A Uniied Approach to Numerical Algorithms for Discrete Gabor Expansions

| The Gabor transform yields a discrete representation of a signal in the phase space 1, 2]. Since the Gabor transform is non-orthogonal, eecient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so-called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of eecient numerical algorithms. This presentation is the rst systematic account of its kind. In particular, it is shown that diierent algorithms for the computation of the dual window correspond to diierent factorizations of the frame operator. Simple number theoretic conditions on the time-frequency lattice parameters imply additional structural properties of the frame operator.