SIGNAL PROCESSING CLASS TEST
Question 1 [8]
Fill in the table at the bottom of this page.
1.1 The system described by y (t ) = e t x(t ) is
a. Linear and time-varying.
b. Nonlinear and time-invariant.
c. Nonlinear and time-varying.
d. Linear and time-invariant.
1.2 The area under the curve
a.
b.
c.
d.
∞.
1.
e jω .
e − jω .
∞
∫ δ (t )e
− jω (t −1)
[2]
dt is
[2]
−∞
1.3 Given x(t ) = sin (t ) is
a.
b.
c.
d.
[2]
An energy signal
A power signal
Neither an energy or a power signal
An energy as well as a power signal.
1.4 An even signal xe (t ) of a signal x(t ) is defined by
1
[x(t ) − x(t )] .
a.
2
1
[x(t ) + x(− t )] .
b.
2
c. x(t ) + x(− t ) .
d. x(t ) − x(− t ) .
1.5 Which of the following systems is causal?
a. y (t ) = x(t − 1) + x(t ) − x(t − 3) .
b. y (t ) = x(t + 1) − x(t − 3) .
c. y (t ) = x(t + 2) .
d. y (t ) + y (t + 1) = x(t ) + x(t + 1) .
1.1
1.2
[1]
[1]
1.3
1.4
1.5
Question 2 [12]
2.1 Sketch the signal x(t ) = 3u (t ) − 2u (t − 1) − u (t − 2 ) and determine its energy.
2.2 Sketch y (t ) = x(− t + 2 ) the transformed signal of x(t ) = 2u (t ) − u (t − 1) .
Question 3 [3+2]
Evaluate the following:
4


 πt 
3.1 ∫ cos(t )δ (t ) + sin  δ (t − 2 ) − δ (t + 2 ) dt =
4

−1 
(
)
3.2 4 − t 3 δ (t + 1) =
[7]
[5]