Abstract
僅使用非高斯信號量測值來鑑別線性非時變 (linear time-invariant(LTI)) 系統在許多研究領域上是非常重要的，如地質信號的反旋捲運算(deconvolution)、通訊中的頻道等化、雷達、聲納、語音處理及影像處理等等。近幾年來，用高階統計量於非最小相位 (nonminimum-phase)LTI 系統之鑑別，在這些信號處理的研究領域上，更是引起了廣泛的注意。因為高階統計量不僅包含了系統振幅的資訊，同時也包含了系統相位的訊息。再者，它天生能免於受高斯雜訊的影響。本篇論文提供了一個新的基於高階統計量 (higher-order statistics)(稱為 cumulant)的線性非時變系統之相位估計方法，僅使用系統之輸出量測信號，而此信號是受高斯 (Gaussian) 雜訊所污染的非高斯量測信號。藉由一個全通(allpass) 濾波器來處理此量測信號，使得這全通濾波器的輸出的一個M-階 cumulant (M 大於或等於 3) 之絕對值為最大，以估計系統的相位。它如同一些只使用高階頻譜之相位 (polyspectra phase) 來估計系統相位的方法一樣，並不涉及系統的振幅估計。再者，眾所週知的基於最小相位-全通之分解 (minimum-phase - allpass decomposition) 的方法，需要一個基於二階統計量 (correlation) 的白化 (whitening) 濾波器來前置處理此量測信號，然後估計系統的相位，而本論文所提出之方法，並不需要任何對此量測信號的前置處理。一些模擬結果及一些使用真實語音資料的實驗結果支持了本篇論文所提供的基於高階統計量之相位估計方法。最後，我們做了一些結論。The identification of a linear time-invariant (LTI) system h(n) with only noisy output measurements is very important inmany signal processing areas such as seismic deconvolution,channel equalization in communications, radar, sonar,speech processing and image processing. Recently, cumulantbased identification of nonminimum-phase LTI systems withonly non-Gaussian output measurements has drawn extensiveattention in the previous signal processing areas becausecumulants, which are blind to any kind of a Gaussianprocess, can be used to not only extract the amplitudeinformation but also the phase information of $h(n)$, meanwhilethey are inherently immune from Gaussian measurement noise.This paper presents a new cumulant based phase estimationmethod with only non-Gaussian measurements x(n) contaminated byGaussian noise for an unknown (minimum or nonminimum-phase)linear time-invariant (LTI) system h(n). The proposed methodestimates the phase of h(n) by processing x(n) with an allpassfilter such that the output y(n) has a maximum Mth-order (Mgreater or equal to 3$) cumulant in absolute value. Amplituderesponse estimation of h(n) is not involved throughout theproposed method as methods which estimate the phase of h(n)only from the phase of polyspectra of x(n). Moreover, it doesnot need any preprocessing of x(n) with a correlation basedwhitening filter, which is noise sensitive and crucially limitsthe estimation accuracy of system phase, as needed by the well-known minimum-phase (MP) - allpass (AP) decomposition basedmethods. Some simulation results followed by some experimentalresults with real speech data are provided to support theproposed cumulant based phase estimation method. Finally, thepaper concludes with some conclusions.