Homework #7

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 #7

  1. Question from a student:

    About problem 4 – can we really calculate this problem and find the inverse transform?

    When I factor the denominator of H(w), I found (iw-i)(iw+i). I tried to use the basic formula of (iw+a), but I think I could not use it since Re(a) must be greater than 0, which in this case is 0.

    Is there any way to continue with this problem?

    • Problem 4 is harder than I intended, but can still be solved.

      Use partial fractions, then look at the terms as i(w+1) and i(w-1). These are part of the transform of shifted heaviside functions.

  2. Question from a student:

    I have a question about the delta function.
    Say you have f(t) multiply with \delta(t-2). Say f(t)=-5t+2.
    Could we simplify it down to (-5(2)+2)*\delta(t-2)=(-8)\delta(t-2)?

    • Yes.

      Reason: if you have f(t)\delta(t-2), eventually you are going to have to integrate it, either explicitly using the transform or inverse transform formula, or implicitly using a basic example.

      When you eventually integrate it, the delta function is going to insist on t=2, so the only value of f(t) that will ever matter is f(2).

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