoff noise of FIR (finite impulse response) and IIR (infinite impulse response) filters. Also, the connection between coefficient sensitivity analysis and roundoff noise analysis is discussed