Smart EDGE ECE Review Specialist
MASTERY QUESTION GUIDES in SIGNALS
INSTRUCTION: Select the correct answer for each of the following questions.
1. This refers to the mathematical representation of a
physical phenomenon that contains some information.
A. system B. function C. signal D. variable
2. Which of the following transform tool can be used to
convert a continuous time signal into discrete
frequency signal?
A. continuous time Fourier transform
B. continuous time Fourier series
C. discrete time Fourier transform
D. discrete time Fourier series
3. Given a CT signal x(t) = sin(2000πt) and uniform
sampling rate fs = 4 Hz. Determine the DT signal x(n).
A. x(n) = sin(500πn)
B. x(n) = sin(25πn)
C. x(n) = sin(250πn)
D. x(n) = sin(50πn)
4. This refers to a classification of signal that takes on
values from a finite set of possible values.
A. continuous time signal B. continuous valued signal
C. discrete time signal
D. discrete valued signal
5. This refers to a signal that can be uniquely
expressed by an explicit mathematical expression.
A. random signal
B. energy signal
C. conjugate antisymmetric D. deterministic signal
6. This refers to a signal, that when subjected to both
time reversal and amplitude inversion, returns to its
original form.
A. symmetric signal
B. conjugate symmetric signal
C. antisymmetric signal D. causal signal
7. Determine the even component of the given signal:
x(n) = {-1, 2, 3, -4, 5}.
A. xe(n) = {-3, 3, 0, -3, 3} B. xe(n) = {2, -1, 3, -1, 2}
C. xe(n) = {-3, 3, 3, -3, 3} D. xe(n) = {2, -1, 0, -1, 2}
8. A signal is said to be _________ if x*(-t) = x(t).
A. symmetric signal
B. conjugate symmetric signal
C. antisymmetric signal D. causal signal
9. A signal is said to be _____ signal if it takes a value
of 0 if t < 0.
A. anticausal B. causal
C. non-causal D. LTI
10. Find the fundamental period of the given signal: x(t)
= sin(20t) + cos(50t).
A. 𝜋/2
B. 𝜋/3
C. 𝜋/4
D. 𝜋/5
11. Find the fundamental period of the given signal:
x(n) = ej(2𝜋/3)n + ej(3𝜋/4)n
A. 6
B. 12
C. 24
D. 10
12. The signal x(t) = 2e−t − 6e−2t, t>0 is an energy
signal. Its energy is
A. 1.5
B. 3
C. 6
D. 12
13. Calculate the power of the given signal: x(t) =
Aosin(𝜔ot).
A. Ao2
B. Ao2/2
C. Ao2/4
D. 2Ao2
14. Calculate the power of the given signal.
A. 56
B. 40
C. 8
D. 5
15. This refers to a collection of devices that operate
on input signal x(t) (or excitation) to produce an output
signal y(t) (or response).
A. function B. formula C. system D. transform
16. If the output of a system depends only on present
values of the input at every instant of time, the system
is said to be:
A. dynamic B. static
C. linear D. time invariant
27. Which of the following is the expression for the
convolution for a continuous time system?
∞
∞
A. ∫−∞ x(τ)h(τ−t)dτ
B. ∫−∞ x(τ)x(τ−t)dτ
∞
C. ∫−∞ x(τ)x(t−τ)dτ
∞
D. ∫−∞ x(τ)h(t−τ)dτ
time interval.
D. The function must be continuous and differentiable
everywhere in the given time interval.
48. This refers to a type of digital filter whose
present output depends on its own past values
y[n−k] and on the past and present values of the
36. Solve for the Fourier transform of the given function:
input.
x(t) = 5 from t = -2 to t = 2 and 0 otherwise.
A. infinite impulse response (IIR) filter
A.5sin(2ω)/ω B.10sin(2ω)/ω C. j10sin(2ω)/ω D. j5sin(2ω)/ω
B. finite impulse response (FIR) filter
37. Solve for the inverse Fourier transform of the given
C. moving average filter
function: F(ω) = 6/(9 + ω2).
