Identification of pole positions in a system Consider the system described by the di...

Identification of pole positions in a system Consider the system described by the difference equation

Let r = 0.9 and x(n) = δ(n). Generate the output sequence y(n) for 0 ≤ n ≤ 127. Compute the N = 128-point DFT and plot

(b) Compute the N = 128-point DFF of the sequence

where y(n) is the sequence generated in part (a). Plot the DFT values What can you conclude from the plots in parts (a) and (b)?

(c) Let r = 0.5 and repeat part (a).

(d) Repeat part (b) for the sequence

where y(n) is the sequence generated in part (c). What can you conclude from the plots in parts (c) and (d)?

(e) Now let the sequence generated in part (c) be corrupted by a sequence of "measurement" noise which is Gaussian with zero mean and variance Repeat parts (c) and (d) for the noise-corrupted signal.