About this previous year paper
This document is a B.Tech (Semester IV) Theory Examination Question Paper for the subject BEC403 – Signal System, from the academic session 2023–2024.
It is a 3-hour, 70-mark examination that evaluates students’ understanding of continuous-time and discrete-time signals, system properties, convolution, Fourier Transform, Z-Transform, Laplace Transform, sampling theory, and LTI system behavior.
The paper is divided into three sections—A, B, and C—covering short fundamental questions, analytical derivations, transform problems, system classifications, and sampling theory.
SECTION A – Short Answer Questions (14 Marks)
Seven short questions (2 marks each) test basic concepts of Signals and Systems:
Fundamental period of x(t) = sin(4t – 1)
Formula for continuous-time convolution
Fourier Transform of δ(t + 1)
Z-transform of δ(n + 1)
Sketching of sampled signal of cos(2πt)
Sketching unit step signal u(-t + 1)
Definition of Parseval’s Theorem
This section checks core signal properties, generalized functions, and simple transform knowledge.
SECTION B – Analytical and Transform-Based Questions (21 Marks)
Students must attempt any three of the following:
Definitions (with mathematical expressions):
Linear system
Stability
Causality
Dynamic system
System function H(z) for a causal LTI system:
y(n) = y(n−1) + y(n−2) + x(n−1)
pole-zero plot and ROC identification
Sketching y(t) = e^(−a|t|) + Fourier Transform with magnitude & phase
Explanation of ROC (Region of Convergence) + three Z-transform properties
Natural Sampling with graphs and equations
This section evaluates transform analysis, system classification, and graphical skills.
SECTION C – Advanced Problems (28 Marks)
Each question contains two options; one must be attempted from each.
3. LTI Systems & Signal Classification
Definition of Time-Invariant system and time-variance check for:
y₁(t) = t x(t)
y₂(n) = 2x(n) + 3
y₃(t) = 2x(−t)
Definitions + mathematical expressions:
Energy & Power Signals
Even & Odd Signals
4. Convolution & Differential-Equation LTI System
Definition of Discrete-Time Convolution, compute y(n) = x(n) * h(n) for x(n) = h(n) = u(n)
LTI system described by: dy/dt + 5y(t) = 3x(t)
Transfer Function H(s)
Output y(t) for x(t) = u(t)
5. Fourier Transform Problems
Properties of Fourier Transform + FT of y(t) = t e^(−4t) u(t)
Inverse Laplace Transform using partial fractions for:
4(s + 3) / [s(s + 1)(s + 2)]
4 / [(s + 1)(s + 2)²]
6. Z-Transform Problems
Inverse Z-transform of Y(z) = z² / (z² + 3z + 2), ROC |z| > 2
Z-transform of x(n) = (1/2)ⁿ u(n) + ROC + pole-zero plot
7. Sampling Theory
Ideal Sampling with time-domain & frequency-domain graphs
Nyquist Rate & Interval calculations for signals:
x₁(t) = cos(20πt) + cos(40πt)
x₂(t) = cos(200πt)cos(400πt)
This section tests deep understanding of system analysis, differential equations, Fourier/Laplace/Z transforms, and sampling concepts.
Overall Purpose of the Document
This exam paper assesses student proficiency in:
Signal classification (CT & DT signals)
LTI system properties (linearity, causality, stability, time invariance)
Convolution (CT and DT)
Fourier Transform and its properties
Laplace & Z-Transforms and their ROC behavior
Sampling (ideal, natural, Nyquist conditions)
Analytical problem solving in signal processing
The structure ensures strong evaluation of theory, mathematical methods, transforms, and system behavior.