In actual application, the third-order cumulants
of [(q+1).sup.2] have to be computed; that is, [C.sub.3y]([[tau].sub.1],[[tau].sub.2]), 0 [less than or equal to] [[tau].sub.1], [[tau].sub.2] [less than or equal to] q.
Data were interpreted using the "method of cumulants
Another common method is signal statistical features, which is an easy method to achieve suboptimal result by obtaining statistical characteristics features, such as high-order cumulants
, wavelet features, and multidimensional signal features.
In the text, without introducing detailed definitions and combinatorial backgrounds, free moments and free cumulants
of operators will be computed.
Li presented a classification algorithm based on wavelet and higher-order cumulants
, whose experiments show that Gaussian white noise can be suppressed effectively by the analysis of extracted characteristics parameters.
Since Gaussian noise is fully characterized by the covariance matrix or the two-body correlation function, any nonvanishing higher-order cumulants
or reduced correlation functions are signatures of non-Gaussianity of the probability distribution function (PDF), P(x).
In , comparatively an efficient algorithm based on cumulants
is proposed for 4D parameter estimation of near-field sources (frequency, range, and 2D DOA), but it also requires a large number of snapshots and ends up with higher mean square error (MSE).
Cornish-Fisher expansion is a well-known mathematical expansion which is able to approximate the quantiles of a random variable based on its first few cumulants
or moments .
Monte Carlo Simulation and Half Invariants (Cumulants
Based on the cumulants
from the CF and MGF, the aggregate interference is approximated to a number of distributions such as
hand concern the moments and free cumulants
of familiar random variables
Higher order cumulants
(HOC) can describe the higher order statistical characteristic of random process.