The maximum delay, in samples, used in creating each output sample is called the order of the filter.
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.
yn = xn is a zero order filter, since the current output yn depends only on the current input xn and not on any previous inputs.
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)
yn = (xn - xn-2) / 2
This filter's order is 2, since the processor must store two previous inputs in order to compute the current output. This is unaffected by the absence of an explicit xn-1 term in the filter expression.
Order of Filter
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