# Dictionary:Normal equations

${\displaystyle \phi _{zx}(\tau )=\sum f_{t}\phi _{xx}(\tau -t).}$
A digitized input xt passed through the filter ft yields the actual output yt which in a least-squares sense is closest to a desired output zt; ${\displaystyle \phi _{xx}(\tau )}$ is the autocorrelation of xt and ${\displaystyle \phi _{zx}(\tau )}$ is the cross-correlation of zt with xt as a function of a time shift ${\displaystyle \tau }$. See Levinson algorithm.