Translations:Prediction-error filters/2/en

—Michelangelo

Let $k=\left(k_{0}{,\ }k_{\rm {1}}{,\ }\dots {\ ,\ }k_{N-{\rm {1}}}\right)$ denote the least-squares prediction filter for prediction distance $\alpha$ The prediction-error filter results directly from the prediction filter. As we saw in equation 12 of Chapter 10, the prediction-error filter is $f={1},0,0,...,0,-k_{0},-k_{\rm {1}},-k_{N-1}$. The prediction-error operator has $\alpha -{\rm {1}}$ zeros that lie between the leading coefficient, which is 1, and the negative prediction-filter coefficients. These $\alpha -1$ zeros constitute the gap.