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.

The table opposite gives the values of the coefficients of each of the filters given as examples in the previous section.

Example Order a0 a1 a2
1 0 1 - -
2 0 K - -
3 1 0 1 -
4 1 1 -1 -
5 1 1/2 1/2 -
6 2 1/3 1/3 1/3
7 2 1/2 0 -1/2


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