System identification Consider an unknown LTI system and an FIR system model, as shown i...

System identification Consider an unknown LTI system and an FIR system model, as shown in Fig. P8.26. Both systems are excited by the same input sequence {x(n)} The problem is to determine the coefficients {h(n), 0 ≤ n ≤M -1) of the FIR model

of the system to minimize the average squared error between the outputs of the two systems.

(a) Use the least-squares criterion to determine the equations for the optimum FIR filter coefficients.

(b) Repeat part (a) if the output of the unknown system is corrupted by an additive white noise (w(n)) sequence with variance .