A filter of the form

G(z)   =  z²/(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?