Abstract: In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters.

Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form ∫ $f_{1}(x)f_{2}(x-\theta )dx$, where ...

The convolution theorem in Section 8.4 is not correct. Multiplication of the DFTs of two signals results in the periodic/circular convolution of the two signals. This is why zero-padding is required ...