| Introduction:
The Signals and Systems course is a foundational subject in electrical, electronics, and communication engineering. It introduces students to the fundamental concepts of analyzing and understanding signals, systems, and their interaction in both continuous and discrete time domains. This course equips students with essential tools and techniques, such as Fourier transforms, Laplace transforms, Z-transforms, and MATLAB simulations, to study and design systems used in signal processing, communication, control, and other engineering applications. |
| Course Objective:
· Introduce the student to the idea of signals, system analysis and its characterization.
· Provide a foundation to numerous other courses that deal with signal and system concepts directly or indirectly: viz: communication, control, instrumentation etc.
· To provide hand on experience of signal & and system techniques using MATLAB |
Course Outcomes:
| COs |
Course outcomes |
| CO1 |
Understand and classify various types of signals and systems, including continuous-time and discrete-time, periodic and aperiodic, and causal and non-causal signals |
| CO2 |
Analyze the time-domain response of Linear Time-Invariant (LTI) systems using mathematical equations, block diagrams, signal flow graphs, and convolution techniques |
| CO3 |
Apply Fourier Series and Fourier Transform techniques to evaluate the frequency-domain representation of continuous-time and discrete-time signals and interpret their properties. |
| CO4 |
Evaluate system stability and performance in the s-domain and z-domain using Laplace and Z-transform methods, including their properties and inversions |
| CO5 |
Design and implement discrete-time systems described by difference equations and analyze their correlation properties, ensuring stability and proper interconnection. |
|
| PSO1 |
Graduates will apply their learning outcome of the program creatively and
productively in the fields of Embedded Systems, VLSI, and Communication Systems |
| PSO2 |
Solving real-life problems, design and develop novel products that are technically sound, economically feasible, and socially acceptable |
| PSO3 |
Add value to interdisciplinary areas in providing solutions in agriculture, manufacturing, and security services |
| CO, PO Mapping Matrix |
| CO/PO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
| CO1 |
3 |
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2 |
2 |
2 |
| CO2 |
3 |
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3 |
2 |
2 |
| CO3 |
|
2 |
2 |
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3 |
2 |
2 |
| CO4 |
3 |
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2 |
2 |
2 |
| CO5 |
3 |
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3 |
2 |
2 |
Syllabus
MODULE – I (6 Hours+4 Hours)
Continuous-Time Signals and Systems:
Continuous and discrete time signals: Some Elementary Continuous-time and Discrete-Time signals. Classification of Signals – Periodic and a periodic even – odd – energy and power signals – Deterministic and random signals – Causal and non causal signals and anti causal signals -- complex exponential and sinusoidal signals ---Simple Manipulations of Continuous and discrete time signals
Practice:
- Generate and plot elementary continuous-time and discrete-time signals (sinusoidal, exponential, step, impulse, and ramp) using MATLAB.
- Perform basic signal manipulations: time scaling, time shifting, and amplitude scaling
MODULE – II (6 Hours+ 4 Hours)
Continuous-Time Systems:
Continuous-Time Systems: Mathematical equation governing LTI Continuous-Time systems, Block diagram and signal flow graph representation, response of LTI Continuous-Time system in time domain, classification of Continuous-Time systems, convolution of Continuous-Time signals.
Practice:
- Classify given signals as periodic/aperiodic, even/odd, energy/power signals, and deterministic/random using MATLAB
- Convolution of Continuous-Time Signals Using MATLAB
MODULE – III (6 Hours+ 4 Hours)
Discrete-Time Signals and Systems:
Input-Output Description, Block Diagram Representation, Classification, Interconnection; Analysis of Discrete-Time LTI Systems: Techniques, Response of LTI Systems, Properties of Convolution, Causal LTI Systems, Stability of LTI Systems; Discrete-Time Systems Described by Difference Equations; Implementation of Discrete-Time Systems; Correlation of Discrete-Time Signals: Cross correlation and Autocorrelation Sequences, Properties
Practice:
- Analyse discrete-time Linear Time-Invariant (LTI) systems by studying their input-output behavior, block diagram representation, and properties like causality and stability using MATLAB
- Simulate the response of LTI discrete-time systems to various inputs (impulse, step, sinusoidal) and plot the results
MODULE – IV (6 Hours+4 Hours)
The Continuous-Time Fourier Series and Fourier Transform:
Basic Concepts and Development of the Fourier series, Calculation of the Fourier Series, Properties of the Fourier Series.
