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利用Hilbert变换作同态反褶积,要求原始信号序列必须是最小相位的。本文提出了对信号作最小相位变换的新的有效方法,即先按本方法求出信号序列[x(n)]的z多项式z~NX(z)的最大模根的估值z~*,然后以|z~*|~(-1)为底对序列[x(n)]进行指数加权,于是构成新的最小相位序列[y(n)]=[x(n)|z~*|~(-n)]。文中给出了对信号序列进行最小相位变换实现同态反褶积的具体步骤和利用递推法实现同态反褶积的简单流程。最后还给出了模拟试验结果。当最大模根移到单位圆内某一窄圆环上时,可以精确地恢复出子波的波形,并允许逆谱的宽度在相当宽的范围内改变。
Using Hilbert transform for homomorphic deconvolution requires that the original signal sequence must be minimum phase. In this paper, we propose a new and effective method for minimum phase transformation of signal, that is, first estimate z ~ * of maximal module root of z-polynomial z ~ NX (z) of signal sequence [x (n) Then the sequence [x (n)] is exponentially weighted with | z ~ * | ~ (-1), thus forming a new minimum phase sequence [y (n)] = [x ~ (-n)]. In this paper, the concrete steps of homomorphic deconvolution for the minimum phase transformation of signal sequence and the simple flow of recursive method for homomorphic deconvolution are given. Finally, the simulation results are given. When the largest root moves to a narrow circle within a unit circle, the waveform of the wavelet can be accurately recovered and the width of the inverse spectrum can be varied over a relatively wide range.