This homework is to learn how to use MATLAB for system identification and the nature of indentification to the original signal and the original signal with noise. Five systems have been tested. The first two systems are the real system (the make-up parameter). The first system is an continous system which has been discretized. The second systeem is discrete by its nature. The last three examples have been made up to show different kinds of system. The third example is a normal linear discrete system. The fourth system is a nonlinear discrete system which nonlinear parameters are in the same degree of delay. The last system is a nonlinear discrete system which nonlinear signals are different in delay.
Two methods of identification have been used. The first one is for batch process, while the other is for the recursive operation. Both of them are working fine with the pure output. When noise is added, both of them do not give a good approximation. Because the noise is quite high, it is difficult to say that the error in the identification comes from the identification method.
Different systems have different effects to the noise also. In some systems, e.g. the last system, the identification process can give a good approximation of the parameter although there is noise in the output signal. If we consider the output from the last system, we can see that the characteristic (trend) of the output does not change much when the noise is added.