How to Solve Inverse Fourier Transform of (10*sin(3*omega)) / (omega+Pi)?

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Discussion Overview

The discussion centers on the steps required to solve the inverse Fourier transform of the function (10*sin(3*omega)) / (omega+Pi). Participants are exploring the mathematical techniques and identities that may be necessary for this transformation.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant suggests integrating the function multiplied by exp(i*omega*t) over omega from -inf to +inf to obtain a time-domain function.
  • Another participant inquires about working through the problem by hand and mentions the potential need for trigonometric identities to simplify the expression.
  • A further reply discusses the relationship between the exponential function and trigonometric functions, indicating that triangle identities may be useful in the calculations.
  • One participant expresses confusion about obtaining a simplified answer and requests assistance in working through the problem to see what kind of answer might be derived.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specific steps to take or the simplifications needed, indicating that the discussion remains unresolved with multiple approaches being considered.

Contextual Notes

There are mentions of integrating and using trigonometric identities, but specific assumptions or definitions that may affect the approach are not fully articulated.

bangell
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Can someone help me and tell me the steps to solve the inverse Fourier transform of the following function

(10*sin(3*omega)) / (omega+Pi)


Thanks!
 
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You will need to integrate "this function times exp(i*omega*t)" over omega from -inf to +inf. The resulting thing is a function of t, which is in the time domain, as usually called.
 
How would I work this out by hand? I know you probably need to use trig identities in order to simplify the problem. Do you have any suggestions.
 
you know exp(iwt)=cos(wt)+i*sin(wt); then you're right, triangle idents are needed. Just treat i as a constant, and it won't hurt other calculation.
 
I'm still just confused of how to get a simplified answer. Do you have time to work the problem out and let me know what sort of answer you get?

Thanks for all your help.
 

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