# Homework #7

## 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 $f(2)$.