Convolution

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

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

Note that this is circular convolution (or ``cyclic'' convolution).^7.3 The importance of convolution in linear systems theory is discussed in §8.3