Lecture 55 of 89Week 8
Laplace Transform : Derivative and Integral
Prof. Hitesh Shrimali Prof. Kushal K. Shah · IISER Bhopal
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- Signals and Systems, IISER Bhopal (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures
- Real and Complex Number
- Sinusoid and Phasor
- Limits and Continuity
- Differentiation and Integration
- L’Hospital’s Rule
- LTI System Examples; Impedance;
- Dirac Delta function; Impulse
- Continuous and Discrete Time Systems
- Even Signal; Odd Signal
- Orthogonality of Signals
- Shifting and Scaling in Continuous Time - I
- Shifting and Scaling in Continuous Time - II
- Shifting and Scaling in Discrete Time
- Signal and Noise
- Signals in the Physical World
- Signals and Sensory Perception
- Frequency Domain Representation
- Definition of Fourier Transform
- Fourier Transform Examples - I
- Dirichlet Conditions
- Inverse Fourier Transform
- Fourier Transform Examples - II
- Frequency-Time Uncertainty Relation
- Fourier Transform : Linearity, Time Shifting and Time Scaling
- Fourier Transform : Derivative Property
- Fourier Transform : Multiplication and Convolution Property
- Fourier Transform : Integral Property
- Fourier Transform Example - III
- Fourier Transform Example - IV
- Fourier Transform of Noise
- Types of Noise
- Overview of Systems and General Properties
- Linearity and Time Invariance
- LTI System Examples
- Frequency Response of RLC circuits - I
- Frequency Response of RLC circuits - II
- LCCDE Representation of Continuous-Time LTI Systems
- Frequency Domain Representation of LCCDE Systems
- Time Domain Representation of LTI Systems
- Continuous-Time Convolution Integral
- Continuous-Time Convolution Example I
- Continuous-Time Convolution Example II
- Continuous-Time Convolution Example III
- LTI Systems : Commutative, Distributive and Associative
- LTI Systems : Memorylessness and Invertibility
- LTI Systems : Causality and Stability
- Fourier Transform in Complex Frequency Domain
- Laplace Transform : Poles and Zeros
- Laplace Transform : Region of Convergence [ROC]
- Laplace Transform Examples I
- Laplace Transform Examples II
- Laplace Analysis of LTI Systems
- Laplace Analysis of RLC Circuits I
- Laplace Transform : Linearity, Shifting and Scaling
- Laplace Transform : Derivative and Integral
- Laplace Transform : Causality and Stability
- Laplace Analysis of LTI Systems Example I
- Laplace Analysis of LTI Systems Example II
- Laplace Analysis of First Order RLC Circuits
- Laplace Analysis of Second Order RLC Circuits
- Fourier Transform of Periodic Signals
- Fourier Series Representation in Continuous-Time
- Fourier Series Properties I
- Fourier Series Properties II
- LTI System Response for Periodic Input Signal
- Fourier Series in Continuous-Time : Examples I
- Fourier Series in Continuous-Time : Examples II
- Discrete-Time Convolution Sum
- Discrete-Time Convolution Sum Examples and Properties
- LCCDE Representation of Discrete-Time LTI Systems
- Impulse Train Sampling
- Reconstruction of Continuous-Time Signal
- Nyquist Sampling Theorem and Aliasing
- Fourier Transform of Sampled Signals
- DTFT Examples I
- DTFT Properties I : Periodicity, Linearity, Time/Frequency shifting, and Conjugation
- DTFT Properties II : Differencing and Accumulation in Time Domain, Differentiation in Frequency Domain
- DTFT Properties III : Time Reversal, Time Expansion, Convolution and Parsevaal's Relation
- DTFT Examples II
- DTFT in Complex Frequency Domain
- Z-Transform : Properties of ROC
- Z-Transform Properties I : Linearity, Time-Shifting, Time-Expansion, Time-Reversal, and Z-Scaling
- Z-Transform Properties II : Conjugation and Convolution
- Z-Transform Properties III : Causality and Stability
- Z-Transform Examples I
- Z-Transform Examples II
- Block Diagram Representation
- Live Session 15-03-2021
- Live Session 06-03-2020