Due February 3, 2010
BME 171, Spring 2010  HOMEWORK 3
Sinusoidal Functions and Sampling
1. Given are two real analog signals
x
(
t
) = cos
10
πt
+
π
3
and
y
(
t
) = cos
30
t

π
4
.
(a) Write formulas for corresponding complex signals ˜
x
(
t
) and ˜
y
(
t
) using exponen
tial notation. Identify phasors.
(b) In the complex plane, sketch positions of vectors representing complex signals
˜
x
(
t
) and ˜
y
(
t
) at time
t
= 0
.
1.
(c) In the complex plane, sketch position of a vector representing complex signal
˜
w
(
t
) = ˜
x
(
t
) + ˜
y
(
t
) at time
t
= 0
.
1.
(d) At what other time (except
t
= 0
.
1) will vector ˜
w
(
t
) be in the same position
and have the same length?
2. For this problem, please use subplots: you should turn in only
one page
of Matlab
graphs.
(a) Use Matlab function
plot
to plot signals
x
(
t
) and
y
(
t
) defined in Problem 1.
Your plot should cover time interval from 0 to 1 s and the time vector should
have sufficient number of elements so that the plots are smooth.
Label the
axes.
(b) Use Matlab to generate two numerical sequences,
x
[
n
] =
x
(
nt
s
)
and
y
[
n
] =
y
(
nt
s
)
,
that represent analog signals
x
(
t
) and
y
(
t
) sampled with the frequency of 30
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 Spring '08
 IZATT
 Signal Processing, Complex number, Sine wave, Complex Signals, real analog signals

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