A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in L 2 (R) was considered by Gabardo and Nashed. In this setting, the associated translation set is a spectrum Λ which is not necessarily a group nor a uniform discrete set, given Λ = {0, r/N} + 2 Z, where 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. In this article, we continue this study based on non-standard setting and obtain some inequalities for the nonuniform wavelet system f µ j,λ (x) = (2N) j/2 f (2N) j x − λ e − ιπA B (t 2 −λ 2) , j ∈ Z, λ ∈ Λ to be a frame associated with linear canonical transform in L 2 (R). We use the concept of linear canonical transform so that our results generalise and sharpen some well-known wavelet inequalities.