A filter of the form
G(z) = z^{2}/(z - p)(z - p)
with p = re^{4ωn} will be studied.
With r = 0.95 and ω_{n} = Π/10 , plot the time response to the input sinusoidal waveform generated in the first question. Show both the transient and steady-state response.
Plot the frequency-domain response of the filter. Explain all your working, particularly how the z transfer function is converted to gain/phase plots.
Find the gain and phase from the time-domain response of part (a), and compare to that expected from the frequency response in part (b). Are the results the same?