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