Reconstruction of multidimensional digital signals

Abstract

We study the reconstruction of multidimensional digital signals in multirate digital signal processing. We show that the composition of sampling operator and interpolation operator forms the frame operator of multivariate discrete time wavelet (MDTW) system of scale matrix [Formula: see text]. By taking a collection of [Formula: see text] filters, we construct dual MDTW tight frames. Also, we discuss the existence and construction of MDTW Parseval frames in multidimensional sequence space. The necessary and sufficient condition for the existence of orthonormal basis of scale matrix [Formula: see text] is discussed. Using dual MDTW tight frame, we characterize biorthogonal pair of Riesz bases. Further, we define multivariate Parseval frame of weighted exponentials, dual multivariate tight frame of weighted exponentials of scale matrix [Formula: see text] in periodic space [Formula: see text]. Finally, we give the applications of MDTW frames in the theory of frames of weighted exponentials of scale matrix [Formula: see text] in periodic space [Formula: see text].