Lesson B Introduction to Higher-order Statistics
When signals are non-Gaussian, higher than second-order statistics can be very useful. These higher-order statistics are called cumulants and are related to higher-order moments. We prefer to use cumulants rather than higher-order moments because cumulants have some very desirable properties, which moments do not have, that let us treat cumulants as operators.
Higher-order statistics are defined in this lesson. In general, they are multidimensional functions; e.g., third-order statistics are functions of two variables and fourth-order statistics are functions of three variables. Cumulants, which are analogous to cor-relation functions, work directly with signals in the time domain. Polyspectra, ...