Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form

Abstract

The roundoff-noise outputs from two transpose configurations, each for the cascade and parallel forms of a digital filter, are analyzed for the case of uncorrelated roundoff noise and fixed dynamic range. Corresponding transpose configurations are compared on the basis of the variance, or total average power, and the peak spectral density of the output roundoff noise. In addition to providing general computational techniques to be employed in choosing an appropriate configuration for the digital filter, these results also indicate useful "rules of thumb" relating to this choice of configuration. Included are indications of good (although not necessarily optimum) sequential orderings and pole-zero pairings for the second-order sections comprising the cascade form. Computational results are presented which indicate that the analysis is quite accurate and useful.