Difference between Laplace transform and Fourier transform ?
Before answering to this question we should understand that why we neeed the transform .
The one can answer that , we need this to convert the time domain signal to frequency domain.
So , the next questions which should pop in our mind is if ,both method do the same , then why we need two methods to convert a signals to time domain I can only study one method which will be more than enough.
Answer to all lies here.
Lets take a signals f(t) for which i want to take the Fourier transform , now if you recall we can not take the transform of this signal until and unless , it should fallow or satisfy the Dirichlet_conditions.
So it means first difference which i can figure out right now is , fourier transform need to fallow the conditions while the laplace transform does not.
Another thing which we can state now , lets take my signal which is not summable ( means area under the function is not finite). Then i can not find the Fourier transform but i can find the Laplace transform.
Another difference is Parseval's_theorem which is only applicable in case of Fourier transform but not in case of Laplace transform.
Now if we look at the graph of e^(-sigma *t) , Laplace transform is trying to converge any signals , so when you applying the Parsevals theorem , then you will get the energy of the modified signal, nut not the original signals.
Before answering to this question we should understand that why we neeed the transform .
The one can answer that , we need this to convert the time domain signal to frequency domain.
So , the next questions which should pop in our mind is if ,both method do the same , then why we need two methods to convert a signals to time domain I can only study one method which will be more than enough.
Answer to all lies here.
Lets take a signals f(t) for which i want to take the Fourier transform , now if you recall we can not take the transform of this signal until and unless , it should fallow or satisfy the Dirichlet_conditions.
So it means first difference which i can figure out right now is , fourier transform need to fallow the conditions while the laplace transform does not.
Another thing which we can state now , lets take my signal which is not summable ( means area under the function is not finite). Then i can not find the Fourier transform but i can find the Laplace transform.
Another difference is Parseval's_theorem which is only applicable in case of Fourier transform but not in case of Laplace transform.
Now if we look at the graph of e^(-sigma *t) , Laplace transform is trying to converge any signals , so when you applying the Parsevals theorem , then you will get the energy of the modified signal, nut not the original signals.
In simple language...most of the practical application has time domain approach but the analysis is complex. So to make analysis simple we transform to frequency domain..
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