(SEM III) THEORY EXAMINATION 2023-24 BASIC SIGNALS & SYSTEMS

This examination is designed to evaluate the student’s understanding of fundamental and advanced concepts in Signals and Systems, an essential subject in Electronics, Electrical, Computer, and Communication Engineering. The paper measures the student’s ability to analyze different types of signals, their mathematical representation, system behaviors, and transformations using tools like Laplace Transform, Z-Transform, Fourier Series, Fourier Transform, State-Space Analysis, and Convolution.

The question paper is divided into three sections — A, B, and C — each focusing on different cognitive levels such as conceptual clarity, analytical thinking, derivation ability, and problem-solving skills.

SECTION A – Short Conceptual Questions (14 Marks)

Section A contains 7 concise conceptual questions, each carrying 2 marks. These questions examine the student's foundational understanding of core ideas like:

Causal vs. Non-Causal systems

Fourier series coefficients

Laplace and Z-Transform differences

Advantages of state-space models

Z-transform properties and ROC

Basic transform evaluation

Students are expected to answer clearly and to the point. This section tests clarity of definitions, basic reasoning, and conceptual memory.

SECTION B – Descriptive & Analytical Questions (21 Marks)

This section includes 5 questions, out of which students must attempt any 3. Each question carries 7 marks, requiring deeper explanation, derivations, examples, and system analysis.
Topics include:

Classification of systems (LTI, memoryless, causal, stable, time-variant, etc.)

Conditions for Fourier transform existence and properties

Transfer function computation from given poles and zeros

State transition matrix derivation, properties, and proof

Z-transform and ROC for various discrete-time signals

This section evaluates a student’s ability to think analytically, derive equations, and apply theory to solve engineering problems.

SECTION C – Long Answer / Application-Based Questions (35 Marks)

Section C contains 5 sets, each with two alternate questions, and students must answer one question from each set.
Each question carries 7 marks and requires problem-solving, derivation, or graphical interpretation.

The topics include:

Graphical representation of composite time-domain signals

Properties of convolution

Fourier transform evaluation

Symmetry types in Fourier series

Inverse Laplace transform and LTI system response

State model derivation from circuits or transfer functions

Impulse response of difference equations

Initial Value Theorem for Z-transform

This section examines a student's ability to apply concepts to engineering-level problems, derive relationships, interpret mathematical expressions, and understand system behavior in real-life scenarios.

Learning Outcomes of This Examination

By the end of the exam, students should demonstrate the ability to:

Distinguish different types of signals and system properties
Apply transformation techniques (Laplace, Fourier, Z-transform)
Analyze LTI systems in both time and frequency domains
Compute transfer functions, impulse responses, and system outputs
Understand and derive state-space models
Solve engineering-level problems involving system dynamics
Interpret graphical signals and apply convolution properties

Additional Questions Added (Optional Enhancement)

You can add the following questions to make the paper even more comprehensive:

SECTION A (Add-on)

h. Define time-invariant and time-variant systems.
i. What is the significance of Region of Convergence (ROC) in Z-transform?

SECTION B (Add-on)

f. Explain the concept of energy and power signals with mathematical expressions.

SECTION C (Add-on)

Derive the convolution of two finite-length discrete-time signals x[n] and h[n].
OR
Explain the relation between Fourier Transform and Laplace Transform.