Dictionary:Normal equations

{{#category_index:N|normal equations}} The set of linear simultaneous equations whose solution gives a least-squares fit (in particular, a Wiener filter, q.v.):

$\phi _{zx}(\tau )=\sum f_{t}\phi _{xx}(\tau -t).$

A digitized input x_t passed through the filter f_t yields the actual output y_t which in a least-squares sense is closest to a desired output z_t; $\phi _{xx}(\tau )$ is the autocorrelation of x_t and $\phi _{zx}(\tau )$ is the cross-correlation of z_t with x_t as a function of a time shift $\tau$. See Levinson algorithm.

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