Negacyclic convolution

In mathematics, negacyclic convolution is a convolution between two vectors $\mathbf{𝐱}=(x_1,\dots ,x_n)$ and $\mathbf{𝐲}=(y_1,...,y_n)$, giving the vector $\mathbf{𝐳}$ whose components are defined as

$z_k=x_0{y}_k+\cdots +x_k{y}_0-(x_{k+1}{y}_{n-1}+\cdots +x_n{y}_{k+1}).$

It is also called skew circular convolution or wrapped convolution. It results from multiplication of a skew circulant matrix, generated by vector a, with vector b.

See also

• Circular convolution theorem
• Circular convolution (a.k.a. cyclic convolution)