Parameters and PDF form

We apply the statistical model (5.7) for ${\bf x}$, which depends on a the $N\times 1$ vector $\bar{{\bf x}}$, where

$$\bar{{\bf x}} = {\bf A} {\bf b},$$ (5.8)

where ${\bf A}$ is the matrix of MEL band functions, and ${\bf b}$ is a $D\times 1$ vector. Thus, ${\bf b}$ is the only parameter of the PDF. We then maximize (5.7) over ${\bf b}$. This maximizing value, denoted by ${\bf b}_{\rm ML}({\bf x})$, is an iteratively-determined feature and will not be the same as the raw MEL band analysis coefficients obtained by the closed form ${\bf z}={\bf A}^\prime {\bf x}$.