### 5.23.1 Cross-correlation of two signals : cross_correlation

cross_correlation takes two arguments, a complex vector v of length n and a complex vector w of length m . The returned value is the complex vector z=v⋆w of length N=n+m−1 which is the cross-correlation of the two input vectors, i.e. such that the following holds :

z_{k}= | | | w_{i}^{∗}, k=0,1,…,N−1, |

where

v^{∗}=[v_{0},v_{1},…,v_{n−1}, | | ] and w^{∗}=[ | | ,w_{0},w_{1},…,w_{m−1}]. |

For example, input :

cross_correlation([1,2],[3,4,5])

Output :

[6.0,11.0,14.0,5.0]