Statistical signal processing

Statistical signal processing is an area of Applied Mathematics and Signal Processing that treats signals as , dealing with their statistical properties (e.g., mean, covariance, etc.). Because of its very broad range of application Statistical signal processing is taught at the graduate level in either Electrical Engineering, Applied Mathematics, Pure Mathematics/Statistics, or even Biomedical Engineering and Physics departments around the world, although important applications exist in almost all scientific fields.

In many applications, a signal is modeled as functions consisting of both a deterministic and a component. A simple example and also a common model of many statistical systems is a signal ${\displaystyle y(t)}$ that consists of a deterministic part ${\displaystyle x(t)}$ added to noise which can be modeled in many situations as white Gaussian noise ${\displaystyle w(t)}$:

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