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Signal and Systems covers the introduction of several types of Elementary Signals and related concepts. We also learn about Fourier Series and Fourier Transforms along with Fourier Series and Transforms of the discussed Elementary Signals. Moving forth, we will study about Time and Frequency Characteristics of Time Variant and Time invariant Systems. We also learn Mathematical Techniques of Laplace Transform and Z Transform which helps in understanding Systems and Signals in a more comprehensive manner.

**What will you learn?**

The complete online syllabus of this course comprises **5** Learning Modules | **84** Topics of Learning | **4.2** Hours of Learning | **30 **Assessments

**Module**

- Signals, System and their classification
- Linear Time-Invariant systems and Fourier Series Representation of Periodic signals
- Fourier Transform
- Time and Frequency Characteristics, Sampling and Communication
- Z-Transform, Laplace Transform and Linear Feedback System

**Topics of Learning**

- Continuous-Time and Discrete-Time Signals
- Transformation of the Independent Variable
- Discrete-Time Complex Exponential and Sinusoidal Signals
- Periodicity Properties of Discrete-Time Complex Exponentials
- Continuous-Time and Discrete-Time Systems
- Causality and Stability
- Time Invariance and Linearity
- Discrete-Time LTI Systems : The Convolution Sum
- The Discrete-Time Unit Impulse Response and The Convolution-Sum Representation of LTI Systems
- The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems
- The associative Property and LTI with and without Memory
- Linear Constant-Coefficient Differential Equations
- Linear Constant-Coefficient Difference Equations
- Block Diagram Representation of First-Order Systems Described by Differential and Difference Equations
- Convergence and its Conditions
- Multiplication
- First Difference and Parseval’s Relation for Discrete-Time Periodic Signal
- Filters and its Types
- Frequency-Shaping Filters
- Frequency-Selective Filters
- A Simple RC Low pass Filter
- A Simple RC High pass Filter
- Introduction to the Continuous-Time Fourier Transform
- Convergence of Fourier Transforms
- The Multiplication Property
- Convergence Issues associated with the Discrete-Time Fourier Transform
- Periodicity of the Discrete – Time Fourier Transform and Linearity of the Fourier Transform and Time Shifting and Frequency Shifting
- The Convolution Property
- The Magnitude-Phase Representation of the Fourier Transform
- The Magnitude-Phase Representation of the Frequency Response of LTI Systems – Linear and Nonlinear Phase
- Group Delay and Log-Magnitude and Bode Plots
- Time-Domain Properties of Ideal Frequency-Selective Filters
- Time-Domain and Frequency-Domain Aspects of Non Ideal Filters
- Examples of Time and Frequency-Domain analysis of Systems- Analysis of an Automobile Suspension System
- Examples of Discrete-Time Non recursive Filters
- Representation of a Continuous-Time Signal by its Samples :The Sampling Theorem
- Reconstruction of a Signal from its Samples using Interpolation
- Discrete-Time Processing of Continuous-Time Signals
- Introduction to the Communication Systems
- Complex Exponential and Sinusoidal Amplitude Modulation – Amplitude Modulation with a Complex Exponential Carrier
- Amplitude Modulation with a Sinusoidal Carrier
- Asynchronous Demodulation
- Single-Sideband Amplitude Modulation
- Amplitude Modulation with a Pulse-Train Carrier – Modulation of a Pulse-Train Carrier
- Amplitude Modulation with a Pulse-Train Carrier – Time Division Multiplexing
- Pulse Amplitude Modulation – Pulse Amplitude Modulated Signals
- Intersymbol Interference in PAM Systems
- Digital Pulse Amplitude and Pulse-Code Modulation
- Sinusoidal Frequency Modulation
- Wideband Frequency Modulation
- Discrete-Time Modulation – Discrete-Time Sinusoidal Amplitude Modulation
- Discrete-Time Transmodulation
- Introduction to laplace Transform
- The Region of Convergence for Laplace Transforms Property 1, 2, 3 and 4
- Property 5, 6, 7 and 8
- Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot
- All Pass System
- Properties of the Laplace Transform
- System Function Algebra and Block Diagram Representations – System Functions for
- Interconnections of LTI Systems
- The Unilateral Laplace Transform
- Properties of Unilateral Laplace Transform
- Introduction to z-Transform
- The Region of Convergence for the z-Transform – Property1,2 and 3
- Property 4, 5 and 6
- Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot – First order Systems
- Stability
- System Function Algebra and Block Diagram Representations – System Functions for
- Interconnections of LTI Systems
- Block Diagram Representation for Causal LTI Systems descibed by Difference Equations and Rational System Functions
- The Unilateral z-Transform
- Properties of Unilateral z-Transform
- Introduction to Linear Feedback Systems
- Linear Feedbak Systems
- Some Applications and Consequences of Feedback – Inverse System Design
- Compensation of Nonideal Elements
- Sampled Data Feedback Systems
- Destabilization Caused by Feedback
- Root-Locus Analysis of Linear Feedback Systems
- Equation for the Closed-Loop Poles and The End Points of the Root Locus : The Closed-Loop Poles
- Properties of the Root Locus
- The Nyquist Stability Criterion
- The Encirclement Property
- The Nyquist Stability Criterion for Continuous for Continuous-Time LTI Feedback Systems
- The Nyquist Stability Criterion for Discrete-Time LTI Feedback Systems
- Gain and Phase Margins