Correlated noise due to roundoff in fixed point digital filters

It is shown that correlation between quantization error sources in finite precision fixed point digital filters can be significant even when a filter is driven by a random input. It is demonstrated that correlation coefficients can be estimated in terms of relative values of multiplying constants and the filter structure. A general formulation of filter output noise is developed in terms of the covariance matrices of the error sources. Thus the effects of correlation can be taken into account analytically for purposes of design and comparison.