The continuous gyrator wavelet transform: Properties and applications

In this paper, a brief introduction to the gyrator transform and its fundamental properties are given. The continuous wavelet transform associated with the gyrator transform is defined and obtained some basic properties. Parseval’s identity, Plarcherel’s theorem and the reconstruction formula for the gyrator wavelet transform are discussed. Exploiting the theory of convolution operator, it is shown that [Formula: see text] is also a gyrator wavelet, under certain assumptions on [Formula: see text] and [Formula: see text]. Last, we have successfully applied some of the derived results to investigate the analytical solutions of the [Formula: see text] order non-homogeneous partial differential equations.