Pipelined VLSI recursive filter architectures using scattered look-ahead and decomposition

The authors explore various approaches to pipelining recursive digital filters. A past attempt to pipeline directly from recursive filters was based on clustered look-ahead computation, which leads to a linear increase in hardware with respect to the number of loop pipeline stages. However, the pipelined filters derived using this technique are not guaranteed to be stable. The authors introduce a new look-ahead approach (referred to as scattered look-ahead) to pipeline recursive filters in a way that guarantees stability. They also propose a decomposition technique to implement the nonrecursive portion (generated due to the scattered look-ahead) in a decomposed manner (for cases where the number of loop pipeline states is a power of two) to obtain pipelined realizations of logarithmic implementation complexity with respect to the number of loop pipeline stages (as opposed to linear). Based on the scattered look-ahead technique, they present fully pipelined and fully hardware efficient bidirectional linear systolic arrays and unidirectional ring arrays for implementation of high speed recursive digital filters