Lecture 44 of 78Week 6: Fourier Transform V
Helpful Relationships for Inverse Fourier Transform
Prof. Andrew Thangaraj and Prof. C. S. Ramalingam · IIT Madras
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- Networks and systems, IIT Madras (at NPTEL)
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All the lectures
- Functions in circuits - constant and sinusoidal functions
- Functions in circuits - Exponential function
- Complex numbers and other topics
- Systems, Signals, Networks
- Representation and Classification of Systems
- Linear systems
- Time-invariance and causality
- Signals, Elementary continuous signals
- Complex frequencies of signals
- Discontinuous signals - step, ramp
- Unit impulse or delta function
- Basic discrete-time signals
- Week 1 Solutions
- Examples of Signals
- Introduction to Systems, Complementary Functions, Initial Conditions
- Special initial conditions
- Characterization of a linear system
- Impulse Response
- Evaluating the Convolution Integral
- Worked-out Problems
- Hints for Assignment 2
- Introduction and Motivation
- Evaluating Fourier series coefficients
- Symmetry conditions
- Symmetry Condition Examples
- Application to Network Analysis
- Hints for Assignment 3
- Exponential Fourier Series
- Frequency Spectrum
- Examples
- Signal Power and Related Ideas
- Convergence of Fourier Series
- Additional Properties of Fourier Series
- Exercises on Fourier Series
- Lab Demo
- From Fourier Series to Fourier Transform
- Continuous Time Fourier Transform
- Fourier Transform Examples
- Examples and Some Properties of Fourier Transform
- Properties of Fourier Transform (contd.)
- More Fourier Transform Properties
- Energy Considerations
- Energy Considerations II
- Helpful Relationships for Inverse Fourier Transform
- Fourier transform of signals that are not absolutely integrable
- Fourier Transform of Periodic Signals, Unit Step and Signum Function
- Truncated Sine wave and Convolution properties
- Integration in Time domain
- Application of continuous-time Fourier transform to system analysis
- Comments about transient analysis
- Sampling Theorem and Exercises on Fourier Transforms
- Introduction to Laplace Transform
- Laplace transforms of important functions
- Recap, Poles / Zeros and Laplace Transform Notation
- Properties: Linearity, differentiation in the time domain
- Application and properties of Laplace transform
- More properties of Laplace transform: Shift in frequency domain
- More properties of Laplace transform
- Properties: Division by `t, Initial value theorem, Final value theorem
- Properties: Convolution in time domain
- Complex convolution and periodic functions
- Examples of Laplace transform
- Laplace transform examples
- Inverse Laplace transform
- Partial fractions: general case
- Inverse Laplace Transform and Contour Integration
- Relating Fourier and Laplace Transform
- Exercises
- Applications of Laplace transform to network transients
- Laplace transform for resistor and system analysis
- Laplace transform method for mutual inductance
- Mutual Inductance Continued
- Examples and Advantages of L-transform
- General LTI systems and more about H(s)
- Many facets of the system function (contd)
- Frequency response and stability
- Full circuit example
- Exercises.