Syllabus
UNIT – I
Introduction to signals and systems
Signals: Definition – Classification of signals : Continuous time – Discrete time – Deterministic & Random – Periodic & Non-periodic – Even & odd – Energy & Power signals – Basic operations on Independent Variable: Time Shifting -Time scaling – Time Reflection – Basic operations on Dependent Variable: Amplitude scaling, Addition, Multiplication, Differentiation and Integration – Basic elementary signals: Complex exponentials & sinusoidal – unit impulse – unit step – unit ramp.
Systems: Definition – Classification of systems: Continuous time – Discrete time systems – Basic system properties: Linearity – Time invariance – Memory and Memory less – Causality – Invertibility and Inverse – Stability.
UNIT – II
Linear Time Invariant Systems
Representation of discrete & continuous time signals in terms of impulses – Convolution sum – Convolution integral – Properties of convolution: Commutative, Associative and Distributive – Properties of LTI systems: Memory and Memory less – Invertibility – Causality – Stability – Unit step response of an LTI systems – Casual LTI systems described by Differential & Difference equations.
Sampling: Sampling theorem, Definition of CTFT and inverse CTFT, Definition of DTFT and inverse DTFT, Definition of Z transform- Region of convergence – Inverse Z transform (Partial fraction method)
UNIT – III
Basic Concepts of Control System
Introduction: Definition of system, control system – Classification of system- open loop and closed loop systems – Mathematical models: Transfer function model, State model.
Transfer function model: Block diagram representation – Reduction of Block Diagram – Techniques – Signal flow graph representation – Mason’s formula – Block diagram to Signal flow graph – Examples and problems – Derivation of transfer function of dc motor.
State Model: Definition of state space & State variables – Modeling of dynamic systems using state variables – Examples.
UNIT – IV
Time and Frequency Response of Linear Systems
Type and order of a system -First order and second order systems – Systems with unity and non – Unity feedback – Impulse response and step response of first and second order linear systems.
Time domain specifications: rise time, delay time, overshoot and settling time of first order and second order systems.
Steady state error and error constants – Generalized error constants – Problems.
Frequency Response
Frequency response specifications: resonant peak, resonant frequency, bandwidth, cut-off rate -correlation between time and frequency response of second order system.
Course Objectives and Outcomes
Course Objectives:
- to represent any arbitrary signals in time and frequency domains and design LTI systems with specific impulse / step responses
- Introduce the basic concepts of control system, its types, transfer function and state space models
- To analyse the linear time invariant system in time and frequency domains and also to find the system specification in both the domains
Course Outcomes:
After completing this course, students should be able to
- Design and test CT / DT LTI systems in both the time and frequency domains
- Apply unit impulse function and basic complex exponentials for system analysis
- Design a control system for a linear time invariant, single input and single output system
- Evaluate the time and frequency responses of the systems
Online Materials
NPTEL – http://www.youtube.com/playlist?list=PL75A2863DF4CE1CE6
NPTEL – http://nptel.ac.in/courses/108102043/
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
| CO |
| CO1 |
3 |
3 |
2 |
1 |
3 |
– |
– |
– |
3 |
3 |
– |
2 |
3 |
– |
2 |
| CO2 |
3 |
3 |
1 |
1 |
3 |
1 |
– |
– |
3 |
3 |
– |
1 |
2 |
1 |
3 |
| CO3 |
3 |
3 |
3 |
2 |
3 |
1 |
– |
– |
3 |
3 |
– |
2 |
3 |
2 |
3 |
| CO4 |
3 |
3 |
3 |
2 |
3 |
– |
– |
– |
3 |
3 |
– |
2 |
3 |
1 |
3 |
