This course explains **signals and systems** representations/classifications and also describe the **time and frequency domain** analysis of continuous time signals with **Fourier series, Fourier transforms** and **Z transforms**.

Demonstrate an understanding of the fundamental properties of linear systems, by explaining the properties to others.

Develop input output relationship for linear shift invariant system and understand the convolution operator for continuous and discrete time system.

Understand the limitations of Fourier transform and need for Laplace transform and develop the ability to analyze the system in s- domain.

### Course Curriculum

- 1. Introduction
- 1. Signals and Systems Introduction – Step Signals
- Impulse Signal
- 3. Ramp Signals and Parabolic Signals
- 4. All Signals Summary
- 5. Standard Signals
- 6. Gate Signal or Rectangular Signal
- 7. Sampling Signal or Sync Signal
- 8. How to perform operations on Signals
- 9. Time Scaling Operation
- 10. Folding Operation (Time Reversal)
- 11. Adding , Subtraction and Multiplication Operations – Part 1
- 12. Adding , Subtraction and Multiplication Operations – Part 2
- 13. Operations on Signals – Differentiation
- 14. Classification of Signals (Constant and Discrete , Real and Imaginary )
- 15. Periodic and Aperiodic signals
- 16. Problems on Periodicity
- 17. Periodicity of Discrete time signals.
- 18. Even and Odd Signals
- 19. Problems on Even and Odd Signals – 1
- 20. Problems on Even and Odd Signals – 2
- 21. Energy and Power Signal.
- 22. Problems on Energy and Power Signal.
- 23. Problems on Discrete time Signal.
- 24. Deterministic and Random Signals.
- Testing

- 2. Systems
- 3. Fourier Series
- 4. Fourier Transform
- Introduction to Fourier Transform.
- Fourier Transform of Different Signals.
- Magnitude and Phase Responses.
- Fourier Transform of Rectangular.
- Properties of Fourier Transform (Linearity).
- Frequency and Shifting.
- Time Scaling.
- Time Folding and Time Differentiation.
- Frequency Differentiation.
- Integration Property.
- Overview on Properties of Fourier Transform.
- Problems on Properties of Fourier Transform – 1.
- Problems on Properties of Fourier Transform – 2.
- Fourier Transform of Sinusoidal Signals – 1.
- Fourier Transform of Sinusoidal Signals – 2.
- Fourier Transform of Triangular Signals.
- Problems on Fourier Transform.
- Fourier Transform of Signum Function.
- Fourier Transform of Unit Step Function.
- Overview of Fourier Transform.

- 5. Laplace Transform
- Limitations of Fourier Transform and Why Laplace Transform
- Introduction of Laplace Transform.
- Laplace Transform of Exponential Signals
- Properties of Region of Convergence (ROC)
- Laplace Transform OF Different Signals
- Laplace Transform of Basic Signals
- Properties of L.T – 1 : Linearity, Shifting( Time and Frequency), and Scaling
- Overview of Properties of Laplace Transform
- Applications of Laplace Transform – 1
- Applications of Laplace Transform
- Inverse Laplace Transform : Part – 1
- Inverse Laplace Transform : Part – 2
- Inverse Laplace Transform : Part – 3
- Linear Time Invariant (LTI) Systems
- Linear Time Invariant (LTI) System Responses
- Differential Equations
- Impulse response of the system
- Sinusoidal Responses
- Initial and Final Values of Function

- 6. Z-Transform
- Introduction to Z-Transform and L.T and Z.T Relation.
- Relation between S-Plane and Z-Plane.
- ROC of Z-Transform.
- Z-Transform of Basic Signals.
- ROC of Basic Signals.
- Z-Transform of Different Signals – 1.
- Z-Transform of Different Signals – 2.
- Inverse Z-Transform.
- Problems on Inverse Z- Transform.
- Problems on Z-Transform – 1.
- Problems on Z-Transform – 2.
- Problems on Z-Transform – 3.
- Problems on Z-Transform – 4.
- Problems on Z-Transform – 5.
- Z-Transform of sinusoidal Signals – 1.
- Z-Transform of sinusoidal Signals – 2.
- Properties of Z-Transform (Amplitude Scaling).
- Properties of Z-Transform (Time Scaling).
- Time Shifting Property – 1.
- Time Shifting Property – 2.
- Multiplication in Time Domain Property.
- Time Folding.
- Overview of Properties of Z-Transform.
- Problems on Z-Transform – 6.
- Problems on Z-Transform – 7.