Smart pixel-based wavelet transformation for wideband radar and sonar signal processing

Recently, there has been a great deal of interest in the application of wavelet transforms to signal processing applications. As an example, to obtain the source density function for a wideband radar or sonar signal from the measurement of scattered signals it is desirable to first perform the wavelet transform of the received signal before processing it. The use of the wavelet transform allows the selection of basis functions which are matched to the transmitted signal. Fundamentally, the wavelet transform of a signal is the correlation of the signal with a basis function derived from a mother wavelet and its scaled versions called daughter wavelets. Thus any real-time correlator can be used for the implementation of the wavelet transform. Since a one-dimensional input signal produces a two-dimensional wavelet transform, optical correlators provide a natural advantage over conventional electronic implementations. The VanderLugt correlator, the joint transform correlator and its derivative, the quasi-Fourier transform joint transform correlator can all be used to implement the wavelet transform, provided a spatial light modulator is used to convert the electrical input signal into an appropriate optical signal. The concept of the smart pixel is to integrate both electronic processing and individual optical devices on a common device to take advantage of the complexity of electronic processing circuits and the speed of optical devices. Arrays of these smart pixels would then bring with them the advantage of parallelism that optics could provide. Smart pixels can function as spatial light modulators providing additional electronic processing features. They are naturally well-suited to realizing wavelet transforms.