HOMEWORK #1
1. Problem 1.1
2. Problem 1.2
3. Determine if
( )
( )
( )
sin
50
sin
200
x t
t
t
=
+
is periodic and, if so, what is its period?
4. Calculate the Fourier Transform
( )
X
ω
of
x t
Ae
bt
t
t
at
b g
b
g
=
≥
<
R
S
T

cos
0
0
0
and sketch a graph of the magnitude
( )
X
and phase
( )
X
∠
for
1
A
a
b
=
=
=
for
0
10
≤
≤
.
5. Later on in the course we will discuss “window functions” in spectral analysis.
When
you discretize or sample data from a random process, and you want to compute the
Discrete Fourier Transform (DFT), you are actually taking a portion of the data by
applying a window to it.
The simplest window to use will be a boxcar or rectangular
window as defined below for a record of length
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 Fall '11
 CATTAFESTA

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