EEE 321 Name:
In-Class Quiz 3 Student ID:
June 10 2016
Question 1 (Each 2 point, total 4 points). Find the impulse response h(t) or h[n] of each
of the following LTI system:
a) y(t) = x(t−t0)b) y[n] = Pn
k=−∞ x[k]
Answer
a)x(t) = δ(t)⇒y(t) = h(t) = δ(t−t0)
b)x[n] = δ[n]⇒y[n] = h[n] =
n
X
k=−∞
δ[k] = u[n]
Question 2 (6 points) . Let h(t) be a rectangular pulse shown in the figure below, and let
x(t) be the impulse train depicted in the figure:
x(t) =
+∞
X
k=−∞
δ(t−kT )
Determine and sketch y(t) = x(t)∗h(t) for a) T= 3 and b) T= 2.
Answer
y(t) = x(t)∗h(t) = Z∞
∞
x(τ)h(t−τ)dτ =Z∞
∞ ∞
X
k=−∞
δ(τ−kT )!h(t−τ)dτ
=
∞
X
k=−∞ Z∞
∞
δ(τ−kT )h(t−τ)dτ =
∞
X
k=−∞ Z∞
∞
δ(τ−kT )h(t−kT )dτ
=
∞
X
k=−∞
h(t−kT )Z∞
∞
δ(τ−kT )dτ =
∞
X
k=−∞
h(t−kT )
