Filter Order

The maximum delay, in samples, used in creating each output sample is called the order of the filter. In the difference-equation representation, the order is the larger of $M$ and $N$ in Eq. (5.1). For example, $y(n) = x(n) - x(n - 1) - 2y(n - 1) + y(n - 2)$ specifies a particular second-order filter. If $M$ and $N$ in Eq. (5.1) are constrained to be finite (which is, of course, necessary in practice), then Eq. (5.1) represents the class of all finite-order causal LTI digital filters.