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 communication. 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 Modified Discrete Cosine Transform), which has linear cost in operator counts.