# Fourier transform (integration!)

Got stuck in the second part, any help is appreciated, cheers.

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vela
Staff Emeritus
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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.

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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vela
Staff Emeritus
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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.

thanks, but how would i integrate u(t+4)e^[t(-1-iw)-4]?

How do i deal with the u(t+4)?

vela
Staff Emeritus
Homework Helper
What is u(t+4) equal to for t>-4?

sorry im really stuck, u(t)?

thanks, i think i might have missed out on that lecture, which explains why.

Is what i've done correct?

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vela
Staff Emeritus
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Well, the first line definitely doesn't equal the second line.

The integrals look okay.

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?

vela
Staff Emeritus
Homework Helper
Perhaps you misunderstood. I meant:

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

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.

thanks! got it now