The Continuous-Time Fourier Transform:
Basic Concepts and Development of the Fourier Transform, Properties of the Continuous-Time Fourier Transform. Discrete-time Fourier series
Practice:
- Compute and visualize the Fourier series coefficients of a periodic continuous-time signal.
- Compute and plot the Fourier transform of a given aperiodic signal. Analyse the amplitude and phase spectra
MODULE – V (5 Hours+4 Hours)
Discrete time Fourier transform (DTFT) :
The discrete time Fourier transform of Aperiodic signal, Convergence of Fourier transform, the Fourier transform of signal with poles on unit circle, frequency domain and time domain signal properties, properties of DTFT.
Practice:
- Compute the DTFT of a given discrete-time signal and study its properties (time and frequency domain characteristics).
MODULE- VI (5 Hours+ 2 Hours)
The Laplace transforms and its application to system analysis:
The Laplace Transform: Laplace Transform as a generalization of FT, Region of convergence, properties of Laplace transform, poles and zeros of rational functions of s, Inverse Laplace transform by partial fraction method and convolution method, Analysis of LTI Continuous-Time system, stability in s-domain,
Practice:
- Simulate and analyze the Laplace transform of continuous-time signals. Perform inverse Laplace transformations using MATLAB
MODULE- VII (5 Hours+ 4 Hours)
The Z-Transform and Its Application to the Analysis of LTI Systems:
The Z-Transform: The Direct Z-Transform, The Inverse Z-Transform; Properties of the Z-Transform; Rational Z-Transforms: Poles and Zeros, Pole Location and Time-Domain Behavior for Causal Signals, The System Function of a Linear Time-Invariant System; Inversion of the Z-Transforms: The Inversion of the Z-Transform by Power Series Expansion, The Inversion of the Z-Transform by Partial-Fraction Expansion; The One-sided Z-Transform: Definition and Properties, Solution of Difference Equations.
Practice:
- Evaluation of Z-transform of discrete-time signals.
- Analyze the properties of Z-transform and solve difference equations using MATLAB.
Text Books:
- Signals and Systems--- Alan V. Oppenheim and Alan S. Willsky, PHI
- Signals and Systems – A Nagoor Kani, TMH
Reference Books:
- Digital Signal Processing – Principles, Algorithms and Applications by J. G. Proakis and D. G. Manolakis, 4th Edition, Pearson.
- Fundamentals of Signals and Systems - M. J. Roberts, TMH
Session Plan
Session 1
Continuous-Time and Discrete-Time Signals
https://www.youtube.com/watch?v=H4hk6N5vC1Q&pp=ygUpQ29udGludW91cy1UaW1lIGFuZCBEaXNjcmV0ZS1UaW1lIFNpZ25hbHM%3D
Session 2
Classification of Signals: Periodic, Aperiodic, Even, Odd
https://www.youtube.com/watch?v=Gj9pDC_OBQU&pp=ygU5Q2xhc3NpZmljYXRpb24gb2YgU2lnbmFsczogUGVyaW9kaWMsIEFwZXJpb2RpYywgRXZlbiwgT2Rk
Session 3
Energy, Power, Deterministic, and Random Signals
https://www.youtube.com/watch?v=zaY7C1clVec&pp=ygUwRW5lcmd5LCBQb3dlciwgRGV0ZXJtaW5pc3RpYywgYW5kIFJhbmRvbSBTaWduYWxz
Session 4
Causal, Non-Causal, and Complex Signals
https://www.youtube.com/watch?v=mqwUtn5cip8&pp=ygUnQ2F1c2FsLCBOb24tQ2F1c2FsLCBhbmQgQ29tcGxleCBTaWduYWxz
Session 5:
Causal, Non-Causal, and Complex Signals
YouTube Link: https://www.youtube.com/watch?v=example5
Session 6:
Manipulation of Continuous-Time Signals
YouTube Link: https://www.youtube.com/watch?v=example6
Session 7:
Manipulation of Discrete-Time Signals
YouTube Link: https://www.youtube.com/watch?v=example7
Session 8:
Basic Signal Manipulations (Time Scaling, Shifting, Amplitude Scaling)
YouTube Link: https://www.youtube.com/watch?v=example8
Session 9:
Mathematical Model of LTI Continuous-Time Systems
YouTube Link: https://www.youtube.com/watch?v=example9
Session 10:
Block Diagram and Signal Flow Representation
YouTube Link: https://www.youtube.com/watch?v=example10
Session 11:
Time-Domain Response of LTI Continuous-Time Systems
YouTube Link: https://www.youtube.com/watch?v=example11
Session 12:
Classification of Signals using MATLAB
YouTube Link: https://www.youtube.com/watch?v=example12
Session 13:
Convolution of Continuous-Time Signals
YouTube Link: https://www.youtube.com/watch?v=example13
Session 14:
Convolution of Continuous-Time Signals (Contd.)
