(SEM IV) THEORY EXAMINATION 2024-25 DIGITAL ELECTRONICS

This document contains the complete B.Tech (Semester IV) Theory Examination 2024–25 question paper for Signal System (BEC403). The paper spans two printed pages, carries 70 marks, and evaluates the student’s understanding of continuous-time and discrete-time signals, LTI system analysis, Fourier methods, Laplace and Z-transforms, sampling, aliasing, and system stability.
 

Section A – Short Conceptual Questions (14 Marks)

Section A includes seven 2-mark questions that test fundamental concepts of signals and systems. As shown on Page 1, topics include:

Definition of energy and power signals with examples

Properties of linear systems

Meaning and significance of convolution in LTI analysis

Comparison of Fourier Series vs Fourier Transform

Definition of ROC for Z-Transform

Explanation of aliasing in sampling

Concept of eigenfunctions of LSI systems

These questions ensure conceptual clarity in the basics of signal processing.

Section B – Medium-Difficulty Analytical Questions (21 Marks)

Students must attempt any three out of the five 7-mark questions. As shown on Page 1, these questions include:

Even–Odd Signal Decomposition

Decompose the given signal
x(t)=cos⁡t+sin⁡t+cos⁡t⋅sin⁡tx(t) = \cos t + \sin t + \cos t \cdot \sin tx(t)=cost+sint+cost⋅sint
into even and odd components.

Impulse Response of LTI System

Solve the differential equation:
dy(t)dt+2y(t)=x(t)\frac{dy(t)}{dt} + 2y(t) = x(t)dtdy(t)​+2y(t)=x(t)

Convolution via Fourier Transform

Compute convolution of
x1(t)=e−4tu(t)x_1(t) = e^{-4t}u(t)x1​(t)=e−4tu(t)
x2(t)=e−8tu(t)x_2(t) = e^{-8t}u(t)x2​(t)=e−8tu(t)

Z-Transform Properties

State, prove, and illustrate time-shifting and frequency-shifting properties of the Z-transform.

Signal Reconstruction

Explain interpolation and how a signal is reconstructed from samples.

These questions assess analytical ability and mathematical handling.
 

Section C – Long, Higher-Order Questions (35 Marks)

Students must attempt one part from each question (Q3–Q7). As shown on Pages 1–2, these involve system testing, convolution, Laplace transforms, Z-transforms, sampling theory, and aliasing analysis.

Q3 – System Properties / Signal Energy

Testing linearity, time invariance & causality of y(t)=t⋅x(t)y(t)=t\cdot x(t)y(t)=t⋅x(t)

OR

Determining if x(t)=e−5tu(t)x(t)=e^{-5t}u(t)x(t)=e−5tu(t) is an energy or power signal

Q4 – Convolution / Step Response

Compute convolution: e−3tu(t)∗u(t)e^{-3t}u(t) * u(t)e−3tu(t)∗u(t)

OR

Find step response and determine BIBO stability of h(t)=e−6tu(t)h(t)=e^{-6t}u(t)h(t)=e−6tu(t)

Q5 – Inverse Laplace / DTFT Analysis

Inverse Laplace of
X(s)=2(s+4)(s−1)X(s)=\frac{2}{(s+4)(s-1)}X(s)=(s+4)(s−1)2​ with ROC: −4<Re(s)<1-4 < \text{Re}(s) < 1−4<Re(s)<1

OR

DTFT of
x(n)=0.5nu(n)+2−nu(−n−1)x(n)=0.5^n u(n) + 2^{-n}u(-n−1)x(n)=0.5nu(n)+2−nu(−n−1)

Q6 – Z-Transform / Inverse Z-Transform

Z-transform of sin⁡(ω0n)u(n)\sin(\omega_0 n)u(n)sin(ω0​n)u(n) & ROC

OR

Inverse Z-transform of
H(z)=0.2z(z+0.4)(z−0.2)H(z)=\frac{0.2z}{(z+0.4)(z-0.2)}H(z)=(z+0.4)(z−0.2)0.2z​ with ROC: ∣z∣>0.4|z|>0.4∣z∣>0.4

Q7 – Sampling Theorem / Aliasing

State & prove the Sampling Theorem and discuss undersampling

OR

Determine aliasing for x(t)=cos⁡(500πt)+sin⁡(700πt)x(t)=\cos(500\pi t)+\sin(700\pi t)x(t)=cos(500πt)+sin(700πt) sampled at 400 Hz
(Nyquist test + aliased frequency)

These questions evaluate high-level understanding of system behavior and frequency-domain 

Summary

The SIGNAL SYSTEM (BEC403) exam paper thoroughly covers:

Basics of signals (CT & DT)

Energy vs power signals

LTI system properties & convolution

Fourier Series & Fourier Transform comparison

Laplace transform & inverse Laplace

Z-Transform, ROC & Inverse Z-Transform

Sampling theorem, aliasing & reconstruction

DTFT & system stability

Step/impulse responses

System testing: linearity, causality, time-invariance

This exam paper is a complete academic resource for students learning the foundations of signals and systems.