1. PSDC ENGINEERING DIPLOMA ASSESSMENT
Signals And Systems – Mid-Term Test 2 (B16 CE/B17 EEA&EEB)
7th January 2009, Wednesday 2:00pm – 5:00pm (3 hours)
Question 1 (Signals and Systems)
(a) Determine whether the following signals are periodic or aperiodic.
If it is a periodic signal, determine its power.
(i) x[n] = 2cos(⅓πn) + sin(½πn)
(ii) x(t) = Odd{cos(2πt)}
(b) If x(t) = (t2 – 1) [u(t) – u(t–4)],
(i) Sketch x(t)
(ii) Sketch x(t – 2)
(iii) Sketch x(–3t – 2)
(iv) Sketch Even{x(t – 2)}
(c) Determine the following systems are casual, linear and time-invariant.
(i) y[n] = 3x2[–2n]
(ii) y(t) = cos (t+ ½ π) x(t)
Question 2 (Convolution)
(a) Evaluate the convolution sum for y[n] = x[n]∗h[n], where x[n] and h[n] are
shown in Fig. Q2 (a).
Fig. Q2 (a)
(b) Define the convolution of two signals x(t) and h(t).
Then, compute the convolution integral for y(t) = x(t)∗h(t) of the following
signals:
h(t) = e–3tu(t) and x(t) = e–3tu(t–1).
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2. PSDC ENGINEERING DIPLOMA ASSESSMENT
Question 3 (Laplace Transform)
(a) Define Bilateral (two-sided) Laplace Transform.
(b) Consider the signal, x(t) = e–3tu(t). Find the Laplace transform of x(t) with
the associated region of convergence (ROC).
(c) Consider a continuous-time LTI system described by
d 2 y( t ) dy( t ) dx( t )
2
−3 − 2 y( t ) = −3 + x( t )
dt dt dt
Using the shifting property, find the unit impulse response h(t).
Question 4 (z-Transform)
(a) Define Bilateral (two-sided) z-Transform.
(b) Consider the signal, x[k] = aku[k]. Find the z-transform of x[k] with the
associated region of convergence (ROC).
(c) Consider a discrete-time LTI system described by
y[k] – y[k–1] – 2 y[k–2] = x[k] + 2 x[k–1] + 2 x[k–2]
Using the shifting property, find the unit impulse response h[k].
"Learning without thought is useless; thought without learning is dangerous."
学而不思则罔,思而不学则殆.
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