Signal Processing

MA means "moving average ",

We assume that the signal whose PSD we want to estimate is the input of an MA filter, and we estimate the output's power from this PSD.

Let x(k) be a time series. We consider that it is an MA process of order p if we can express its value at time t as a linear combination of random errors (white noise).

Mathematically, we translate this as:

\(\forall\ t:x(k)=\epsilon_k+\sum_{1}^{p}{a_i\epsilon_{k-i}}\) (39)

The noise \(\epsilon_k\) being white with power \(\sigma_u^2\) and (𝛼₁, ..., 𝛼_p) of the real numbers.