The order of a digital filter can be defined as the number of previous inputs (stored in the processor's memory) used to calculate the current output.
This is illustrated by the filters given as examples in the previous section.
- Example (1): yn = xn
- This is a zero order filter, since the current output yn depends only on the current input xn and not on any previous inputs.
- Example (2): yn = Kxn
- The order of this filter is again zero, since no previous outputs are required to give the current output value.
- Example (3): yn = xn-1
- This is a first order filter, as one previous input (xn-1) is required to calculate yn. (Note that this filter is classed as first-order because it uses one previous input, even though the current input is not used).
- Example (4): yn = xn - xn-1
- This is again a first order filter, since one previous input value is required to give the current output.
- Example (5): yn = (xn + xn-1) / 2
- The order of this filter is again equal to 1 since it uses just one previous input value.
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