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 ...

This code example demonstrates the convolution theorem with the use of the Complex Fast Fourier Transform (FFT), complex-by-complex multiplication, and support functions, which are part of the ...

Abstract: Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant ...

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 ...