Error analysis of digital filter employing floating-point arithmetic

The error accumulation in a digital filter employing floatingpoint arithmetic is studied. Sources of errors are considered to originate from 1) roundoff in the arithmetic operations, 2) quantization of both the input and the initial states, and 3) effects of coefficient inaccuracies. Existing methods of analysis for the case of deterministic input (case A) and the case of stochastic input (case B) are reviewed and presented in the context of the canonical realization of a digital filter. A unified treatment of all these sources of errors is indicated, and results complementary to the existing results on the direct realization are thus obtained. A comparison is made of the roundoff error accumulation of the canonical realization with that of the direct realization, with the general conclusion that both realizations of any filter exhibit the same roundoff error distortion for any arbitrary wide-sense-stationary stochastic input.