Filter Order
Refers to the [see page 3, number] of coefficients (past inputs or outputs (not both)) of the filter that is involved in the current calculation.
Filter complexity is often characterised by it's order.
The degree to which a practical filter [approximates](/brain/20201120235414-filter_approximation/) it's idealised form is a function
of its order.
Note: We consider any filter that uses the current input as a first-order filter.
For example a biquad-filter has an order of 2 (because it uses 2 previous inputs/outputs) and it has 2 poles and 2 zeros alongside the current input meaning it has 5 coefficients.