A linear time invariant system has an impulse response given by h[n] = (0.M)$^n$ u[n].
(M is the number in the last digit of your student ID number, or the number in the previous digit if
the last digit is zero).
a) Write h[n]. Compute the z-domain transfer function H(z).
b) Draw pole-zero plot of the system and indicate the ROC.
Is the system stable? Justify your answer.
Is the system causal? Justify your answer.
c) Find and plot the input x[n] to the system if the output is given by y[n] = 2 ?[n – 4].
d) Provide a linear constant coefficient difference equation representation of the system.
Sketch a block diagram representation of the system using multipliers, adders, and unit delays.
e) Find the frequency response H($e^{j\omega}$).
Compute its magnitude |H($e^{j\omega}$)| at ? = 0, $\frac{\pi}{2}$, ? [rad] and plot the magnitude variation for 0 ? ? ?
?. Is this system a low-pass filter, a high-pass filter, or a bandpass filter?
