Course Title: Continuous Signals and Linear Systems
Type of Course: Compulsory, Theory
Offered to: EEE
Pre-requisite Course(s): None
Classification of signals and systems: signals - classification, basic operation on signals, elementary signals, representation of signals using impulse function; systems- classification.
Properties of Linear Time Invariant (LTI) systems: Linearity, causality, time invariance, memory, stability, invertibility.
Time domain analysis of LTI systems: (i) Differential equations - system representation, order of the system, solution techniques, zero state and zero input response, system properties; (ii) impulse response - convolution integral, determination of system properties; (iii) state variable - basic concept, state equation and time domain solution.
Frequency domain analysis of LTI systems: (i) Fourier series - properties, harmonic representation, system response, frequency response of LTI systems; (ii) Fourier transformation - properties, system transfer function, system response and distortion-less systems.
Applications of time and frequency domain analyses: solution of analog electrical and mechanical systems, amplitude modulation and demodulation, time-division and frequency-division multiplexing.
Laplace transformation: properties, inverse transform, solution of system equations, system transfer function, system stability, frequency response and application.
Solution of analog electrical and mechanical systems
To develop a solid foundation on the continuous time signals and systems, and the essential techniques required for their analysis and synthesis for pursuing further studies in the field of telecommunications and signal processing
To study the most widely used techniques for transforming and analyzing signals and systems, both in time domain and frequency domain
To investigate the behavior of linear time invariant (LTI) systems with continuous time signals as input using various techniques, such as convolution, differential equations and state equations.
To explore the analogy between the electrical systems and mechanical or electromechanical systems, and apply this analogy for problem solving
Fundamental concepts of mathematics, fundamentals of electrical circuits and mechanical systems.
| CO No. | CO Statement | Corresponding PO(s)* | Domains and Taxonomy level(s)** | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) |
|---|---|---|---|---|---|
| CO1 | Understand the properties of different continuous time signals and basic operations on them | PO(a) | C2 | Lectures, Discussions | Assignment, Class test, Final exam |
| CO2 | Apply the fundamental concepts of continuous time signals and basic operations on them to analyze input/output behavior of LTI systems in time-domain. | PO(a) | C3 | Lectures, Discussions | Assignment, Class test, Final exam |
| CO3 | Apply the concept of frequency domain transformation (Fourier series and Fourier transform) of continuous time signals to analyze LTI system behaviour | PO(a) | C3 | Lectures, Discussions | Assignment, Class test, Final exam |
| CO4 | Analyze input/output behavior of LTI systems using Laplace transform | PO(b) | C4 | Lectures, Discussions | Assignment, Class test, Final exam |
Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 🗸 | 🗸 | 🗸 | 🗸 | 🗸 | 🗸 | 🗸 |
| Week | Lectures | Topic |
|---|---|---|
| 1-2 | 1-6 | Classification of signals and systems: signals - classification, basic operation on signals, elementary signals, representation of signals using impulse function; systems- classification. |
| 3 | 7-9 | Properties of Linear Time Invariant (LTI) systems: Linearity, causality, time invariance, memory, stability, invertibility. |
| 4-6 | 10-18 | Time domain analysis of LTI systems: (i) Differential equations - system representation, order of the system, solution techniques, zero state and zero input response, system properties; (ii) impulse response - convolution integral, determination of system properties; (iii) state variable - basic concept, state equation and time domain solution. |
| 7-8 | 19-24 | Frequency domain analysis of LTI systems: (i) Fourier series - properties, harmonic representation, system response, frequency response of LTI systems. |
| 9-10 | 25-30 | Frequency domain analysis of LTI systems: (ii) Fourier transformation - properties, system transfer function, system response and distortion-less systems. |
| 11 | 31-33 | Applications of time and frequency domain analyses: solution of analog electrical and mechanical systems, amplitude modulation and demodulation, time-division and frequency-division multiplexing. |
| 12-13 | 34-39 | Laplace transformation: properties, inverse transform, solution of system equations, system transfer function, system stability and frequency response and application. |
| 14 | 40-42 | Solution of analog electrical and mechanical systems. |
Class participation will be judged by in-class evaluation; attendance will be recorded in every class.
Continuous assessment will be done in the form of class tests, assignments, in-class evaluations.
Final Examination: A comprehensive term final examination will be held at the end of the Term following the guideline of academic Council.
Homework, Assignment and Quizzes 20%
Final Examination 70%
Total 100%
Continuous and Discrete Signals and Systems (2nd edition) - Samir S. Soliman and Mandyam D. Srinath
Signals and Systems (2nd Edition) - Alan V. Oppenheim, Alan S. Willsky and S. Hamid Nawab
Analysis of Linear Systems – David K. Chen
Signals, Systems, and Transforms – Charles L. Phillips, John M. Parr, Eve A. Riskin (4th Ed)
Signal Processing and Linear Systems – B. P. Lathi (2nd Ed)
Continuous-Time Signals and Systems – Michael D. Adams
Besides going through relevant topics of the textbooks, it is strongly advised that the students follow the class Lectures and discussions regularly for a thorough understanding of the topics.