On the rank of the discrete Gabor transform matrix

dBy using the discrete Gabor transform or expansion, the time domain sequen ces are mapped into joint time-frequency domain matrices or vice versa. In many applications, it is more effective to process signals, i.e., two-dimen sional matrices, in the joint time-frequency domain than in the time or fre quency domain alone. From the mathematical point of view, the processing of the discrete Gabor coefficients is no more than matrix computation. So it is beneficial to understand the properties of the Gabor coefficient matrix. In this letter, we shall investigate the rank of the Gabor coefficient mat rix of a one-dimensional time domain signal, which is one of the most impor tant matrix properties. (C) 2001 Elsevier Science B.V. All rights reserved.