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 ...

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 ...

正整数 $N$ に対して, $Q_N$ を $\lfloor {N \over x} \rfloor$ で表される正整数全体とする. 数列 $f,g:\mathbb{N} \to \mathbb{F}_p$ について ...

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 ...