Uncorrelated roundoff noise in digital filters

Methods for the analysis of uncorrelated roundoff errors in one-dimensional digital filter structures are discussed, and the types of arithmetic calculations employed in manipulating binary numbers and the quantization of binary numbers are briefly reviewed. Models for the analysis of quantization errors in fixed-point and floating-point digital filters are presented for first order and scaled fixed-point digital filters. Attention is given to the computer algorithm for examining digital filter structures, including roundoff noise and first-order sensitivity analysis. The correlation between coefficient sensitivity and quantization noise, as well as the use of interval arithmetic for determining the interval bounds on quantization noise is examined.