Filter generating function
= Filter generating function
{title2=$A(z)=\sum_{j\in\mathbb Z}a_jz^j$}
For absolutely summable linear-filter coefficients, the generating function is the displayed <Laurent series>, absolutely convergent on the <unit circle>. If the filter is one-sided, it is a <power series> analytic inside the <unit disk>. A two-sided filter need not have a nonempty larger annulus of convergence. Substituting the <backshift operator> gives the formal notation $Y=A(B)X$.