Module stats 

Second- and fourth-order statistics of complex sequences.

• Moments: the moments $\mathbb{E}[r^{2}]$, $\mathbb{E}|r|^{2}$, $\mathbb{E}[r^{4}]$, $\mathbb{E}[r^{2}|r|^{2}]$ and $\mathbb{E}|r|^{4}$, of a sample (the means) or of a discrete distribution (the points and their probabilities): the cumulants of the blind estimators, the M2M4 estimator and the radius of the constant modulus algorithm all start from them;
• Correlation: the cross-correlation $\sum_{k} a_{k} b_{k}^{*}$ of two sequences and their energies, with the normalised correlation

$$ \rho = \frac{\left|\sum_{k} a_{k} b_{k}^{*}\right|}{\sqrt{\sum_{k} |a_{k}|^{2} \sum_{k} |b_{k}|^{2}}} \in [0, 1], $$

the quality of a frame synchronisation, the effective SNR of a sequence against another and the test of the singularity of a 2 × 2 equaliser.

Examples

use comnum_math::C64;
use comnum_math::stats::{Correlation, Moments};
let a = [C64::new(1.0, 0.0), C64::new(0.0, 1.0)];
let m = Moments::sample(&a);
assert_eq!((m.m21, m.m42), (1.0, 1.0));
assert_eq!(m.m20, C64::new(0.0, 0.0)); // 1 and -1
let b: Vec<C64> = a.iter().map(|v| v * C64::new(0.0, 2.0)).collect();
assert!((Correlation::between(&a, &b).rho() - 1.0).abs() < 1e-15);

Structs

Correlation

The cross-correlation of two sequences and their energies (see the module).

Moments

The moments of order two and four of a complex random variable $r$ (see the module).