This section presents approaches for pipelining 1st-order recursive digital filter topologies using look-ahead techniques. With look-ahead technique, cancelling poles and zeros with equal angular spacing at a distance from the origin the same as that of the original pole are introduced. The pipelined realizations require a linear increase in complexity in the number of loop pipeline stages, and are always guaranteed to be stable for 1st-order IIR filters provided that the original filter is stable. A decomposition technique is then presented to implement the nonrecursive portion generated due to the look-ahead process in a decomposed manner to obtain an implementation with logarithmic increase in hardware with respect to the number of loop pipeline stages. The decomposition technique is the key in obtaining area-efficient implementations, and makes pipelined realizations attractive for high speed VLSI IIR filter implementations.
Consider a 1st-order IIR filter designed by the transfer function
The output sample y(n) can be computed using the input sample u(n) and the past output sample as follows:
The sample rate of this recursive filter is limited by the computation time of one multiply-add operation because there is only one delay ...