随机包络的各种计算法及其统计特征

An Analysis of Various Methods for Computing Envelope of a Random Signal

基于求算随机信号的希氏（Ｈｉｌｂｅｒｒ）变换的不同途径构成了计算随机包络的不同方法。现有的几种实算希氏变换的途径，主要是傅氏（Ｆｏｕｒｉｅｒ）反变换法和具有固定系数的双边滑动和方法，虽然离线计算时各法所得的包络的统计特征大体相同且有效，但均不能用来作在线（Ｏｎ—ｌｉｎｅ）计算包络的瞬时值。本文提出了以“双边最佳（系数）滑动和”或“单边最佳滑动和”计算希氏变换的途径，其中的最佳系数可根据被处理的信号统计特性确定，并给出了各种途径所求包络结果的统计特征公式。文中就二个海浪记录和二个实船的摇摆记录作了计算，对各种方法进行检验比较。结果表明，本文方法计算速度较快、结果较稳定，并适合于包络的在线或准在线计算。

Basing on different approaches for computing the Hilbert tranSformation of a random signal, varinus methodfor computed envelocpe of the random signal are produced. So far there are mainly two Kinds of approaches for computing theHilbert transformation, One based on the Fourier analysis of the shoal series and the other by constituting some MovingAverage (MA) of the signal series with two-sided fixed coefficients. Although statistical characteristics of the envelopes bythese methods agree in seneral to ones of an ideal envelope when off-line computing, they can not be used to compute theinstantaneous envelope in on- line computing. This P8per proposes new kind of apptoaches for computing the Hilberttransformation by constituting MA with two-sided or one-sided optimum coefficientS which can be determined according to theStatistical characteristics of the signal.The statistical charactsristics of computed envelopeS by using various methods are derived. With two records of wavesmeasured in Bobal Sea and Taiwan Coast and two records of ship motions in a seaway their envelope and statisticalcharaotristics are computed by using above methods and derived formulas. The compeison shows that:1.The statistical characteristics including the spectra of theoretical envelope and computed envelocpe Obtained by usingabove methods are in good agreement in most cabal2. The methods of MA with optimum coefficients Proposed here are superior to the previous ones. Especially the Presentmethod are feasible for on-line or nearly on-line compunction of random envelope.