PIPELINED RECURSIVE FILTER WITH MINIMUM ORDER AUGMENTATION

Pipelining is an efficient way for improving the average computation speed of an arithmetic processor. The higher the degree of pipeline segmentation, the faster the possible pipeline clock speed. However, for an M-stage pipeline, the result of a given operation is available only M clock periods after initiating the computation. In a recursive filter, the output at the nth sampling instance, y(n), is a function of its previous outputs, y(n - 1) through y(n - N). Hence, the computation of y(n) cannot be initiated before the computations of y(n - 1) through y(n - N) are completed. Voelcker et al. and Kogge et al. independently devised two augmentation techniques for resolving the dependence problem in the computation of y(n). The advantage of their techniques is that the number of nonzero denominator coefficients of the augmented filter is the same as that of the prototype filter. However, using their techniques, the augmentation required to ensure stability may be excessively high resulting in a very complex numerator realization. In this paper, we present a technique which results in a minimum order augmentation. The complexity of the filter designed using our technique is very much lower. Various pipelining architectures are presented. It is also demonstrated by using an example that when compared to the prototype filter, the augmented filter has a lower coefficient sensitivity and better roundoff noise performance.