Extreme value estimates for arbitrary bandwidth Gaussian processes using the analytic envelope

A procedure is presented for the estimation of extreme values of stationary Gaussian random processes with arbitrary bandwidths. This approach is based on the analytic envelope defined by the Hilbert Transform; this envelope is Rayleigh distributed regardless of bandwidth. For experimentally derived data that has been converted into digital form, the Hilbert Transform is approximated using algorithms implemented on a digital computer to produce samples of the envelope's time history. Next, the degree of correlation between these envelope samples is taken into account using a method developed from simulation studies of a series of synthetic Gaussian time histories with varying bandwidths. Once this correlation effect has been estimated, the standard methods of order statistics are applied to these samples using the Rayleigh probability density function. Examples of applying this procedure to experimentally derived data are presented.