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 { ψ H ma0,nb0 (t) : m, n ∈ 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 ψ or the dilation and translation parameters a0 and b0 are perturbed.
