Homework #6

Download here. Solutions here, or below.

With a PDF Plugin, the exercises should load here.

With a PDF Plugin, the exercises should load here.

4 thoughts on “Homework #6

  1. Question from a student:

    For question 1B, which theorem should I use?

    You are meant to (somehow) use the inversion formula:
    f(t) = \frac{1}{2\pi}\int_{-\infty}^\infty\widehat{f}(\omega)e^{+i\omega t}\,d\omega

    We’ve been writing the inversion formula since we first talked about Fourier transform 30-Jan. What’s new ( and theorem ) is that you can actually trust the inversion formula to tell the truth.

    See 06-Feb, slide 5

  2. Question from a student:

    For question 2B, partial fraction clearly won’t work on this. And if I complete the square, the equation looks horrible. How should I tackle this question?

    You have the right idea – you just need to stick with it.

    You can factor the denominator as:
    \widehat{g}(\omega) = \frac{1}{(i\omega+A)(i\omega+B)},
    with constants A and B not too horrible. Then use partial fractions.

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