Statistical signal processing is an area of signal processing dealing with signals and their statistical properties (e.g., mean, covariance, etc.). It is primarily covered by the field of electrical and computer engineering, although important applications exist in almost all scientific fields. Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability theory and statistics, the covariance between two real-valued random variables X and Y, with expected values and is defined as: where E is the expected value. ... Electrical and Computer Engineering is a major at many institutes of higher education. ...

Statistical signal processing is founded on the principle that signals are not deterministic functions. Rather, signals are modeled as functions consisting of both deterministic and stochastic components. A simple example and also a common model of many statistical systems is a signal x(t) that consists of a deterministic part s(t) with added Gaussian noise: . Given information about a statistical system and the random variable from which it is derived, we can increase our knowledge of the output signal; conversely, given the statistical properties of the output signal, we can infer the properties of the underlying random variable. Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ... Gaussian noise is noise that has a probability density function (pdf) of the normal distribution (a. ... A random variable is a mathematical function that maps outcomes of random experiments to numbers. ...

These statistical techniques are developed in the fields of estimation theory, detection theory, and numerous related fields that rely on statistical information to maximize their efficiency. It has been suggested that this article or section be merged with estimator. ... Detection theory, or signal detection theory, is a means to quantify the ability to discern between signal and noise. ...