Kreatryx Subject Test
Signals and Systems www.kreatryx.com
KST- General Instructions during Examination
1. Total Duration of KST is 60 minutes. 2. The question paper consists of 2 parts. Questions 1-10 carry one mark each and Question 11-20 carry 2 marks each. 3. The question paper may consist of questions of Multiple Choice Type (MCQ) and Numerical Answer Type. 4. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. 5. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of / marks for a 1-mark question and / marks for a 2-mark question. 6. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE . 7. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed during the Examination.
1
Q.1 Which one of the following is the region of convergence (ROC) for the sequence n n x n b u n b u n 1 ; b 1?
(A) Region
z
1
(B) Annular strip in the region (C) Region
z
b
z
1 b
b
z
1 b
1
(D) Annular strip in the region Q.2 The final value of F s
1
s j s j
is __________
(A) 1 (B) 0 (C) -1 (D) Not defined Q.3 Given x t
t
. Find the inverse Laplace transfer of
e u t
t 3
(A)
2
e
u t
3
(B)
t 2
(C)
e
3
u t
2
(D)
Q.4 What is the convolution of x1 t
(A) (B) (C) (D)
2 5 3 5 2 5 3 5
sintu t , x 2 t
1
e
3s
t 3
e
2
2 1 2
X 2s
u t
3
2
t 2
e
3
u t
cos 2tu t
2
5 cos 3tu t
cos 2tu t
3
cos 2tu t
sin 2tu t
5 2 5
cos 3tu t
cos 3tu t
sin 3tu t
2 5
cos 2tu t
2
sin 4000t Q.5 Nyquist rate of x t is _______________ . in Hz t
2
Q.6 Determine the time signal corresponding to the magnitude and phase spectra as shown in the with 0
4 sin 4 2 cos 3t 8 4 (C) x t 4 cos 4 t 2 cos 3 t 8 4 (A)
j 4t 3
Q.7 What is the time period of x t 6e
(A)
2 cos 3t 8 4 (D) x t 4 cos 2t 2 sin 3t 8 4
x t
(B)
2
Q.9 What is the value of
(A) 1 + cos4
x t
4 sin 2t
j 3t 4
8e
3
(C) 2
4
Q.8 What is the power and RMS value of
(A) 150, 150
(B)
x t
(D) Not periodic
12 cos 20t 16 sin 30t 3 3
(B) 144, 144
(C) 256, 256
(D) 200, 200
t cos 2t t 2 sin2t dt (B) cos4
(C) 1+sin4
(D) sin4
Q.10 What is the energy of x t A sin 0 t _____________
(A)
A
2
2
(B) A2
(C)0
(D)
Q.11 If an input output relation of a system is given by, y n nx n then this system is
(A)LTI, causal
(B)Non LTI, causal
(C)Non LTI, causal, stable
(D)LTI, non causal
3
Q.12 The minimum sampling frequency of signal
2
3
2.3 10 sinC
300t *1.6
3
10 sinC
2
600t to
avoid aliasing should be _______________ (Hz). (*Denotes convolution)
Q.13
D = Delay element of 1 The value of ‘a’ for the system to behave as all pass filter is____________ Q.14 Match list I (Properties) with list II (characteristics of the trigonometric form) in regard to
Fourier Series of periodic f(t) and select the correct answer:
List I
List II
P
f(t) + f(-t) = 0
1
Even harmonics can’t exist.
Q
f(t) - f(-t) = 0
2
Odd harmonics can’t exist.
R
f t f t
T 0 2
3
The dc and cosine terms can exist.
S
f t f t
4
Sine terms can exist.
5
Cosine terms of even harmonics can exist.
T
0 2
(A) P – 4, Q – 5, R – 3, S – 1 (B) P – 3, Q – 4, R – 1, S – 2 (C) P – 5, Q – 4, R – 2, S – 3 (D) P – 4, Q – 3, R – 1, S – 2
4
Q.15 For the signal given below, which of the following statements is correct?
2 n 2 sin n 3 5
sin
1) This signal comprise of total 30 unique samples. 2) This signal posses only 5th and 6th harmonics components. 3) This signal posses only 10th and 11th harmonics components. 4) Average power of the signal is 2.0 W 5) Average power of the signal is 1.25 W (A) Only 1, 5 are correct
(B) Only 2, 5 are correct
(C) Only 1, 2, 4 are correct
(D) Only 2, 4 are correct
Q.16 Determine the Fourier Transform of the waveform shown below:
(A) 2 sin c2 f 1 0.5 cos 2f (B) 2sinc 2 f 1 j0.5sin2 f (C) sin2 f 1 j0.5sin4f (D)None of these
Q.17 Consider a signal x[t] as shown below
t t 0 1 t 0 Let r t ; u t 0 t 0 0 t 0 x[t] can be represented in terms of r[t] or u(t) or both as (A) r (t + 2) – r(t) – r (t - 3) + 2r(t - 5) – r(t - 7)
(B)r (t + 2) – r(t) – r (t - 3) + 2r(t - 5) + r(t - 7)
(C) r (t + 2) – u(t) – r (t - 3) + 2r(t - 5) + u(t - 7)
(D)r (t + 2) – u(t) – r (t - 3) + 2r(t - 5)–u(t - 7)
5
Q.18 The impulse response h(n) of the causal LTI discrete-time system that satisfying the
difference equation y(n) 0.5y n 2
2x n
x n 2 is equal to k n then the value of k
is_____. Q.19 The z – transform of a discrete-time sequence
(A) Z
2
(C) Z
1
x n
1 1z 1 z 1 3 1 1z 1 z 1 3
A
1
S s
2
n u n is
(B) Z
(D)
Q.20 The Laplace transform of f(t) shown in the figure is
F s
2
B Ce2s De4s
The sum of A, B, C and D is _______________.
6
1
1 z 1 1 z 1 3
1z
1z
1
1
3