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Roundoff noise generated by arithmetic operations in a digital-filter computational sequence is undesirable in that it serves to distort the true signal at the output. Furthermore, coefficient wordlength is directly related to the generated noise. It is shown that a minimization of the filter attenuation sensitivity, which is characteristic of wave digital filters, serves to reduce the noise. Analytical results confirm this for both floating-point and fixed-point systems. A simulation where the actual noise is measured produces results which demonstrate the superior performance of the wave digital filter over the standard z-transform filter.