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 ...

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.

Convolution is a remarkable property of the Fourier transform, often cited in the literature as the “faltung theorem”. Convolution is a remarkable property of the Fourier transform, often cited in the ...