Fourier transform of a Gaussian

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Homework Help Overview

The discussion revolves around finding the Fourier transform of a Gaussian function, a topic within the field of mathematical analysis and signal processing.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to evaluate the Fourier transform by breaking down the exponential terms but encounters difficulties in integration. Some participants suggest combining the exponentials and completing the square as an alternative approach.

Discussion Status

The conversation includes various approaches to the problem, with some participants providing guidance on how to proceed. There appears to be a focus on clarifying the method rather than reaching a definitive conclusion.

Contextual Notes

Participants discuss the potential complexity of the integral involved and question whether there are subtleties in the problem that need to be addressed.

Kolahal Bhattacharya
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Homework Statement



I need to have the Fourier transform of a Gaussian

Homework Equations





The Attempt at a Solution



∫(exp[-ax^2])(exp[-ikπx]) dx

I tried by braking the last exponential into sine and cosine terms.The sine term is odd and it cancels.Then,I cannot evaluate the remaining part.Please help.
 
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Don't do that. Combine the exponentials, complete the square in x and do a change of variables.
 
OK,what I am getting is a standard gamma function type of integral(that I can find) and the 2nd part is an ordinary constant exponential.
So,is this what you meant?I hope there is no more subtlity in this problem.
 
You should be getting that the Fourier transform of a gaussian in x is a constant times a gaussian in k. No, it's not subtle.
 

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