Showing papers by "Keshab K. Parhi published in 1988"

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

Abstract: 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. >

Two-dimensional recursive digital filtering: pipelining, one- and two-dimensional block processing

Abstract: Unlike one-dimensional recursive systems, two-dimensional recursive digital filter algorithms possess a large amount of inherent concurrency which can be exploited for pipelining and/or parallelism. The locus of these concurrent computations is referred to as the concurrent computation region. The authors describe the use of this concurrency to derive pipelined and one-dimensional block architecture for implementation of two-dimensional recursive digital filters by appropriate interleaving (or indexing) of the input samples, without requiring any algorithm transformation and without any hardware overhead. They also derive a two-dimensional incremental block filter using look-ahead computation and incremental computation techniques. Pipelined two-dimensional block structures and the index mapping functions for various architectures are presented. Finally, it is shown that for an N-dimensional recursive filter, the concurrent computation region corresponds to an (N-1)-dimensional hyperplane. >

Algorithm and architecture designs for high-speed digital signal processing

Abstract: This thesis explores systematic approaches to design of high-speed algorithms and architectures for real-time signal and image processing in general, and for one- and two-dimensional recursive and adaptive digital filters in particular. First we address rate-optimal software-programmable multiprocessor implementation of signal processing algorithms described by data-flow programs. We introduce the notion of perfect data-flow programs, and prove that fully-static rate-optimal multiprocessor schedules can always be constructed for such programs using no retiming at all. We study properties of program unfolding transformations, and derive an expression for the optimum unfolding factor to reduce any data-flow signal processing program to an equivalent perfect data-flow program, which can then be scheduled rate-optimally in a fully-static manner. An upper bound on the number of processors to achieve a rate-optimal schedule is also derived. Next we develop high-speed algorithms for one- and two-dimensional recursive adaptive digital filters. Look-ahead algorithms are proposed to change the basic linear filter structures (while maintaining identical input-output behavior) and to create additional concurrency. Scattered look-ahead and decomposition algorithms are used to implement high-speed recursive and adaptive digital filters using fine-grain pipelining, with logarithmic increase in hardware for a linear increase in the sample rate. A technique of incremental output computation is proposed and used to derive incremental block digital filters of linear multiplication complexity in block size, as opposed to the square multiplication complexity in all previous block filter structures. Two-dimensional recursive digital filters inherently possess large amount of concurrency. An index mapping transformation is used to exploit this concurrency, and to derive fine-grain pipelined and one-dimensional block implementation of two-dimensional recursive digital filters. Look-ahead and incremental computation techniques are extended to two-dimensions, and are used to derive an efficient incremental two-dimensional recursive block digital filter architecture. Look-ahead and program unfolding transformations are performed on general iterative data-flow signal processing programs to increase concurrency. These transformations are useful where the designed algorithms are unable to meet the real-time requirements of the target application.