I have some doubts about the meaning of order for digital filters. All I'll put here is taken from these slides.
1) Let's start from the definition of FIR filters:
From this definition we see that order means the number of delayed input values in the input - output equation of the filter.
So my question is: is there a link with the concept of "order" in control theory? For instance, in control theory a second order system (or filter) has a transfer function with a second - degree polynomial at the denominator, and this happens also in analog filters (where it is sometimes equal to the number of reactive components of the circuit). Is it applicable also here?
2) Let's consider the so called windows design method:
Basically it tries to realize (in an approximate way) a filter by selecting a window of the desired pulse response of the filter, and you may see from the expression of w(n) that the length of the window is equal to the order of the filter (M-1).
So my question is: which is the link between the order of the filter (as described in 1) and the number of samples of the window?