(SEM III) THEORY EXAMINATION 2022-23 BASIC SIGNALS & SYSTEMS

This question paper is designed to evaluate the student’s understanding of fundamental and advanced concepts of Signals and Systems, including Fourier analysis, Laplace Transform, Z-Transform, State-Space modelling, and system classification. The paper is divided into three sections — A, B, and C, each testing different levels of learning outcomes as per the course curriculum.

SECTION A — Short Answer Questions (Conceptual Understanding)

This section contains 10 compulsory questions, each carrying 2 marks.
The questions are aimed at assessing the student's grasp of basic definitions, properties, and formulae used in signal classification, Fourier Transform, Laplace Transform, Z-Transform, and state-space concepts. Students are expected to answer briefly, focusing on clarity and correctness.

Topics covered include:

Energy and power signals

Standard signals and signal transformations

Time-shifting properties of Fourier Transform

Region of Convergence

Transfer function

Stability conditions in z-domain

Advantages of state-space representation

Properties of the state transition matrix

This section tests fundamental knowledge required for solving analytical and numerical questions in later sections.

SECTION B — Analytical & Derivation-Based Questions (Detailed Answers Required)

Attempt any three questions out of given choices, each carrying 10 marks.
This section examines the student’s ability to:

Analyze properties of systems

Derive mathematical expressions

Compute Fourier series coefficients

Use Laplace Transform theorems

Determine initial and final values using ILT and FLT

Analyze the Region of Convergence (ROC)

Convert system description into transfer function

Write and interpret state-space equations

Compute state-transition matrix

Students are expected to provide step-by-step solutions, diagrams when necessary, and correct justification for each mathematical step.

Examples of tasks in this section include:

Distinguishing linear vs. nonlinear, causal vs. non-causal systems

Deriving Fourier series coefficients for periodic signals

Applying Laplace Transform theorems

Solving state-space models

Finding ROC properties for Z-transform

This section evaluates the student’s analytical ability, mathematical rigour, and command over system representation.

SECTION C — Long, Application-Based Problems (Numerical / Derivation / Case Study)

Attempt any one part from each question number, each carrying 10 marks.

This section includes higher-level problems, requiring deeper conceptual understanding and multi-step reasoning.
Questions may involve:

Converting real-world signals into mathematical expressions using unit step/ramp functions

Drawing even–odd components of signals

Creating electrical analogies of mechanical systems and writing differential equations

Fourier Transform spectral calculations

Determining system response using convolution or transfer function

Deriving CTFT–Laplace Transform relationships

Solving circuits using Laplace domain

Computing inverse Z-Transform using long division

Finding impulse responses from difference equations

Representing systems fully using state-space methods

Obtaining system response (y(t)) for given inputs

This section tests problem-solving ability, conceptual application, and clarity in mathematical modelling.

Overall Purpose of the Examination

This question paper aims to check whether the student can:

Understand fundamental signal operations

Apply Fourier, Laplace, and Z-Transform for system analysis

Develop state-space models and interpret system behaviour

Solve problems related to stability, time-domain and frequency-domain systems

Demonstrate both theoretical understanding and practical problem-solving skills

The paper is structured to comprehensively evaluate both conceptual clarity and computational proficiency.