Gabor dual spline windows

Gabor Dual Spline Windows

An algorithm is presented for constructing dual Gabor window functions that are splines. The spline windows are supported in [−1, 1], with a knot at x = 0, and can be taken C smooth and symmetric. The translation and modulation parameters satisfy 0 < ab ≤ 1/2. The full range 0 < ab < 1 is handled by introducing an additional knot. Many explicit examples are found.

Fast computation of dual Gabor windows for non-separable lattices

In this paper we present an attractive computation technique for approximating the continuous-time dual window for the Gabor signal expansion on a non-separable time-frequency lattice instead of on the traditional rectangular lattice. This non-separable lattice is described by means of a lattice generator matrix. The computation technique is based on a generalized Wexler-Raz identity and avoids...

Gabor windows supported on [ - 1, 1] and dual windows with small support

Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...

Image processing by alternate dual Gabor frames

‎We present an application of the dual Gabor frames to image‎ ‎processing‎. ‎Our algorithm is based on finding some dual Gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying Hilbert space‎. ‎The advantages of these duals‎ ‎constructed by a polynomial of Gabor frame generators are compared‎ ‎with their canonical dual‎.

Spline-type Spaces in Gabor Analysis