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.

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