On transforms between Gabor frames and wavelet frames

We describe a procedure that enables us to construct dual pairs of wavelet frames from certain dual pairs of Gabor frames. Applying the construction to Gabor frames generated by appropriate exponential Bsplines gives wavelet frames generated by functions whose Fourier transforms are compactly supported splines with geometrically distributed knot sequences.

There is also a reverse transform, which yields pairs of dual Gabor frames when applied to certain wavelet frames.