LAPLACE TRANSFORM - Utah ECE
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by Neil E. Cotter
Research Assistant Professor
Last Updated: 10/19/08
[pic] († = missing, * = article)
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Laplace transform
Definition
Step functions
Piecewise function defs
Example (pdf)
Transform pairs:
Table of basic transforms | (pdf)
Impulse function
Step function
Sine
Example (pdf)
Example 2 (pdf)
Identities:
List | (pdf)
Multiplication by constant
Addition
Differentiation
Integration
Delay
Frequency shift
Scaling time
Multiplication by time (pdf)
Example 1 (pdf)
Example 2 (pdf)
Example 3 (pdf)
Example 4 (pdf)
Example 5 (pdf)
Example 6 (pdf)
Example 7 (pdf)
Example 8 | (pdf)
Example 9 (pdf)
Inverse transform
†Definition
Partial fractions
Complex root identity (pdf)
Example 1 (pdf)
Example 2 (pdf)
Example 3 (pdf)
Example 4 (pdf)
Example 5 (pdf)
Example 6 (pdf)
Example 7 | (pdf)
Matching forms
Example 1 (pdf)
Complex roots
Example 1 (pdf)
Poles and zeros
Impulse response vs pole location
RC Filter
Example 1 | (pdf)
Example 2 (pdf)
Example 3 | (pdf)
Example 4 (pdf)
Initial/final value theorems
†Initial value theorem (pdf)
Example (pdf)
Example 2 | (pdf)
Example 3 (pdf)
Circuits
s-domain circuit elements
Example (pdf)
s-domain solutions
Example (pdf)
Example 2 (pdf)
Example 3 (pdf)
Example 4 (pdf)
t-domain waveforms
Example (pdf)
Example 2 (pdf)
Example 3 (pdf)
Example 4 (pdf)
Example 5 (pdf)
Example 6 (pdf)
Impulse function
Example (pdf)
Basis functions
Sinusoids as eigenfunctions
Transfer functions
Magnitude and phase
j encodes phase
Matrix differential equations
Transfer function stability
Final value theorem
State-space equations
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