Wideband processing of acoustic signals using wavelet transforms. Part I. Theory

Wideband processing of acoustic signals is described and applied to the problem of source localization in an environment with multiple sensors and sources. To localize sources, the wideband correlation receiver output is expressed as an affine convolution equation. This expression for the wideband correlation receiver output is then deconvolved to obtain a minimum mean-square estimate of the wideband spreading function (also called the density function or the source distribution function). This deconvolved estimate is first derived for the case of one sensor actively imaging the environment. An estimate is then derived for the case of three or more passive sensors. This wideband processing removes many of the narrow-band restrictions and allows for significant motion between the sources and sensors. The underlying tool used is the wavelet transform.