Approximate band-pass limiter envelope distributions

An approximate distribution is computed for the envelope of sine wave plus noise after passage through a wide-band filter, limiter, and narrow-band filter. It is shown that as the input bandwidth to the limiter increases, the output envelope distribution converges to the usual sine wave in noise envelope distribution, without limiting, but with a definite db loss. First-order correction terms are supplied which make it possible to compute first-order statistics for the output envelope when the output signal-to-noise ratio is on the order of one.