Sampling and multiplicative filtering associated with the quadratic-phase Fourier transform

The quadratic-phase Fourier transform is a recent addition to the class of quadratic-phase integral transforms and embodies several signal processing tools including the Fourier, fractional Fourier, linear canonical, Fresnel and special affine Fourier transforms. The aim of this article is twofold: first, to obtain the sampling theorem associated with the quadratic-phase Fourier transform; second, to demonstrate the construction of computationally reliable multiplicative filters in the quadratic-phase Fourier domain. To facilitate the motive, we formulate a novel convolution structure in the quadratic-phase Fourier domain and also demonstrate its efficiency in filtering-out the unwanted components from a signal by employing the well-known Wigner distribution.