Inverse Fourier Transform

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Emil09

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I'm trying to understand how to find the inverse Fourier transform of sin(2w). I'm relatively certain that the answer is
**broken link removed**
but I can't formulate how to get to this answer. Normally I use a table to look-up transforms but this particular transform is not in the table and I can't see how to manipulate sin(2w) so that it could be solved using the table.

Any ideas?
 
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Emil09,


OK, here is how you do it. The definiton of the inverse Fourier transform is found on this link. https://www.electro-tech-online.com/custompdfs/2010/11/fourier.pdf Using F(ω) = sin(2ω) we get:

f(t) = (1/2pi)*∫from -∞ to ∞ of [sin(2ω)*exp(i*ω*t)]*dω .

Since the integal of sin(2ω) from -∞ to ∞ is undefined, then so is the inverse Fourier of sin(2ω). That is because sin(2ω) does not converge within those limits.

Ratch
 

Hello,

Were you able to obtain the form for sin(w) at all? You could try that first. Once you get that you can get any multiple of w inside sin(). It's interesting you got something close to the right answer though.
Hint #1: instead of using sin(w) directly try using the exponential form.
 
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