how to decide when to calculate FOURIER,LAPLACE,Z-TRANFORM.

[wajahat]

laplace, fourier and z-transformation

Hi all i want to know what are the rules which make us possible to decide that laplace ,fourier or z tranform would be the better choice in a particular situation.
There must be some limitations in one transform that force us to use the other transform.
Any detail in this regard would be helpful.
regards
wajahat

 

[harsha_jois]

z-tranform

Simple.
Basically all signals are represented in standard amplitude over time format.
If you need to know the behavior of the signal in the frequency domain, that is
how the magnitude of the signal behaves over each frequency the signal is composed of, you have to obtain Fourier Transformation.
Now if you have a system and need the stability, you find the Z transformation.
That is z transform is applied to system functions and not signals.
Now comes Laplace transform,
Once again its applied to systems and not signals. In order to obtain the Laplace coordinates in complex time space we obtain L transform

Fourier- Frequency domain- Signals
Laplace and Z - Complex Space time - systems

 

[wajahat]

Re: how to decide when to calculate FOURIER,LAPLACE,Z-TRANFO

harsha_jois quoted

Basically all signals are represented in standard amplitude over time format.
If you need to know the behavior of the signal in the frequency domain, that is
how the magnitude of the signal behaves over each frequency the signal is composed of, you have to obtain Fourier Transformation.
Now if you have a system and need the stability, you find the Z transformation.
That is z transform is applied to system functions and not signals.
Now comes Laplace transform,
Once again its applied to systems and not signals. In order to obtain the Laplace coordinates in complex time space we obtain L transform

Fourier- Frequency domain- Signals
Laplace and Z - Complex Space time - systems

Can u give any example of signal and the complex systems that u mentioned.If u hav any literature to exlain the difference it would be helpful.
regards
wajahat

Can u give any example of signal and the complex systems that u mentioned.If u hav any literature to exlain the difference it would be helpful.
regards

 

[rag_perfect]

Re: how to decide when to calculate FOURIER,LAPLACE,Z-TRANFO

if signal is bounded and continuous:go for fourier
unbounded n contin:laplace
unbounded n descrete:z trans...

simple...

 

[likechip]

Re: how to decide when to calculate FOURIER,LAPLACE,Z-TRANFO

something to consider....

LT is more suitable for problems with initial values
FT is more suitable for problems with boundary value condition