EE 312 Linear Systems II—Final Exam Review
Test is 2 hr. open book, open notes; Calculator (no computer) Allowed. Exam is Comprehensive
(material from entire semester).
NOTE: SHOW YOUR WORK! BOX ALL ANSWERS! EXPRESS ALL LAPLACE, Z-
AND FOURIER TRANSFORMS AND TRANSFER FUNCTIONS AS RATIONAL
POLYNOMIALS!
REVIEW (Post Mid-term) (We will fill out missing info in class)
Z Transform
-One sided
n
n
ZznfnfZzFnf −
∞
=
∑
==→←
0
][])[()(][
Directly from definition (sum geometric series)
S = 1 + a + a2 + ... + an = a
a
a
n
k
n
k−
−
=
+
=
∑1
11
0
IF |a| <1, S = 1 + a + a2 + ... = a
ak
k−
=
∑
∞
=1
1
0
Thus
a
z
z
aZn
−
→← (Pole Locations)
- Use Tables
- Use Properties:
Linearity
Time shift (z-1 = unit delay)
Convolution;
x[n]*y[n] ↔ X(z)Y(z) = ∑
∞
−∞=
−
k
knykx ][][
-IVT: )(lim zF
z∞→
-FVT: )(
1
lim
1zF
z
z
z
−
→ IF (z-1)F(z) has NO poles in |z| ≥ 1
- Inverse Z Transform: PFE of
z
zF )( . Use tables
- Easy if F(z) is power series (or polynomial) in z-1
- Symbolic long division (to get a few terms)
- Integral definitions (don’t use)
