# Auto-correlation of a signal: auto_correlation

### 15.2.7 Auto-correlation of a signal: auto_correlation

The auto correlation of a vector is its cross correlation with itself (see Section 15.2.6). The auto_correlation command computes the auto correlation of a vector.

- auto_correlation takes one argument:
  v, a complex vector.
- auto_correlation(v) returns the cross-correlation of v with itself, v⋆ v.

#### Example.

Input:

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

Output:

⎡ ⎣ | 2.0,9.0,15.0,28.0,37.0,44.0,58.0,58.0,68.0,91.0,68.0,58.0,58.0,44.0,37.0,28.0,15.0,9.0,2.0 | ⎤ ⎦