SHORT-TIME FOURIER-TRANSFORM AND WAVELET TRANSFORM WITH FOURIER-DOMAIN PROCESSING

We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processin g, which is suitable for optical implementation. We also systematicall y analyze the selection of the window functions, especially those base d on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid fun ction that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inve rse STFT and the inverse WT. A couple of optical architectures based o n Fourier-domain processing for the STFT and the WT, by which real-tim e signal processing can be realized, are proposed.