Negacyclic convolution

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In mathematics, negacyclic convolution is a convolution between two vectors ${\displaystyle \mathbf {x} =(x_{1},\dots ,x_{n})}$ and ${\displaystyle \mathbf {y} =(y_{1},...,y_{n})}$, giving the vector ${\displaystyle \mathbf {z} }$ whose components are defined as

${\displaystyle z_{k}=x_{0}y_{k}+\cdots +x_{k}y_{0}-(x_{k+1}y_{n-1}+\cdots +x_{n}y_{k+1}).}$

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

See also

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

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