Consider the following three data sets, which are the same data set given in Example 10.2 but corrupted with varying levels of white Gaussian noise. Three different SNRs are used to generate the noisy output, namely 1 dB, 10 dB, and 50 dB. It can be seen that as the SNR is increased the output values approach those given in the example. Assuming the input to be a unit impulse, repeat the identification for each of the three noisy cases, and compute how the poles of the identified transfer function differ from the actual poles. Also, plot the percentage error in the estimated poles versus the actual poles against the increasing
levels of SNR.

Example 10.2

Consider the following impulse response data for a SISO discrete-time LTI system with
a sampling time of T = 0.01 s. The output is measured at the sampling time instants
t = 0, 0.01, 0.02, c, 0.08, as shown in Fig. 10-2.

Transcribed Image Text:

1. SNR 1 dB k y(k) K y (k) 0 0.979 2. SNR 10 dB 1 0.7483 k y (k) 0 1 0.0106 0.5743 3. SNR 50 dB 0 1 -0.0026 0.9929 2 0.3272 2 0.0585 3 -1.8435 3 0.0959 4 5 -0.2816 -0.7421 4 -0.0608 2 3 4 -0.3017 -0.0165 0.0275 5 -0.0009 6 -1.4067 6 -0.084 7 8 0.4538 0.2511 7 -0.5524 5 6 7 -0.0051 0.0005 0.001 8 -0.0905 8 -0.0003