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Digital Filter 
The order of a filter is the amount of previous values taken into account to calculate the current value.
A FIR filter has a finite impulse response and its output only depends previous inputs.
The output of an IIR filter depends on previous input values and previous output values
For example, an analog RC low pass filter is an IIR filter because its impulse response is of the form and therfore not zero for and infinite time.