Digital filter coefficients

All of the digital filter examples given in the previous section can be written in the following general forms:

Zero order:	yn = a0xn
First order:	yn = a0xn + a1xn-1
Second order:	yn = a0xn + a1xn-1 + a2xn-2

Similar expressions can be developed for filters of any order.

The constants a₀, a₁, a₂, ... appearing in these expressions are called the filter coefficients. The values of these coefficients determine the characteristics of a particular filter.