Finite Gabor systems and uncertainty principle for block sliding discrete fourier transform

In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual tight frame using discrete time Zak transform is given. Also, a method to calculate coefficients expansion in case and necessary sufficient condition existence biorthogonal pair Riesz basis l2(ZL) Further, introduce notion block sliding Fourier (BSDFT) which reduces computational complexity give uncertainty principle BSDFT. An two Parseval frames terms sparse representations Finally, numerical sparsity, an