Discrete Frames of Non‐Uniform Shifts in Frequency Domain

ABSTRACT Non‐uniform frames play a significant role in the stable analysis and decomposition of signals (functions) when the indexing set may not be a group or non‐uniform lattice. We analyze frame conditions for a collection of functions obtained by non‐uniform shifts of matrix‐valued functions. Necessary and sufficient conditions for the existence of matrix‐valued discrete Bessel sequences over non‐uniform displacement parameters in terms of the Fourier transform of window functions are given. We also present perturbation results for matrix‐valued non‐uniform discrete frames.