Analysis of the effect of finite register length on the efficiency of digital filters for the detection of signals on a noise background

The present study examines the effect of errors caused by the finite register length of the arithmetic and memory units on the parameters of digital filters (based on discrete and fast Fourier transforms) for the detection of signals on a noise background. An analysis of the statistical characteristics of such errors is used to obtain expressions for determining the necessary number of digits of the memory and arithmetic unit registers, guaranteeing an admissible magnitude of losses in efficiency. Mathematical-modeling results are presented, which confirm the validity of the relationships derived.