Unknown filter

Given inputs and outputs, the problem of finding an unknown filter appears to be overdetermined, so we write $\bold y \approx \bold X \bold f$where the matrix $\bold X$ is a matrix of downshifted columns like (19). Thus the quadratic form to be minimized is a restatement of equation (25) using filter definitions:

$$Q(\bold f', \bold f) \eq (\bold X\bold f - \bold y)' (\bold X\bold f - \bold y)$$ (27)

The solution $\bold f$ is found just as we found (26), and it is the set of simultaneous equations $\bold 0 = \bold X'(\bold X\bold f - \bold y)$.