Rounding noise in Mstage recursive digital filter
Abstract
Noise at the output of an Mstage recursive digital filter caused by rounding the results of arithmetic operations with a floating decimal point, results of additions and multiplications, is analyzed starting with the difference equation for the ith stage of an ideal biquadratic array. In the direct configuration of a real biquadratic array the response of the ith filter stage with a transfer function H(sub i)(z) = B(sub i)(z) A(sub i)sup 1 (z) (the transfer function of the nonrecursive part = B(sub i)(z), the recursive part = A(sub i)sup 1 (z), and i = 1,...,M) is treated as the response of a recursive digital filter with the transfer function A(sub i)sup 1 (z) to white sieve noise. In the canonical configuration of a real biquadratic array noise in both parts is also shown to be equivalent to white sieve noise. The dispersion of the rounding error is calculated accordingly, whereupon is determined the number of digits in the mantissa in the summators necessary for not exceeding the allowable dispersion.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 April 1987
 Bibcode:
 1987RpEEE........1G
 Keywords:

 Digital Filters;
 Signal Processing;
 White Noise;
 Difference Equations;
 Transfer Functions;
 Communications and Radar