Fourier Transform of a Gaussian Pulse...????

[aryajur]

fourier transform gaussian pulse

What is the fourier transform of the gaussian pulse:

f(t) = A exp(- a(t-to)²)

Any references or help would be appreciated !

 

[steve10]

gaussian pulse fourier transform

Find a book - any book, which has the Cauchy problem of heat equations. There is a standard way to deal with the Fourier transform of this type of functions. You'll see that everything boils down to an integral which can be calculated by differentiation under the integration. If you care, it is actually a very good exercise of your calculus.

 

[claudiocamera]

fourier transform of gaussian pulse

The Fourier transform of a Gaussian Pulse is a Gaussian pulse.

See the file attached.
I hope I have helped

 

[aryajur]

fourier transform of a gaussian pulse

Yes I finally found the transform, from google. Thanks !

 

[hamidr_karami]

gaussian pulse fourier

hi

fourier(exp(-t^2))--------------->pi^(1/2)*exp(-1/4*w^2)

bye

 

[pangpangfish]

gaussian pulse

It is well-known that FT of a Gaussian pulse will give a Gaussian in frequency domain. My question is that if this Gaussian pulse is unique? In other words, if there exits other pulse shapes that will also give identical shapes in frequency domain?

This question has puzzled me for some time. Anyone here knows the answer from the top of your head? Thanks.