Roundoff noise prediction in short-wordlength fixed-point digital filters

Consideration is given to recursive fixed-point digital filters employing a signal wordlength in the range of 4 to 8 bits. Experimentally determined values of roundoff-noise variance are found to deviate markedly from those predicted in the normal manner. Such deviation is caused mainly by correlations between signal and error sequences. A method is proposed whereby improved predictions of noise variance may be obtained in the case of first order filters. Finally, it is demonstrated that, when the `coefficient slicing¿¿ realisation is used to realise filters with sufficiently quantised coefficients, such filters yield both a very low level of roundoff noise, and also excellent agreement between the predictions of a simple model and measured noise levels