D. non-recursive filter
A. e-2|t|
B. e3|t|
C. e-|2t|
D. e-3|t|
49. Determine the difference equation
38. Find the Fourier transform of x(t) = e3tu(-t).
corresponding to the digital filter shown in the
A. 1/(jω + 3) B. 3/(jω + 3) C. 1/(3 - jω) D. 3/(3 - jω)
figure.
39. Determine the inverse Fourier transform of e-|ω|.
A. π-1/(1 + t2) B. π(1 + t2) C. π/(1 + t2) D. π-1(1 + t2)
28. Solve for the convolution: x(t) = sin(t)u(t) and h(t) =
cos(t)u(t).
t
A. y(t) = sin(t)
B. y(t) = tcos(t)
40. The Fourier transform of a conjugate symmetric
function is always
A. imaginary
B. real
C. conjugate antisymmetric D. conjugate symmetric
C. y(t) = cos(t)
41. The z-transform is a signal analysis technique utilized
for examining discrete-time signals. It transforms discretetime signals into their complex frequency domain
representation. The variable z is equal to
A. ejΩ
B. e-jΩ
C. rejΩ
D. re-jΩ
2
t
2
D. y(t) = tsin(t)
29. Solve for the convolution: x(t) = e-2tu(t) and h(t) = e3tu(t-3).
A. (e-2t – e-3t)u(t-3)
B. (e-2(t+1.5) – e-3t)u(t-3)
C. (e-2(t+3) – e-3t)u(t-3) D. (e-2t – e-3(t-3))u(t-3)
30. Solve for the discrete-time convolution of: x(n) =
2nu(n) and h(n) = 3nu(n)
A. y(n) = −(2n+1 −3n+1 )u(n) B. y(n) = −(2n −3n−1 )u(n)
C. y(n) = −(2n−1 −3n )u(n) D. y(n) = −(2n −3n )u(n)
31. Solve for the discrete-time convolution given the
finite-length sequence: x(n) = {1, 2, 4}and h(n) = {1, 4,
17. Classify the given system: y(t) = x(sin(t)).
3, 8}
A. static
B. dynamic C. A & B D. None of these. A. y(n) = {1, 6, 15, 30, 28, 32}
18. If the output of the system depends only on future B. y(n) = {1, 6, 10, 15, 30, 24}
C. y(n) = {1, 3, 4, 5}
values of the input, then the system is said to be
A. causal B. non-causal C. anticausal D.memoryless D. y(n) = {1, 6, 2, 10}
32. Which of the following is the expression for the
19. Classify the given system: y(t) = 5x(t-2).
for a continuous time real signal, x(t)?
A. causal B. non-causal C. anticausal D.memoryless autocorrelation
∞
∞
A. ∫−∞ x(τ)h(τ−t)dτ
B. ∫−∞ x(τ)x(τ−t)dτ
∞
∞
20. A system is said to be linear if it follows the law of
C. ∫−∞ x(τ)x(t−τ)dτ
D. ∫−∞ x(τ)h(t−τ)dτ
superposition. The law of superposition is combination
33. Solve for the cross-correlation of x(t) = e-3tu(t) and
of what two principles?
y(t) = e2tu(-t).
A. homogeneity & additivity B. continuity & stability
B. rxy(t) = (1 – e-2t + e3t)u(t)
C. reciprocity & time-invariance D.modularity & scalability A. rxy(t) = (1 – e-t)u(t)
C. rxy(t) = (1 – e-2t)u(t) D. rxy(t) = (e-2t – e-3t)u(t)
21. Classify the given system: y(t) = x(sin(t)).
34. Solve for the autocorrelation of the given discreteA. nonlinear B. linear C. causal D. anticausal
time sequence: x(n) = {1, 2, 3}
22. This refers to the property of a system which
A. rxx(n) = {1, 4, 10, 12, 9} B. rxx(n) = {-3, -8, -14, -8, -3}
makes the behavior of the system independent of time.
