Necessary and sufficient conditions for discrete wavelet frames in CN

We present necessary and sufficient conditions with explicit frame bounds for a discrete wavelet system of the form {DaTkϕ}a∈U(N),k∈IN to be a frame for the unitary space CN. It is shown that the canonical dual of a discrete wavelet frame for CN has the same structure. This is not true (well known) for canonical dual of a wavelet frame for L2(R). Several numerical examples are given to illustrate the results.