Laplace,Z and Fourier

[electronics_kumar]

how laplace ,Z and fourier transform are differ from each other....i know the realtion between Laplace and fourier trnasform

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..

but what is the relation between Laplace and Z also between Z and fourier transform

 

[vahidkh6222]

as far as i know, z transform is the equivalent of laplace transform, for the discrete time domain signals.
laplace is for continiuos signals and z is for discrete signals....
if u know the relationship between laplace and fourier transform of continiuos signals, the same relationship exists between z transform and fourier in discrete time domain....

 

[neils_arm_strong]

I think z=exp(s) will completely give the relation between laplace and Z transform.

 

[Nazgul]

Mr. Armstrong, z = exp(s) is not correct. A more accurate relationship between, Z and S transforms were given by vahidikh622: Z transform applies to functions that are discrete while S transform works for continues signals.

 

[v_c]

You can approximate s-domain transfer function by z-domain transfer function by using a number of transformations. The transformation depend on what kind of difference equation you will use to approximate a derivative. You can use forward-Euler, backward-Euler, etc. A good summary of all the techniques can be found in this document **broken link removed**

I hope this help you out.

Best regards,

\[v_c\]

 

[shanthan_33]

Please refer the book by P.B.Lathi
"linear systems and signals"
All your doubts will be cleared .....