The distributions of local extrema of Gaussian noise and of its envelope

Cramer and Leadbetter's (1967) result for the distribution of the local maxima of stationary Gaussian noise is studied and plotted. Its derivation is used for finding the distributions of the local maxima and minima of the envelope of narrowband Gaussian noise. These distributions, too, are studied and plotted, including the limiting cases of very wide and narrow noise spectra.