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Computationally efficient MIMO system identification using Signal Matched Synthesis Filter Bank

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.