Seat No.: ________ Enrolment No.

___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V (NEW) EXAMINATION – SUMMER 2024
Subject Code: 3150912 Date:21-05-2024
Subject Name: Signals and Systems
Time:02:30 PM TO 05:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
Marks
Q.1 (a) Explain the Periodic and Non Periodic signal 03
(b) Explain the classification of signals 04
(c) Draw below signals 07
1.u(-t)
2.-4r(t)
3.u(t+4)
4.4cos(wt+𝜋/2)

Q.2 (a) Draw and explain the discrete type of test signals. 03
(b) If signal cos(13πt)+ 2sin(4πt) is periodic or not? 04
If it is periodic then find its fundamental period.
(c) Define the System and classified it. 07
OR
(c) Determine whether the system is (i) Linear (ii) causal, (iii)time -invariant(iv) 07
stable .y(n)=nx(n)

Q.3 (a) Explain Aliasing and its effects and how to remove it. 03
(b) Determine the Nyquist sampling rate and Nyquist sampling interval for 04
x(t)=2sinc(100πt).
(c) Find the convolution of the following sequences: 07
X(n)=3 δ(n+1)-2δ(n)+ δ(n-1)+4δ(n-2)
h(n)= 2 δ(n-1)+5δ(n-2)+3 δ(n-3)
OR
Q.3 (a) State and prove Sampling Theorem. 03
(b) Compute convolution: y(n)=x(n)*h(n), x(n)={1,1, 0 ,1,1}.0 is mid point,h(n)={1,- 04
2,-3, 4}4 is mid point.
(c) Define convolution and explain the initial value and final value theorem. 07

Q.4 (a) State and prove Time shifting and Duality properties of continuous time 03
Fourier transform.
(b) Write modulation property of Fourier Transform. Use frequency 04
differentiation property to find the Fourier Transform of X(t)=t e-at u(t).
(c) Give relation between Fourier transform and Laplace transform. 07
OR
Q.4 (a) Define Z-transform. Explain region of convergence. 03
(b) Explain the trigonometric Fourier series. 04
(c) Find Fourier Series representation for the square wave. 07

1
Q.5 (a) Explain Fourier series with any two properties 03
(b) Find the Z-transform of the unit step signals 04
(c) 07
Explain the Types of sensors.
OR
Q.5 (a) Write Differentiation in Z-domain property of z- transform. 03
(b) Determine the inverse Z-transform of the following X(z) 04

(c) Write a short note on Arduino. 07

**************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V(NEW) EXAMINATION – SUMMER 2022
Subject Code:3150912 Date:07/06/2022
Subject Name:Signals and Systems
Time:02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS

Q.1 (a) Explain odd and even signals with diagram. 03

(b) Define the following: Energy signal, Causal System, Analog signal, 04
Periodic signal.
(c) Explain the Standard / Elementary signals in signal processing in 07
continuous and discrete time.
processing processing
Q.2 (a) A 100 Hz sinusoid x(t) is sampled at 240 Hz. Has aliasing occurred? 03
Also state the minimum sampling frequency.
(b) What is a system? Explain different types of system in brief. 04
(c) Determine whether the following system given as y(t)= 10x(t) +5 is 07
static, causal, linear, time invariant and stable.
OR
(c) For LTI system with unit impulse response h(t)= e-2t u(t), determine 07
output to the input x(t)= e-t u(t).

Q.3 (a) Find Z transform for sequence x(n)={1,2,4,5,0,7} and specify ROC. 03
(b) Explain trigonometric fourier series with all equations. 04
(c) Sketch the following signals if x(n)= { 1,1,1,1,1,1/2} 07
↑
1. x(n-4) 2. x(n).u(2-n) 3. x(n-1) + δ(n-3)
OR
Q.3 (a) State and prove the time shifting property of Fourier transform. 03
(b) Find Fourier transform of unit step function. 04
(c) Find inverse Z transform of X(z)= 1 / (1-1.5z-1+0.5z-2) for 07
1. ROC: |z| >1, 2. ROC: |z| < 0.5.

Q.4 (a) Find the energy or power of the signal x(n)= u(n) . 03
(b) Explain any two properties of convolution sum. 04
(c) Find the linear convolution of : x(n)= {1,1,1,1} and h(n)={2,2} 07
↑ ↑
using basic convolution equation or graphical method.
OR
Q.4 (a) Define Laplace transform and prove its linearity property. 03
(b) Obtain Fourier transform of a rectangular pulse given as : 04
x(t)= A rect (t/T).
(c) The difference equation of system is given as below: 07
y(n)= 0.5y(n-1) +x(n). Determine the system function and the
impulse response h (n) of the system.
1
Q.5 (a) Find Z transform of x(n)= (1/3)n u(n) and also sketch its ROC. 03
(b) State and prove any two properties of Z transform. 04
(c) Give equation for Z transform. What is ROC for Z transform? State 07
the properties of ROC.
OR
Q.5 (a) State and explain sampling theorem with necessary equations. 03
(b) Explain any three sensors used in Internet of Things. 04
(c) Find Z transform of x(n)= cos(ωn) u(n) 07

