Linear prediction

Linear prediction tries to estimate what the value a sample will have, based on previous samples. The general equation is:

$x'(n)=\sum _{i=1}^{p}a_{i}x(n-i)$

The trick with linear prediction is to choose the coefficients $a_{i}$ in such a way that the difference between the estimated value $x'(n)$ and the real value $x(n)$ is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example $x'(n)=x(n-1)$ or $x'(n)=2x(n-1)-x(n-2)$, where the first assumes a function of the form $y=a$ and the second assumes a function of the form $y=ax+b$).