EE 200 Fall 2009 (Weber)
Homework 1
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Date
EE 200, Homework #
Show intermediate steps whenever possible.
1.
Write the expression(s) that define the function plotted below.
y
1
1
2
1
2
1
x
2.
For the signal shown in the graph below,
a.
What is the period of the signal?
x(t)
4
2
t (msec)
6
8
4
4
b.
What is the frequency of the signal in Hz.?
c.
What is the amplitude of the signal (approximately) if the units on the vertical axis are Volts?
d.
What is
ω
, frequency of the signal in radians/second?
3.
The “signum” function
sgn
(
x
) is defined as
sgn(
x
) =
−
1
x <
0
0
x
= 0
1
x >
0
Using the following functions
f
1
(
x
) =
3
2
sgn(
x
)
f
2
(
x
) =
2
3
sin(
πx
)
plot these composition functions over [2, 2]
1
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a.
(
f
1
◦
f
2
)(
x
)
b.
(
f
2
◦
f
1
)(
x
)
4.
Do the following matrix operations.
a.
bracketleftbig
−
4
6
bracketrightbig
bracketleftbigg
3
−
1
bracketrightbigg
=
b.
bracketleftbigg
5
6
bracketrightbigg
bracketleftbig
−
4
−
3
bracketrightbig
=
c.
bracketleftbig
−
1
4
2
bracketrightbig
3
−
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 '08
 ZADEH
 upper right corner, trig identity cos, VP eak sin, corresponding VP eak

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