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER- V EXAMINATION-SUMMER 2023
Subject Code: 3150912 Date: 27/06/2023
Subject Name: Signals and Systems
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Explain with Example following properties of system. 03
(1) Linearity (2) Homogeneity (3) Shift invariance
(b) Define energy for continuous-time and discrete-time signals. 04
(c) Write the properties of convolution and explain them with suitable 07
example.
Q.2 (a) Give expression of trigonometric Fourier Series. Define coefficients 03
of DC, fundamental and harmonics.
(b) State and prove a condition for a discrete time LTI system to be 04
invertible.
(c) Perform Linear convolution of following: 07
1. x(n) = {1, 1, 0, 1, 1} & h(n) = {1, -2, -3, 4)

2. x(n) = {1, 2, 3, 1} & h(n) = {1, 2, 1, -1}

3. x(n) = {1, 2, 1, -1} & h(n) = {1, 2, -3, 4}

OR
(c) An LTI system is described by the difference equation 07
𝑦(𝑛) = 𝑥(𝑛) + 0.81𝑥(𝑛 − 1) − 0.81𝑥(𝑛 − 2) − 0.45𝑦(𝑛 − 2)
Determine transfer function of the system. Draw pole zero plot and
assess stability.
Q.3 (a) Define Fourier transform for continuous-time signal. 03
(b) Find the Fourier transform of cosine wave cos 𝜔0 𝑡. Draw its 04
magnitude spectrum.
(c) State and explain each properties of ROC of z-transform. 07
OR
Q.3 (a) Give relationship between Laplace transform and Fourier transform. 03
(b) Using properties of Z transform, compute Z transform for following 04
signals. (1) x(n)= u(-n), (2) x(n)= u(-n-2)
(c) State and prove time shifting and time-differentiation properties of 07
Laplace transform.
Q.4 (a) Define the terms (1) Zero-order hold (2) First-order hold (3) Ideal 03
interpolation.
(b) Distinguish continuous time systems and discrete time systems 04

1
 (c) Explain the any application of modulation for communication in 07
signal and system.
OR
Q.4 (a) What is Aliasing? 03
(b) What are the effects of under sampling of a signal? 04
(c) Explain in detail of mathematical model for reconstruction. 07
Q.5 (a) What is IOT? Draw the block diagram of any application of an IOT 03
based system.
(b) Explain with diagram any four sensors which used in IOT 04
application
(c) Explain with circuit diagram of any application based on Arduino 07
with sensor & actuators.
OR
Q.5 (a) Explain Input and output pins of Arduino. 03
(b) Explain the different types of Actuators. 04
(c) Explain with the circuit diagram of temperature measurement 0 to 07
100 ºC using LM35 with 16x2 LCD display using Arduino. Also
write the program.

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V (NEW) EXAMINATION – WINTER 2022
Subject Code:3150912 Date:09-01-2023
Subject Name:Signals and Systems
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Find whether the given signals are periodic or not? If yes, give its 03
fundamental period.
(i) x(t) = 3 sin 200πt + 4 cos 100t
(ii) x(n) = e j (π / 2) n
(b) Check whether the signal x (t) =2cos (100πt) +5sin (50t) is periodic or 04
not.
(c) Determine the convolution sum of two sequences using graphical 07
method x(n) = {1, 4, 3, 2}; h(n) = {1, 3, 2, 1}
↑ ↑

Q.2 (a) Determine the energy and power of a signal x (t) = u (t). 03
(b) List and prove any two properties of convolution sum. 04
(c) Sketch signal x (t) = u (t + 2) – u (t - 2) + u (t + 1) – u (t - 1). 07
Also sketch (i) x(2t) (ii) x(1 - t) (iii) x(t) .u(t).
OR
(c) Check whether the system described by the equation y(t)=10x(t)+5 is 07
linear, static, time invariant, causal and stable .

Q.3 (a) State the linearity and time shifting property of Fourier transform. 03
(b) Prove convolution property of Fourier transform. 04
(c) Find inverse Fourier transform of 07
2jω
X(ω)= ----------
(2+jω)2

OR
Q.3 (a) Find the Fourier transform of the signal x (t) = e-at u (t). 03
(b) Explain the Differentiation property of Z-Transform. 04
(c) Explain working of any system based on Arduino. 07

Q.4 (a) Give the convolution sum and integral formulas. 03

(b) State and prove the time shifting property of the Z-transform. 04
(c) Define ROC and explain the property of ROC. 07
OR
Q.4 (a) Find DTFT of the sequence x (n) = {1, 0, 4, 2} . 03
(b) Determine the Z – Transform & ROC of the following sequence X (n) 04
= (3) n u (n) - (2) n u (-n-1).
(c) Solve the difference equation y (n) - 0.5y (n-1) = δ (n) using Z- 07
transform.
1
 Q.5 (a) Explain the reconstruction of a signal from its samples. 03
(b) Find the DFT of the sequence x (n) = {1, 1, -2, -2} . 04
(c) State & Prove Sampling Theorem. 07
OR
Q.5 (a) What is zero-order hold in sampling? 03
(b) What are the effects of under sampling of a signal? 04
(c) Describe various types of sensors used for IoT applications. 07

