Consider the problem of performing system identification as shown previously in Figure 9.49. Suppose the system to be identified is the following IIR filter.
Write a MATLAB program that uses the FDSP toolbox function f lmscorr to identify a model of order m = 50 for this system. Use an input consisting of N = 2000 samples of white noise uniformly distributed over [-1, 1], a relative step size of α = 1, and the default smoothing parameter β.
(a) Plot the learning curve.
(b) Plot the step sizes.
(c) Plot the magnitude response of H(z) and W(z) on the same graph using a legend where W(z) is the adaptive filter using the final values for the weights.