無限脈衝響應濾波器之設計及分析

蕭開龍 ； 李純慧 ； 鄭睿賢

《電腦與通訊應用》 1期 (2007/01) Pp. 59-70

https://doi.org/10.6602/JCCA.2007.1.7

摘要

本文的研究，針對無限脈衝響應濾波器(IIR Filter)爲了偵測訊號濾波之目的，而使用微分方程式之探討模式進行分析。其演算法收斂特性也經由常微分方程進行探討解析。它利用數位信號處理程序而顯示證實訊號頻率的估計，結果證實了經由數位信號處理轉換後所得之估測值與理論解十分接近。此種演算法首先使用拉普拉斯變換，再藉由(1)脈衝不變轉換法(2)雙線性轉換法等兩種轉換方式，將連續性訊號轉換爲使用Z-轉換的離散系統，本文中並利用MATLAB軟體將其結果計算分析，並將結果以圖形繪出，證實該兩種演算法則所得之Z-轉換計算結果與正確解十分近似，使用MATLAB軟體是爲了計算之便利性，與藉由它的分析結果得以支持轉換結果之正確性。

關鍵字

無限脈衝響應濾波器 ； Z-轉換 ； MATLAB

並列摘要

In this study, for the purpose of detect the signal about IIR (infinite impulse response) filters; we use an ordinary differential equation to simulate and deal with the problems. The convergence characteristic of algorithm for differential equation has been preceded analysis in this study. It takes the advantage of digital signal estimate processing to show a confirm signal frequency's estimate. The problems use the transformation algorithm by using Laplace transformation first for continuous system, then again by means of (1) pulse invariance transformation methods (2) bilinear transformation methods of two kinds of conversion modes, convert continuity signal to a discrete system Z-transfer result. This paper takes the advantage of MATLAB software. From the processing of calculation obtains the needed results, and draws its result as diagram. At last, we confirm the two kinds of numerical algorithm calculations for Z-transfer. The calculations results compare to exact solutions are approximate. MATLAB software is very convenient tool for calculation using and its analysis results can prove the accuracy of convert results.

並列關鍵字

digital active optical lattice filters ； MATLAB ； signal processing