Minimization of Roundoff Noise in Digital Filters.
STANFORD UNIV CALIF STANFORD ELECTRONICS LABS
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One limitation of the digital filter is the error caused by the rounding of the data to fit in the prescribed word length. Another important constraint is on the dynamic range of the filter which is set by the finite-purpose computer, fixed-point arithmetic is usuallly preferred to floating point because it leads to simpler construction. Representation as additive white noise is made of the roundoff error resulting from fixed-point arithmetic operations under the assumption of independence of the error sequence from sample to sample and from source to source. Synthesis procedures are described based on the minimax noise principle for the minimization of the roundoff noise within the limitations imposed by the dynamic range constraints. The minimax noise principle developed in the thesis asserts that the roundoff noise is minimized if the states of the filter are chosen such that they are well-behaved. Applications of the principle have led to digital filter structures modeled on classical lumped inductor-capacitor networks in both ladder and lattice forms. The most important application lies in its incorporation into the cascade canonical realization of the filter. Computer predictions of the roundoff noise of sample filters serve to verify the principle. The cascade structure designed according to the minimax principle is shown to possess noise characteristics superior to those arising from other known cascade design methods. Author
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