Time-Recursive Architectures and Wavelet Transform

The time-recursive computation has been proved as a particularly useful tool in real-time data compression and in transform domain adaptive filtering, with applications in the areas of audio, radar, sonar and video. 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 high degree of parallelism. In this paper, we propose 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 define a shift property of the linear operators and reveal its relation with the time-recursive implementation. We demonstrate the potential of the proposed framework by designing a time-recursive architecture for the Discrete Wavelet Transform.