LINEAR CANONICAL WAVELET FRAMES AND THEIR STABILITY

The aim of this study is to address this issue by constructing a novel family of wavelets in L-2(R) based on the linear canonical transform having certain extra degrees of freedom. At the outset, we present a necessary condition and three sufficient conditions for the canonical wavelet system {psi(H)(ma0, nb0) (t) : m, n is an element of Z, H = (A, B, C, D) } to be a frame for L-2(R) without any decay assumptions on the generator of the system. Secondly, we show that under certain assumptions, a canonical wavelet frame remains a frame in L-2(R) when the generator of the wavelet frame psi or the dilation and translation parameters a(0) and b(0) are perturbed.