Translations:Least-squares prediction and smoothing/3/en

Before an actual digital filter can be designed, it is necessary to build a model. The time-honored least-squares model requires three signals: the input signal $x=(\ x_{0},x_{1},x_{2},...)$, the actual output signal $y=\left(y_{0}{,\ }y_{\rm {l}}{,\ }y_{2}{,\ .\ ..}\right)$, and the desired output signal $z=(\ z_{0},z_{1},z_{2},\ldots )$. The filter is a finite-impulse-response (FIR) filter. Let such a filter k have a finite number of coefficients, given by