It is a well known fact that the time-frequency domain is very well adapted for representing audio signals. The main two features of time-frequency representations of many classes of audio signals are sparsity (signals are generally well approximated using a small number of coefficients) and persistence (significant coefficients are not isolated, and tend to form clusters). This contribution pr...

This paper extends the e cient factorization of the Gabor frame operator developed by Strohmer in [17] to the Gabor analysis/synthesis operator. The factorization provides a fast method for computing the discrete Gabor transform (DGT) and several algorithms associated with it. The factorization algorithm should be used when the involved window and signal have the same length. An optimized imple...

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this function. The frame hounds are calculated by means of the eigenvalues...

We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier corresponds to a side-diagonal of this matrix. This representation is especially useful for operators whose associated matrix possesses some offdiagonal decay. In thi...

We give necessary and suÆcient conditions for g 2W (L1; `) to generate a Gabor frame over certain irregular lattices.

We show that (g2, a, b) is a Gabor frame when a > 0, b > 0, ab < 1 and g2(t) = ( 1 2πγ) 1 2 (cosh πγt)−1 is a hyperbolic secant with scaling parameter γ > 0. This is accomplished by expressing the Zak transform of g2 in terms of the Zak transform of the Gaussian g1(t) = (2γ) 1 4 exp(−πγt2), together with an appropriate use of the Ron-Shen criterion for being a Gabor frame. As a side result it f...