General Linear Model

From Some Linear Models we know that the general linear model can be written as

$$x=A{g}_1(t)+B{g}_2(t)+C{g}_3(t)+w$$

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Rewriting this as a discrete function, where we have

• Parameter vector: $\Theta =[{\theta }_0,\dots ,{\theta }_{d-1}]$
  • Which is based on a set of $N$ observations $\{x[n]\}$. Which lets our rewrite our general model to

$$x[n]=\sum _{d=0}^{M-1}{\theta }_d{f}_d[n]+w[n]$$

And in matrix form

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Formula

$x=H\Theta +w$ Where $w[n]\sim N(w;0,{\sigma }^2)$, we have $N$ observations and the parameter vector has $d$ elements.

Any model that can be written on the form above is a Linear Model.