.
*************

2
 Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V (NEW) EXAMINATION – WINTER 2023
Subject Code:3150912 Date:11-12-2023
Subject Name: Signals and Systems
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Define a periodic continuous time and discrete time signal. 03
(b) Give examples of continuous time and discrete time causal systems. 04
(c) (i) State whether the following system is linear and time-invariant? 07
y(n)=u[n] 2
(ii) State whether the following system is causal, stable and memoryless ?
y[n]=nu[n]
Q.2 (a) Define energy signal and power signal. Give an example of each type. 03
(b) Write the equations for coefficients Cn and C-n of complex exponential 04
Fourier series.
(c) Obtain the complex exponential Fourier series expansion of the signal 07
x(t)=2+3cos 2πt +4 sin 3πt.
OR
(c) Find the Fourier transform of the signum function sgn(t). 07

Q.3 (a) State and prove time shifting property of Fourier transform. 03
(b) Find the Laplace transform of x(t)= tu(t). 04
(c) Find the inverse Laplace transform of 07
F(s)=(2s-1)/(s2+2s+1)
OR
Q.3 (a) State and prove time scaling property of Fourier transform. 03
(b) Find Fourier transform of x(t)= 10 sin ω0t. 04
(c) Find the Fourier transform of a rectangular pulse with amplitude A and 07
width T.
Q.4 (a) Define Z-transform and its ROC. 03
(b) State the properties of ROC of Z-transform. 04
(c) Find the Z-transform of sin ωn u(n). 07
OR
Q.4 (a) State any three properties of Z-transform. 03
(b) Find the Z-transform of 0.5n u(n) + 0.33n u(n) 04
(c) Find the inverse Z-transform of X(z)= z/(3z2-4z+1) for ROC |z|>1. 07

Q.5 (a) List the types of sensors. 03

(b) State and prove the sampling theorem. 04
(c) Give an example of Arduino based minor project. 07
OR
Q.5 (a) List the types of actuators. 03
(b) Draw the spectra of sampled signal. Explain aliasing. 04
(c) Explain interfacing of sensors and actuators with Arduino. 07

1
 Enrolment No./Seat No_______________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER–V (NEW) EXAMINATION – WINTER 2024
Subject Code:3150912 Date:02-12-2024
Subject Name:Signals and Systems
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

Marks

Q.1 (a) 1 03
Check linearity of a system described by y[n] = x[n] +
2 x[n − 2]
(b) Prove commutative, distributive and associative properties of convolution integral 04

(c) Convolve x[n] = {−1,4,3,2, −2} and h[n] = {1,2, −1,1} 07

Q.2 (a) Define (i) Periodicity of a signal (ii) Non-causal signals (iii) Even signal and give 03
example of each
(b) 1 1 04
Check stability of a system described by y[n] = x[n] + x[n − 1] + x[n − 2]
2 4
(c) Given impulse response of the system h(t ) = e−2t u (t ) .Obtain the output of the system for 07
−4 t
x(t ) = e [u (t ) − u (t − 2)]
OR
(c) Given impulse response of the system h(t ) = u(t − 3) .Obtain the output of the system for 07
x(t ) = u(t + 2)
3t
Q.3 (a) 03
Check causality of a system described by y(t ) =  x( )d
−

(b) State and prove linearity and convolution property of z- transform 04

(c) Find Fourier transform of x[n] = 2n sin[( / 4)n] u[−n] 07
OR
Q.3 (a) State Dirichlet conditions for existence of Fourier transform 03
(b) Obtain the energy of the signal x(t ) shown below 04

1
 (c) Obtain Fourier transform of (a) x(t ) = e −2(t −1)u (t − 1) (b) x(t ) =  (t + 2) +  (t − 2) 07

Q.4 (a) Prove the nonexistence of Fourier series co-efficients a0 and an for a periodic waveform 03
with odd symmetry
(b) Obtain Laplace transform of x(t ) = e− at u (t ) by direct integration. 04
(c) Explain zero order hold with its mathematical representation. Write at least three 07
advantages and disadvantages of zero order hold
OR
Q.4 (a) Compare Fourier series and Fourier transform 03
(b) Obtain Laplace transform of x(t ) = (e2t − 2e−t )u (t ) 04
(c) Explain aliasing by taking a suitable example 07

Q.5 (a) Explain signal reconstruction from its sampled form 03

(b) State and prove the final value theorem 04
(c) List at least four types of actuators used with Arduino with their application 07
OR
Q.5 (a) State and explain sampling theorem 03
(b) State the properties of ROC of z-transform 04
(c) List at least seven types of sensors used with Arduino with their application in brief 07

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