- #1
izelkay
- 115
- 3
Homework Statement
Mainly concerned with part (a). Here's the answer:
I understand where the answers inside the bracket came from, but I don't understand how they got their bounds (-infinity to 3, 3 to 5, and 5 to infinity)
Homework Equations
x is the impulse function here so y(t) = ∫h(τ)x(t-τ)dτ [-∞,∞]
The Attempt at a Solution
Since x was chosen to be the impulse function, I start by reflecting it across the y-axis and then shifting it by t to get the graph x(t-τ):
(minor mistake in my graph here: that τ-5 should be t-5 and the τ-3 should be t-3)
I then start "sliding" this graph into h(τ):
And this is where my confusion starts. If I perform the integration it'll be:
∫e^(-3τ)dτ [0, t-3]
and I get the answer they have for when 3 < t ≤ 5
So basically my question is why is it 3 < t ≤ 5 here?