The authors investigate the roundoff noise for infinite-impulse-response (IIR) digital filters realized in some canonical forms. The minimum roundoff noise realization of this class is achieved by letting the finite-impulse-response (FIR) coefficients be identical to the corresponding partial impulse response of the desired filter. When the order of the numerator of the transfer function of the desired filter is greater than or equal to that of the denominator, there is an optimal decomposition which is shown to reduce the roundoff noise without adding additional multipliers or adders. The proposed structure is applied to parallel and cascade forms, with real as well as complex arithmetic and shown to result in lower roundoff noise. By increasing the order of the FIR filter, the optimal synthesis becomes a noise reduction scheme at the cost of additional computational complexity.
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