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1
1.
Calculate the (continuous) Fourier transform of
( )
sin5 cos3
gx
x
x
=
.
Sketch this transform
in a “3D”plot whose “
y
” and “
z
”axis represent the transform’s imaginary and real part, respec
tively, whereas the “
x
”axis represents frequency.
Prepare a separate sketch for the magnitude
spectrum of this transform.
(Hint:
No integration is required; instead, results from the lectures and previous homework can
be applied.
(In particular problem 2 of HW 1 should get you started.)
Make sure your sketches
use the actual frequency
f
and
not
the angular frequency.
Label all parts of your sketches ade
quately, including the positive directions of the axes.
Note:
Pay special attention to the small details in this relatively easy problem!)
2.
Consider the function
()
1i
f
1
0i
f1
x
x
⎧
≤
⎪
=
⎨
<
⎪
⎩
.
a.
Sketch a graph of
.
b.
Use the definition of the continuous Fourier transform to calculate
( )
Gf
.
(Include all steps
of your derivation.
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 Spring '08
 Volkmar

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