Generating simulated reverberation using noiselets

Abstract

Of the approaches to generating stochastic realizations of reverberation time series, the simple point scatterer model (PSM) is appealing because the statistics evolve naturally as the number of scatterers increases. Unfortunately, the number of eigenrays required is often overwhelming, especially for broadband signals. The more common ‘‘variance factorization model’’ (VFM) uses far fewer eigenrays to compute a time‐dependent estimate of the variance of the reverberation, and applies the spectral factorization theorem to generate a sequence of short‐time spectra, which is inverse transformed and concatenated to form the desired time series. However, the variance and factorization steps scale with the square and the cube, respectively, of the number of receiver channels, so the advantage is lost for element‐level simulations of complex receivers. The ‘‘noiselet model’’ is conceptually similar to the PSM, but the transmit pulse is replaced by an ensemble of precomputed ‘‘noiselets,’’ which are sums of randomly weighted and delayed copies of the original transmit pulse. The number of eigenrays is thus comparable to the VFM, but scaling is linear in the number of channels, rendering this method tractable for real‐time broadband element‐level simulation. Examples are shown for a linear FM pulse at 10 kHz and 400‐Hz bandwidth.