the subject makes itself clear. i need a thorough discussion of how these 2 important transformations are related. when do we use laplace transform when do we use fourier?
the factor s=σ+jω... ie σ refers to attenuation and ω stands for angular frequency..
if basis function used is e**(-st) then it is laplace transform..if transform relinqushes attenuation(a nondamping system) then basis function becomes
e**-jωt.. this is called as fourier transform..
Dear electronics_kumar,
When u get Laplace Transform of a fn as a function in s , You can substitute
s=sigma + j*omega.
and then plot this as a function of both sigma and omega which is shown as the surface on the RHS. If you put sigma =0 (cutting the surface by a plane) I get Fourier Transform of the function...This is of course only valid if we use Laplace Transform by integrating from -infinity to infinity (Generalised case),
or considering functions which are zero for t<0 (such as causal systems impulse response).
So we imagine that Laplace Transform is a generalised Fourier Transform in which poles and zeros are shown...
For more information see: https://www.dspguide.com/
chapter 32
Best wishes,