Roundoff Noise Reduction in IIR Digital Filters via Parallel Decomposition

A class of digital filter realizations is defined by decompos- ing the desired filter into a parallel connection of a direct form FIR filter and a residual IIR filter realized in direct form II. The minimum roundoff noise realization of this class is achieved by letting the 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, then there is an optimal decomposition, which is shown to reduce the roundoff noise without adding additional multipliers or adders. The case of filters with direct coupling is of particular interest, since it results naturally in designs obtained by the bilinear transformation, 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. Finally, by increasing the order of the FIR filter, the optimal synthesis becomes a noise reduction scheme at the cost of additional computational complexity.