(SEM IV) THEORY EXAMINATION 2023-24 SIGNAL SYSTEM

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.