  We propose a multi input multi output(MIMO) system identification framework
by interpreting the MIMO system in terms of a multirate synthesis filter bank.
The proposed methodology is discussed in two steps: in the first step the MIMO
system is interpreted as a synthesis filter bank and the second step is to
convert the MIMO system into a SISO system "without any loss of information",
which re-structures the system identification problem into a SISO form. The
system identification problem, in its new form, is identical to the problem of
obtaining the signal matched synthesis filter bank (SMSFB) as proposed in Part
II. Since we have developed fast algorithms to obtain the filter bank
coefficients in Part II, for "the given data case" as well as "the given
statistics case", we can use these algorithm for the MIMO system identification
as well. This framework can have an adaptive as well as block processing
implementation. The algorithms, used here, involve only scalar computations,
unlike the conventional MIMO system identification algorithms where one
requires matrix computations. These order recursive algorithm can also be used
to obtain approximate smaller order model for large order systems without using
any model order reduction algorithm. The proposed identification framework can
also be used for SISO LPTV system identification and also for a SIMO or MISO
system. The efficacy of the proposed scheme is validated and its performance in
the presence of measurement noise is illustrated using simulation results.
