Pipeline interleaving and parallelism in recursive digital filters. II. Pipelined incremental block filtering

For pt.I see ibid., vol.37, no.7, p.1099 (1989). Block implementation and fine-grain pipelined block implementation of recursive digital filters are discussed. A new technique of incremental output computation is introduced which requires a linear complexity in block size. Based on the clustered look-ahead and incremental output computation approaches, incremental block-state structure is derived for block implementation of state-space filters of multiplication complexity linear in block size. The incremental block-state structure is also extended for the multirate recursive filtering case. The techniques of scattered look-ahead, clustered look-ahead, decomposition, and incremental output computation are combined to introduce several pipeline stages inside the recursive loop of the block filter. Deeply pipelined block filter structures are derived for implementation of direct-form and state-space-form recursive digital filters. The multiplication complexity of these pipelined block filters is linear with respect to the block size and logarithmic with respect to the number of loop pipeline stages, and the complexities due to pipelining and block processing are additive.<>