Negacyclic convolution

In mathematics, negacyclic convolution^[1] 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.

References

↑ Knuth, Donald (1997). The art of computer programming (Third ed.). Reading, Mass: Addison-Wesley. p. 521. ISBN 978-0-201-89684-8.

References

See also