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.
