### 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 :

zk= |
N−1
∑
i=k
vi−k∗
| wi∗, k=0,1,…,N−1,

where

v∗=[v0,v1,…,vn−1, |
0,0,…,0
◥ |  | ▼ |  | ◤
m−1
| ] and w∗=[ |
0,0,…,0
◥ |  | ▼ |  | ◤
n−1
| ,w0,w1,…,wm−1].

For example, input :

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

Output :

[6.0,11.0,14.0,5.0]