Vectorizing IIR filters

In the clustered look-ahead technique for pipelining a recursion, an Nth-order infinite impulse response (IIR) filter is transformed into an (N+M-1)th-order filter which can be implemented as a vector recursion, with M output values determined simultaneously. A difficulty with pipelining in this manner is that the transformed filter is not necessarily stable, for a stable original filter. In this work, the stability problem is partially resolved. The stability problem for second-order filters is completely solved, and some partial results are given on the stability of vectorized digital Butterworth and Chebyshev filters