Correlated noise effects of structure in digital filters
Girard, Paul Edward
Parker, Sydney R.
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Noise generation caused by quantization of signals in digital filters is considered using matrix state-space techniques. The results are expressed in terms of the correlation of the errors so that the assumptions made about the statistical properties of the noise sources can be evaluated. The effect of correlation, which is shown to be significant, depends upon the specific structure of the filter and the relative location of the error source both topologically and temporally. Specifically, the results are applied to a newly extended set of canonic realizations of second order filters which are presented in the form of canonic arrays of coefficients. Output noise formulae for these realizations are presented for the two extreme assumptions of uncorrelated error sources and constant noise generation and are confirmed by experiment. These formulae are directly useful in analysis, design, and comparison. Additionally, new algorithms are presented, one for performing circular convolutions and the other for calculating the Discrete Fourier Transform.
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