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Roll No.
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Total No. of Questions : 09
Total No. of Pages : 03
B.Tech.(Electronics Engg.) (2012 Onwards)
B.Tech.(ECE/ETE/Electronics & Computer Engg.) (2011 Onwards)
(Sem.-4)
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SIGNAL AND SYSTEMS
Subject Code : BTEC-402
M.Code: 57594
Time : 3 Hrs.
Max. Marks : 60
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INSTRUCTION TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
SECTION-A
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Q1. Answer briefly :
- Differentiate between continuous time and discrete time systems.
- Determine whether the system is linear or non-linear y(n) = x(n²).
- State Parseval's relation for discrete-time aperiodic signals.
- Give the significance of ROC in Z-transform.
- Determine the Nyquist sampling rate and Nyquist sampling interval for the signal x(t) = sin c² (200pt)
- What is the necessary and sufficient condition on impulse response for stability of a causal LTI system?
- What do you mean by statistical independence?
- What are the Dirichlet's conditions of Fourier series?
- How can you classify Random processes?
- List two properties of DTFT.
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SECTION-B
Q2. Find the trigonometric Fourier series for the periodic signal shown
x(t)
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1
-3 -2 -1 0 1 2 3
1
T
Fig.1
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Q3. Consider the probability density f(x) = ae-b|x| where x is a random variable whose allowable value range from x = -8 to x = + 8. Find :
- The cumulative distribution function F(x)
- The relationship between a and b and
- The probability that the outcome x lies between 1 and 2.
Q4. Determine the Z-transform and sketch the ROC of :
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n=0
-n, n<0
Q5. What is Fourier transform? Write down its properties.
Q6. A discrete random variable has k equally likely possible values 0, a, 2a, 3a (k-1) a. Find mean, second moment and standard deviation.
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SECTION-C
Q7. The input and output of a causal LTI system are related by the differentia equation,
d²y(t)/dt²+6dy(t)/dt+8y(t)=2x(t)
- Find the impulse response of the system.
- What is the response of this system if x(t) = t e-2t u(t)
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Q8. a) Find whether the following signals are periodic or not?
- x(t) = 2cos(10t + 1) – sin(4t-1)
- x(t) = 3cos4t + 2sint
b) Determine whether the following signals are energy signals or power signals and why?
- x(t) = eat
- x(t) = sin @1 t + cos 02 t
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Q9. a) A box contains 3 red, 4 white and 5 black balls. One ball is drawn at random. Find the probability that it is :
- red ball
- not black ball
- black or white ball.
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b) In a random experiment a trial consists of five successive tosses of a coin. If we define a random variable X as the number of tails appearing in a trial, determine and plot CDF for the random variable.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.
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This download link is referred from the post: PTU B.Tech 4th Semester Last 10 Years 2009-2019 Previous Question Papers|| Punjab Technical University
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