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Q#1 Fourier Transform GATE EC 2023 MCQ +1 mark -0.33 marks

The Fourier transform  of  is

Note:

Explanation:

To find the Fourier transform  of

1. Use the Fourier transform definition:

 

2. Complete the square in the exponent:

 

3. Substitute  :

 

4. Use the given integral result:

 

5. Therefore:

 

So the answer is:

 

Which matches option (C).

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