C. rxx(n) = {-1, -4, -10, -12, -9} D. rxx(n) = {3, 8, 14, 8, 3}
A. causality B. linearity C. time invariance D. additivity
35. Which of the following does not belong to the
For 23-26 choices:
Dirichlet conditions necessary for the existence of a
A. L, TI, C, S
B. L, TV, C, S
Fourier series of a given function?
C. L, TV, NC, S
D. NL, TI, C, US
A. The function must have a finite number of maxima
23. Classify the given system: y(t) = 5x(t).
and minima.
24. Classify the given system: y(t) = sin(4t)x(t).
B. The function must have a finite number of
25. Classify the given system: y(n) = log(x(n))
discontinuities in the given time interval.
26. Classify the given system: y(n) = x(n-2) + x(2-n)
C. The function must be absolutely integrable in the
given
42. Solve for the z-transform of u(n).
z
A. X(z) =
B. X(z) = z-1 C. X(z) = −
z−1
z
z−1
D. X(z) = 1
43. Solve for the z-transform of x(n) =
1 n
1 n
( ) u(n)− ( ) u(−n−1).
3
A. X(z)=−
B. X(z)=−
z
2
1
−
1
+
z−3
z
z−3
z
1
C. X(z)=
1
D. X(z)=
z−2
z
z−2
z
1
−
1
+
z−3
z
z−3
z
1
z−2
z
A. y(n) + 1/6 y(n-1) + 1/6 y(n-2) = 4x(n)
B. y(n) – 1/6 y(n-1) – 1/3 y(n-2) = 4x(n)
C. y(n) + 1/6 y(n-1) + 1/3 y(n-2) = 4x(n)
D. y(n) – 1/6 y(n-1) – 1/6 y(n-2) = 4x(n)
50. Find y(n) given the IIR filter shown if x(n) =
0.4nu(n) with y(-1) = 10. Assume that the system is
causal.
A. y(n) = -2(0.4)n + 9(0.6)n
B. y(n) = -1.5(0.4)n + 3(0.6)n
C. y(n) = 2(0.4)n - 9(0.6)n
D. y(n) = 1.5(0.4)n - 9(0.6)n
1
z−2
44. Solve for the z-transform of x(n) = n2u(n).
𝑧 −1
A. (1−𝑧−1 )2, |z|>1
C.
(1+𝑧 −1 )𝑧 −1
(1+𝑧)3
, |𝑧| < 1
𝑧
B. (𝑧+1)2 , |𝑧| < 1
D.
(1+𝑧 −1 )𝑧 −1
(1−𝑧 −1 )3
, |𝑧| > 1
45. Solve for the z-transform of x(n) = 3nu(-n-4).
1
𝑧4
1
𝑧4
A. (− )
, |𝑧| < 3 B. ( )
, |𝑧| > 3
C. −
27 𝑧−3
𝑧4
𝑧−3
, |𝑧| < 3
D.
27 𝑧−3
𝑧4
𝑧−3
, |𝑧| > 3
46. Find the z-transform of x(n) = {1, 0, 1, 0, 0, 1}.
A. z-2 + z3 + 2, 0 < |z| < ∞ B. z2 + z-3 + 1, 0 < |z| < ∞
C. z2 + z-3 + 1, 0 < |z| ≤ ∞ D. z-2 + z3 + 2, 0 ≤ |z| < ∞
47. A causal signal has a z-transform given by:
3
2− z−1
2
H(z) =
1
(1−2z−1 ) (1+ z−1 )
2
Solve for h(n).
A. x(n) = (2n + (1/2)n)u(n)
B. x(n) = (2n + (-1/2)n)u(n)
C. x(n) = (2n - (-1/2)n)u(n)
D. x(n) = ((-2)n + (-1/2)n)u(n)
“Be the best-prepared ECE Examinee.”