Fourier transform (integration!)

  • Thread starter gomes.
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  • #1
gomes.
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Got stuck in the second part, any help is appreciated, cheers.
 

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  • #2
vela
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What's the definition of the Fourier transform? The problem is asking you to find the Fourier transform of that function using it.
 
  • #3
gomes.
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thanks, i tried doing that but im not sure what to do with the u(t+4) bit.

btw is my first part correct? (question 1)
 

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  • #4
vela
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The step function makes the integrand equal to 0 when t+4<0, so that lets you replace the lower limit of the integral with -4.
 
  • #5
gomes.
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thanks, but how would i integrate u(t+4)e^[t(-1-iw)-4]?

How do i deal with the u(t+4)?
 
  • #6
vela
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What is u(t+4) equal to for t>-4?
 
  • #7
gomes.
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sorry im really stuck, u(t)?
 
  • #9
gomes.
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thanks, i think i might have missed out on that lecture, which explains why.

Is what i've done correct?
 

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  • #10
vela
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Well, the first line definitely doesn't equal the second line.

The integrals look okay.
 
  • #11
gomes.
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sorry, im really really stuck. What should the next line be, after the first line? Could someone possibly show me how to proceed from the 1st line?
 
  • #12
vela
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Perhaps you misunderstood. I meant:

[tex]u(t) \ne \int_{-\infty}^\infty u(t+4) e^{t(-1-i\omega)-4}\,dt[/tex]

The integral in the second line is fine to calculate the Fourier transform you're looking for, but it's definitely not equal to u(t) as you wrote.

Try the substitution t'=t+4 to evaluate the integral.
 
  • #13
gomes.
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thanks! got it now
 

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