Relationship between Laplace Transform and Fourier Transform The Fourier Transform for Continuous Time signals is infact a special case of Laplace Transform. This fact and subsequent relation between LT and FT are explained below. Now we know that Laplace Transform of a signal 'x'(t)' is given by:
The s-complex variable is given by
But we consider
From the above discussion
it is clear that the LT reduces to FT when the
complex variable only consists of the imaginary part . Thus LT
reduces to
FT along the
|
and therefore
's' becomes completely imaginary.
Thus we have
.
This means that we are only considering the vertical strip at
.
(Imaginary axis).
 |
 |