YouTube Link: https://www.youtube.com/watch?v=example14
Session 15:
Classification of Continuous-Time Systems
YouTube Link: https://www.youtube.com/watch?v=example15
Session 16:
Convolution of CT Signals using MATLAB
YouTube Link: https://www.youtube.com/watch?v=example16
Session 17:
Discrete-Time Systems: Input-Output and Block Diagram
YouTube Link: https://www.youtube.com/watch?v=example17
Session 18:
Analysis of Discrete-Time LTI Systems
YouTube Link: https://www.youtube.com/watch?v=example18
Session 19:
Properties and Stability of Causal LTI Systems
YouTube Link: https://www.youtube.com/watch?v=example19
Session 20:
MATLAB Analysis of Discrete-Time LTI Systems
YouTube Link: https://www.youtube.com/watch?v=example20
Session 21:
Discrete-Time Systems by Difference Equations
YouTube Link: https://www.youtube.com/watch?v=example21
Session 22:
Solution of Discrete-Time Systems by Difference Equations
YouTube Link: https://www.youtube.com/watch?v=example22
Session 23:
Correlation of Discrete-Time Signals
YouTube Link: https://www.youtube.com/watch?v=example23
Session 24:
MATLAB Simulation of LTI DT Systems
YouTube Link: https://www.youtube.com/watch?v=example24
Session 25:
Fourier Series: Basics and Calculation
YouTube Link: https://www.youtube.com/watch?v=example25
Session 26:
Properties of Fourier Series
YouTube Link: https://www.youtube.com/watch?v=example26
Session 27:
Fourier Transform: Basics and Development
YouTube Link: https://www.youtube.com/watch?v=example27
Session 28:
MATLAB – Fourier Series Coefficients
YouTube Link: https://www.youtube.com/watch?v=example28
Session 29:
Properties of Continuous-Time Fourier Transform
YouTube Link: https://www.youtube.com/watch?v=example29
Session 30:
Properties of Continuous-Time Fourier Transform (Contd.)
YouTube Link: https://www.youtube.com/watch?v=example30
Session 31:
Discrete-Time Fourier Series
YouTube Link: https://www.youtube.com/watch?v=example31
Session 32:
MATLAB – Fourier Transform of Aperiodic Signals
YouTube Link: https://www.youtube.com/watch?v=example32
Session 33:
DTFT of Aperiodic Signals
YouTube Link: https://www.youtube.com/watch?v=example33
Session 34:
Convergence and Poles on Unit Circle
YouTube Link: https://www.youtube.com/watch?v=example34
Session 35:
Frequency and Time Domain Properties
YouTube Link: https://www.youtube.com/watch?v=example35
Session 36:
Properties of DTFT
YouTube Link: https://www.youtube.com/watch?v=example36
Session 37:
Laplace Transform: Basics and ROC
YouTube Link: https://www.youtube.com/watch?v=example37
Session 38:
MATLAB – DTFT of Signals
YouTube Link: https://www.youtube.com/watch?v=example38
Session 39:
Properties and Inverse Laplace Transform
YouTube Link: https://www.youtube.com/watch?v=example39
Session 40:
Analysis of LTI Systems in s-Domain
YouTube Link: https://www.youtube.com/watch?v=example40
Session 41:
Analysis of LTI Systems in s-Domain (Contd.)
YouTube Link: https://www.youtube.com/watch?v=example41
Session 42:
MATLAB – Image Brightness & Contrast Enhancement
YouTube Link: https://www.youtube.com/watch?v=example42
Session 43:
Stability in s-Domain
YouTube Link: https://www.youtube.com/watch?v=example43
Session 44:
Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example44
Session 45:
Evaluation of ROCs and Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example45
Session 46:
MATLAB – Laplace Transform Simulation
YouTube Link: https://www.youtube.com/watch?v=example46
Session 47:
Properties of Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example47
Session 48:
Inverse Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example48
Session 49:
Solution of Discrete-Time Systems using Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example49
Session 50:
MATLAB – Evaluation of Z-Transform
YouTube Link: https://www.youtube.com/watch?v=example50
Session 51:
Poles, Zeros, and Time-Domain Behavior
YouTube Link: https://www.youtube.com/watch?v=example51
Session 52:
MATLAB – Z-Transform Properties & Difference Equations
YouTube Link: https://www.youtube.com/watch?v=example52