Gujarat Technological UniversityWinter 2025 examination

GTU BE03000171 Signals and Systems Winter 2025 Question Paper & PDF

B.E. · EC Engineering · Semester 3 · Subject code BE03000171
Download official PDFView PDF here
Share with your class
Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:00 PM
Questions
5 with internal choice
No solutions on this paper yetNeed them for your exam? Ask once. Papers that students ask for are solved first, and we aim to add them within 24 hours.

Q.1

14 Marks
(a)
3 marks

For the signal x(t) , plot x(1−t2)x\left( 1 - \dfrac{t}{2} \right)

GTU Signals and Systems (BE03000171) Winter 2025 Question 1(a) Diagram
(b)
4 marks

Define periodic and aperiodic signal. Determine whether the following signals are periodic or not? If periodic determine the fundamental period.

1x(t)=cos⁡(4πt)x(t) = \cos(4\pi t)
2x(n)=cos⁡(n6)⋅cos⁡(nπ6)x(n) = \cos\left( \dfrac{n}{6} \right) \cdot \cos\left( \dfrac{n\pi}{6} \right)
(c)
7 marks
Derive Fourier co-efficients of the Trigonometric Fourier series of a even symmetry periodic signal.

Q.2

14 Marks
(a)
3 marks

Define following systems.

1Invertible system 2. FIR system 3. IIR system
(b)
4 marks

Determine whether the following system is linear, stable, causal and time-invariant using appropriate test. y(t)=x(t2)y(t) = x\left( t^2 \right)

(c)
7 marks
State and prove sampling theorem.
(c)
7 marks
Explain reconstruction of a signal from its samples using interpolation process.

Q.3

14 Marks
(a)
3 marks
Define autocorrelation function of a signal. List its properties.
(b)
4 marks
State and prove a condition for a discrete time LTI system to be stable.
(c)
7 marks
The impulse response of the circuit is given as h(t)=e−2tu(t)h(t) = e^{-2t}u(t). This circuit is excited by an input of x(t)=e−4t[u((t)−u((t−2)]x(t) = e^{-4t}[u((t) - u((t - 2)]. Determine the output of the circuit.
(a)
3 marks

For, x(n)=δ(n)+2δ(n−1)−δ(n−3)x(n) = \delta(n) + 2\delta(n - 1) - \delta(n - 3) and h(n)=2δ(n+1)−2δ(n−1)h(n) = 2\delta(n + 1) - 2\delta(n - 1). Compute y(n)=x(n)∗h(n)y(n) = x(n) * h(n)

(b)
4 marks

Determine whether the following system is linear, stable, causal and time-invariant using appropriate test. y(n)=x(n)−x(n−1)y(n) = x(n) - x(n - 1)

(c)
7 marks
Define convolution integral for a continuous time and a discrete time signals. List properties of convolution.

Q.4

14 Marks
(a)
3 marks
State and prove time shifting property of Fourier transform.
(b)
4 marks
Find the Fourier transform of the following signal.

x(t)={2−4≤t≤−222≤t≤40otherwisex(t) = \begin{cases} 2 & -4 \le t \le -2 \\ 2 & 2 \le t \le 4 \\ 0 & \text{otherwise} \end{cases}

(c)
7 marks
Obtain the trigonometric Fourier series for the waveform shown below.
GTU Signals and Systems (BE03000171) Winter 2025 Question 4(c) Diagram
(a)
3 marks
State and prove differentiation in time domain properties of Fourier transform.
(b)
4 marks
Using properties of Fourier transform, find the Fourier transform of x(t)=e−3tu(t−2)x(t) = e^{-3t}u(t - 2).
(c)
7 marks
Using Fourier transform, find the convolution of the signals x1(t)=e−2tu(t)x_1(t) = e^{-2t}u(t) and x2(t)=e−3tu(t)x_2(t) = e^{-3t}u(t).

Q.5

14 Marks
(a)
3 marks
State and prove multiplication by exponential sequence property of z-transform.
(b)
4 marks

Using long division, determine the inverse z-transform of X(z)=z−1+2z−21−3z−1+4z−2+z−3; ROC;∣z∣>1X(z) = \dfrac{z^{-1} + 2z^{-2}}{1 - 3z^{-1} + 4z^{-2} + z^{-3}};\ ROC; |z| > 1

(c)
7 marks

Determine the impulse response h(n) of the causal system described by the difference equation y(n)−34y(n−1)+18y(n−2)=x(n)+13x(n−1)y(n) - \dfrac{3}{4}y(n - 1) + \dfrac{1}{8}y(n - 2) = x(n) + \dfrac{1}{3}x(n - 1) .

(a)
3 marks
Explain differentiation property in the z- domain.
(b)
4 marks

Using appropriate properties, find z-transform of x(n)=n(13)nu(n−2)x(n) = n \left( \dfrac{1}{3} \right)^n u(n - 2)

(c)
7 marks

Find the inverse z-transform of X(z)=2z−7z2−5z+6; ROC;∣z∣<2X(z) = \dfrac{2z - 7}{z^2 - 5z + 6};\ ROC; |z| < 2

More Signals and Systems papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202670 marks · 5 questions

Other Semester 3 subjects

BE EC

3131101
Control Systems
3131102
Digital System Design
3131103
Network Theory
BE03000161
Network Theory

Preparing with friends?

Send this paper to your class group. Every question has its own link.

About this paper

Official Gujarat Technological University (GTU) examination paper for Signals and Systems (Winter 2025, B.E. · EC Engineering, Sem 3). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

Download official PDF All Signals and Systems Papers (2) →Report a typo or correction
ViewDownload PDF