Convolution

circular convolution cyclic convolution

The convolution of two signals $x$ and $y$ in ${\bf C}^N$ is denoted ``$x\ast y$'' and defined by

$$\zbox {(x\ast y)_n \isdef \sum_{m=0}^{N-1}x(m) y(n-m)}$$

Note that this is circular convolution (or ``cyclic'' convolution).^7.2 The importance of convolution in linear systems theory is discussed in §8.3