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.

Using free harmonic analysis and the theory of regular variation, we show that the monotonic strict domain of attraction for the standard arc-sine law coincides with the classical one for the standard ...

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 ...

1 Mathematical Sciences Department, University of Mines and Technology, Tarkwa, Ghana. 2 Faculty of Science and Technology, University of Silesia in Katowice, Sosnowiec, Poland. The existence of an ...

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: The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and ...