Non-separable windowed linear canonical transform

The non-separable linear canonical transform (NSLCT) is a remarkable addition to the class of integral transforms which is based on generic 2n x 2n free, symplectic matrix M with n(2n + 1) degrees of freedom. However, the NSLCT is inadequate for localized analysis of non-transient signals, particularly chirp-like signals. In the present article, we introduce a novel integral transform coined as the non-separable windowed linear canonical transform (NSWLCT), which is endowed with higher degrees of freedom primarily meant for an efficient localized analysis of chirp signals. Firstly, we provide the time-frequency analysis of the proposed transform in the non-separable LCT domain. Secondly, we investigate the basic properties of the proposed transform including the orthogonality relation, inversion formula and the range theorem. Finally, we present examples of some well-known window functions in the non-separable LCT domain.