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 and in Eq.(5.1). For example, specifies a particular second-order filter. If and 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.
Causal Recursive Filters