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D R . T A R E K T U T U N J I
P H I L A D E L P H I A U N I V E R S I T Y
2 0 1 4
The Laplace Transform
Laplace Transform
One-sided Laplace
The one-sided Laplace transform is defined as
where f (t) is either a causal function or made into a causal function by multiplication with step function, u(t)
The one-sided Laplace transform is of significance given that most of the applications deal with causal systems and signals
Example
Impulse:
Step:
Pulse
Differentiation
Example
Integration
Convolution
Transfer Function
Example
Laplace Transform
Transfer Function
Poles and Zeros
Example
One-sided Laplace Transforms
Properties of One-Sided Laplace Transforms
Conclusion
The Laplace transform provides a complementary representation to the time representation of a signal Damping and frequency, poles and zeros, together with regions of
convergence, conform a new domain for signals.
The solution of differential equations are obtained
algebraically with the Laplace transform. The Laplace transform provides a simple solution to the
convolution integral. The Laplace transform provides the concept of transfer
function A fundamental concept in analysis and synthesis of linear time-invariant
systems.
Reference
Chapter 3, Signals and Systems using MATLAB by Luis Chaparro. Elsevier Publisher 2011