FIR Order

The order of a filter is defined as the order of its transfer function, as discussed in Chapter 6. Thus, from Eq. (5.8), the order of the general, causal, length $N=M+1$ FIR filter is $M$ (provided $b_M\neq 0$).

Note from Fig.5.5 that the order $M$ is also the total number of delay elements in the filter. When the number of delay elements in the implementation (Fig.5.5) is equal to the filter order, the filter implementation is said to be canonical with respect to delay. It is not possible to implement a given transfer function in fewer delays than the transfer function order, but it is possible (and sometimes even desirable) to have extra delays.