Laplace Transform

Saturday, 20 April 2019

1:30 PM

The Fourier transform can only be applied to a limited range of signals (ie those that are periodic)

We now study a more general transform to that is applicable to a wider range of functions;
and is better suited to transient responses;
and is more convenient for linear systems analysis

 

 

 

 

 

 means that the lower limit includes the origin

 

 is a complex frequency domain

 

 is a complex quantity:

 

// Consider  to be like a decay

 

 is evaluated over

 

A Laplace transform exists if

For some , then the region of convergence is

 

 

Inverse Laplace Transform

Applies for when  | ie along a line inside the region of convergence

But this is difficult to evaluate, so a table of Laplace transform pairs is often used