Windowed linear canonical transform and its applications

In this paper, we generalize the windowed Fourier transform to the windowed linear canonical transform by substituting the Fourier transform kernel with the linear canonical transform kernel in the windowed Fourier transform definition. It offers local contents, enjoys high resolution, and eliminates cross terms. Some useful properties of the windowed linear canonical transform are derived. Those include covariance property, orthogonality property and inversion formulas. As applications analogues of the Poisson summation formula, sampling formulas and series expansions are given.

► We generalize windowed Fourier transform (WFT) to windowed linear canonical transform (WLCT).
► WLCT offers local contents, enjoys high resolution, and eliminates cross-terms.
► It has similar properties as WFT, including covariance, orthogonality and inversion.
► The analogues of the Poisson summation formula, sampling formulas and series expansions are given.