Wavelet frames associated with linear canonical transform on spectrum

The linear canonical transform(LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we in this paper construct associated wavelet frames. To be precise we introduce wavelet frames whose construction depends on the nonuniform multiresolution analysis associated with linear canonical transform(LCT-NUMRA) whose translation set is not necessarily a group. The translation set is taken for elements in A = {0, r/N} + 2 Z, N >= 1 (an integer) and r is an odd integer with 1 <= r <= 2N - 1 such that r and N are relatively prime and Z is the set of all integers. Furthermore we establish necessary and sufficient condition for such nonuniform wavelet frames associated with linear canonical transform.