EE32a Introduction to Linear Systems
November 11, 2001
Midterm Examination Solutions
R. J. McEliece
162 Moore
Problem 1. (Graded by Donald) This was straightforward. The answers are
(a) y (t) =
1
2
sin(t)
1+ 2
cos(t) =
1
1+ 2
sin(t ), where = arctan .
(b
EE32a : Introduction to Linear Systems
Solutions to Homework Assignement N#2
Problem 2.21.
(a) Using the convolution sum:
y =
n
+K
k6
n
> J k u K n?k u ? k
k=?K
+K
= > J k K n?k 6u
n
k= 0
+K
= Kn >
k= 0
y =
n
k
J
K
J n+ 1 ?K n+ 1
J?K
6u
n
u
n
Using the z-
EE32 Problem Set 1 Solutions:
Problem 4:
y[n]= vcfw_ [n 1] =
x
d)
1
cfw_x[n 1]+ x[ n]
1
2
1- System is not memoryless: y[n] depends on the future for n < 0 .
1
2- System is not time invariant: y[n ]= cfw_ [n 1 ]+ x[ n + ] . However,
x
1
2
if we define x
EE32a Signals, Systems, and Transforms
December 15, 2001
Final Examination Solutions
R. J. McEliece
162 Moore
Problem 1. (Graded by Muhammed) The rst step is to decompose X (s) into partial
fractions:
1
4/7
(3s + 1)/7
s1
=
+
+2
2 + s + 1)
(s + 2)(s + 3)(s