Analysis of multiwindow Gabor-type schemes by frame methods
The authors generalize the Gabor scheme by using several windows instead of a single window, i.e., \[ f(k)= \sum^R_{r= 0} c_{r,m,n} g_{r,m,n}(x),\quad g_{r,m,n}= g_r(x- na)e^{2\pi imbx}. \] Combining the Zak transform with the concept of frames, they characterize properties of the expansion coefficients \(g_{r,m,n}\) for the case where the product \(ab\) is a rational number. They consider the use of different sampling rates for each window as well as the application of nonexponential kernels. The authors examine the Balian-Low phenomenon in their context of multiwindows.
scientific article; zbMATH DE number 1038810
scientific article