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The time-recursive computation has been proven a particularly useful tool in real-time data compression, in transform domain adaptive filtering, and in spectrum analysis. Unlike the FFT-based ones, the time-recursive architectures require only local communication. Also, they are modular and regular, thus they are very appropriate for VLSI implementation and they allow a high degree of parallelism. In this two-part paper, we establish an architectural framework for parallel time-recursive computation. We clonsider a class of linear operators that consists of the discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We show that the structure of the realization of a given linear operator is dictated by the decomposition of the latter with respect to proper basis functions. An optimal way for carrying out this decomposition is demonstrated. The parametric forms of the basis functions are identified and their properties pertinent to the architecture design are studied. A library of architectural building modules capable of realizing these functions is developed. An analysis of the implementatioin complexity for the aforementioned modules is conducted. Based on this framework, the time-recursive architecture of a given h e a r operator can be derived in a systematic routine way. Since 1991, he has been the Director of the Center for Satellite and Hybrid Communication Networks, a NASA Center for the Commercial Development of Space, which he co-founded. He has numerous publications in control and communication systems, and is the co-editor of Recent Progress in Stochastic Calculus (Spnnger-Verlag, 1990). His current research interests include stochastic systems and signal processing and understandmg with emphasis on speech and image signals, real-time architectures, symbolic computation, intelligent control systems, robust nonlinear control, dxtributed parameter systems, hybnd communication network simulahon and management.

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The time-recursive computation has been proved particularly useful for the real-time evaluation of one and two-dimensional block transforms. Unlike the FFT based ones, time-recursive architectures require only local cornmunication. Also, they are modular and regular, thus they are very appropriate for VLSI implementation and they allow high degree of parallelism.In this paper, we establish an architectural framework for parallel time-recursive computation. We consider a class of linear operators that consists of the discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We specify the properties of the linear operators that can be implemented efficiently in a time-recursive way. Based on these properties, we develop a routine that produces a time-recursive architectural implementation for a given operator. This routine is instructive for the design of a CAD tool that will facilitate the architecture derivation.Using this background, we design an architecture for the Modulated Lapped Transform (commonly called Modifled Discrete Cosine Transform), which has linear cost in operator counts.