AN ANALYSIS OF VARIOUS METHODS FOR COMPUTING THE ENVELOPE OF A RANDOM SIGNAL

Based on different approaches for computing the Hilbert transform of a random signal, various methods for computing the envelope of a random signal are discussed. At present there are two main methods for computing the Hilbert transform, one is based on the Fourier analysis of the signal series and the other by constituting some moving average (MA) of the series with two-sided fixed coefficients. Although the statistical characteristics of the envelopes produced by these methods agree in general with those of an ideal envelope with off-line computing, they cannot be used to compute the instantaneous envelope in on-line computing. This paper proposes a new kind of approach for computing the Hilbert transform by constituting a MA with two-sided or one-sided optimum coefficients which can be determined according to the statistical characteristics of the signal. The statistical characteristics of computed envelopes by using various methods are derived. With two records of waves measured in the Bohai Sea and off the Taiwan Coast and two records of ship motions in a seaway, their envelopes and statistical characteristics are computed using the above methods and derived formulae. The comparisons show that: 1. The statistical characteristics including the spectra of the theoretical envelope and computed envelopes obtained by using above methods are in good agreement. 2. The methods of MA with optimum coefficients proposed here are superior to previous methods. Especially, the present method is feasible for on-line or nearly on-line computation of the random envelope.