The order of a filter is defined as the order of its transfer function, as discussed in Chapter 6. For FIR filters, this is just the order of the transfer-function polynomial. Thus, from Equation (5.8), the order of the general, causal, length FIR filter is (provided ).
Note from Fig.5.5 that the order is also the total number of delay elements in the filter. This is typical of practical digital filter implementations. 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.
FIR Software Implementations
FIR Transfer Function