Research themes include: relations between fractional transforms (in particular the fractional Fourier transform) and other mixed-signal representations (in particular the Wigner distribution and the ambiguity function); applications of fractional transforms and bilinear mixed-signal representations to partially coherent optical signals; variations on the Gabor transform with a non-rectangular sampling lattice (possibly of interest to video compression and digital communications); relations between time-scale and time-frequency representations (of interest to audio/speech compression); generalized `windowed’ transforms such as the local Kautz transform; efficient implementation of various transforms by means of filter banks (crucial, for example, for high-data rate transmission and storage systems); extensions of these concepts to multi-dimensional signals (as encountered, for example, in digital communications and in video signal processing).
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