The Laplace Transform
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by Dr. Robert Akl
1
Generalizing the Fourier Transform
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Generalizing the Fourier Transform
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Generalizing the Fourier Transform
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4
Complex Exponential Excitation
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Complex Exponential Excitation
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Pierre-Simon Laplace
3/23/1749 - 3/2/1827
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7
The Transfer Function
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8
The Transfer Function
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9
Cascade-Connected Systems
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10
Direct Form II Realization
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Direct Form II Realization
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Direct Form II Realization
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Direct Form II Realization
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Direct Form II Realization
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15
Direct Form II Realization
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Inverse Laplace Transform
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17
Existence of the Laplace Transform
Time Limited Signals
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18
Existence of the Laplace Transform
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Existence of the Laplace Transform
Right- and Left-Sided Signals
Right-Sided Left-Sided
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Existence of the Laplace Transform
Right- and Left-Sided Exponentials
Right-Sided Left-Sided
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21
Existence of the Laplace Transform
Right-Sided Exponential
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Existence of the Laplace Transform
Left-Sided Exponential
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Existence of the Laplace Transform
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24
Existence of the Laplace Transform
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25
Laplace Transform Pairs
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Region of Convergence
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Region of Convergence
Some of the most common Laplace transform pairs(There is more extensive table in the book.)
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28
Laplace Transform Example
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Laplace Transform Example
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Laplace Transform Example
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Laplace Transform Example
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MATLAB System Objects
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MATLAB System Objects
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34
Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Partial-Fraction Expansion
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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Inverse Laplace Transform Example
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50
Use of MATLAB in Partial Fraction Expansion
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Laplace Transform Properties
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Laplace Transform Properties
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Laplace Transform Properties
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Laplace Transform Properties
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Final Value Theorem
Laplace Transform Properties
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Use of Laplace Transform Properties
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Use of Laplace Transform Properties
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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The Unilateral Laplace Transform
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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Pole-Zero Diagrams and Frequency Response
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