A Wideband Wavelet Based Estimator Correlator and its Properties

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is in the time-scale or wavelet transform domain. This paper presents a wideband wavelet transform domain implementation of an estimator-correlator (EC) detector and details the components of this processor, including weighted wavelet transforms and cascaded scattering functions. Key properties associated with this wavelet based wideband EC are also presented. The theoretical developments of the processor are based on group theory which provides a unified approach to detector development for both narrowband and wideband processors. The group theoretic concepts provide a powerful analysis tool for complex signal processing problems.