Weighted convolutions in the quadratic-phase Fourier domains: Product theorems and applications

Abstract

Convolution and product operations play a pivotal role in different aspects of signal and image processing, including quantum mechanics, sampling, filter designing and so on. In this article, we formulate two types of novel weighted convolutions, Type-I and Type-II, in the framework of the quadratic-phase Fourier transforms. Besides presenting the efficacy of the weighted convolutions of Type-I via the well-known Wigner distribution, we also show that a variant of novel weighted convolution of Type-II is convenient to implement in constructing computationally reliable multiplicative filters in the quadratic-phase Fourier domain.