VLSI architectures to compute the Wigner Distribution

Abstract

The Wigner Distribution has always drawn the attention of researchers due to its capability of representinh the time-frequency or space-frequency characterization of signals. Its qualities have not been exploited till now due to the enormous amount of computations. needed. In recent years parallel computers have become available and with the advent of VLSI technology it is possible to conceive of concurrent arrays for computing and manipulating multiple data. The purpose of this paper is to analyze existing VLSI architectures for implementing the Wigner Distribution and to propose and discuss new hybrid designs for its computation in any dimension. We review the Wigner Distribution of one-dimensional signals. It is shown that the lower bound on AT p 2 for computing the Wigner Distribution is O( N 2 log 2 N) for a one-dimensional signal. This paper bestowes two contributions in the analysis of pipelined VLSI architectures for DSP. The first is in introducing the notion of asymptotic area efficiency ( E) which, in addition to AT 2, is used as another focal point in our analyses. The second contribution is in presenting a basic design methodology for pipelining arrays under constraints of I/O bandwidth by matching their data rate ratios. Well matched arrays yield good area time performance with hifh efficiency. Existing architectures for computing the Wigner Distribution are analyzed and discussed for area time tradeoff and efficiency. The pipeline methodology forms the basis for new architectures by a systematic construction from arrays that compute subproblems. The purpose of this paper is to systematically search for an optimal structure for computing the Wigner Distribution. For the computation of the one-dimensional Wigner Distribution we propose: • (i) Serial designs based on the single cell correlator pipelined with the N cell DFT or the cascade. These circuits are well matched with the single cell correlator and yield an AT 2 product of O( N 3 log 3 N) with an area efficiency of 0.5 and 1, respectively. • (ii) The N cell correlator pipelined with the butterfly. These two arrays are inherently well matched. They yield an optimal AT 2 product and their overall efficiency is 1. • (iii) The perfect shuffle and the N cell correlator arrays mismatch. By applying the pipelining technique yields several structures are extracted of which one is optimal.