Identification of pole positions in a system consider the system described by the difference equation
y(n) = -r2y(n – 2) + x(n)
(a) 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 {Y(k)} and {|Y(k)|}.
(b) Compute the N = 128 point DFT of the sequence
ω(n) = (0.92)-ny(n)
Where y(n) is the sequence generated in part (a). Plot the DFT values |W(k)|.
Where can you conclude from the plots in part (a) and (b)?
(c) Let r = 0.5 and repeat part (a).
(d) Repeat part (b) for the sequence
ω(n) = (0.55)-ny(n)
Where y(n) is the sequence generated in part (c). What can you conclude from the plots in part (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 σ2 = 0.1. Repeat parts (c) and (d) for the noise-corrupted signal.