應用離散Walsh轉換於二維離散非時變系統之判別與簡化

Abstract

本篇論文主要探討離散Walsh轉換在二維離散非時變系統上的一些應用。在此，我們利用離散Walsh轉換於二維離散非時變系統響應的計算、系統判別以及模式簡化。另外，我們基於類神經網路提出一個可即時運算離散Walsh轉換的線路。 藉助移位離散Walsh轉換及矩陣Kronecker乘積，將原本表示系統輸入輸出關係的差分方程式轉換為線性聯立方程式來解，我們可以求出在零初值下，對任何形態之輸入的二維系統響應。其二，將有限項的輸入與受雜訊干擾的輸出作離散Walsh轉換，以Walsh頻譜匹配的觀點，解出由轉換函數的係數及Walsh頻譜構成的線性聯立方程式，我們可得到在系統輸出受干擾下所判定的二維系統之轉換函數。就Walsh頻譜匹配的觀點，離散Walsh轉換亦被用來簡化二維離散非時變系統，簡化後的模式在該階數中與原系統的Walsh頻譜有最小平方誤差。以上離散Walsh轉換在二維系統的三種應用，均有例子來驗證其可行性及優越性。 源自類神經網路用於解決線性規劃問題的觀念，我們設計一個類神經網路架構的電路來計算離散Walsh轉換，對電路褸態與暫態響應作了分析並探討裝配成超大型積體電路的可行性。模擬的結果顯示，所提出的方法確實可用來作離散Walsh轉換的即時運算。

The discrete Walsh transform (DWT) is applied to response analysis, identification and model reduction of the 2-D discrete-time LSI system. The data arrays are transformed into discrete Walsh spectrum matrices using DWT. First, with the shift DWT being utilized and the Walsh spectra manipulated by Kronecker product of two matrices, the response of 2-D system can be easily evaluated for arbitrary in- put with zero initial conditions. Next, from the point of view of data matching, the transfer function of 2-D system is identified from finite input-output data, where the output is mixed with uniformly distributed disturbance. In the third part, the 2-D discrete Walsh spectrum matching approach is also used for reducing the transfer function of a given 2-D system to a lower order model. Examples are illustrated to demonstrate the usefulness. Moreover, an electronic circuit, based on a neural net, to compute the DWT is also presented. The circuit behavior is analyzed and the fabrication problem is considered as well. Simulation results show that the proposed circuit is suitable for real-time DWT computation.