Homework #5

Download here. Solutions here, or below.

With a PDF Plugin, the exercises should load here.

With a PDF Plugin, the exercises should load here.

7 thoughts on “Homework #5

  1. for question two when I split the integral into three parts and end up with only the integral from -4\pi to 4\pi of (e^{-|w|})(e^{iwx})dw I’m drawing a blank on how to get rid of the absolute value.


    • Absolute value is a piecewise function, and you can always get rid of it the same way.
      |\omega| = \left\{\begin{aligned} \omega &&&\text{ if } \omega\geq 0\\ -\omega &&&\text{ if } \omega < 0\end{aligned}\right.[/latex] (Split the integral again.)

  2. Question from a student:

    I am having trouble with determining the domain of this \widehat{g}(\omega) function in question 2. It says it is |\omega| < 4\pi[/latex]. How can I determine the domain from this?

    When you are taking the Fourier transform, the domain is always the entire real line, here -\infty<\omega<\infty[/latex]. This is different from Fourier series. Note that the transform does not involve a period [latex]{\mathtt T}[/latex].

  3. for question 4. writing q(x) in terms of f(x), the signal from question 1, and rect(x), are you implying to take the derivative of q(x) to get the square wave and then use the differentiation identity as a short-cut?

Leave a Reply

Your email address will not be published. Required fields are marked *