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Laplace,Z and Fourier

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electronics_kumar

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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

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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....
 

Nazgul

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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

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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 https://www-ccec.ece.ucsb.edu/people/smith/classnotes/147b/lecture4_small.pdf

I hope this help you out.

Best regards,

\[v_c\]
 
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shanthan_33

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

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