Homework #10
Due: Thursday, April 29, 2010
Note
: Use of Matlab (or any other software) is not permitted.
I.
(see Exercise 4.2) Use Poisson’s relation to find the Fourier series for each of
the following pperiodic functions on
R
:
a.
(1pt)
∑
∞
−∞
=
−
−
=
m
mp
x
e
x
f
2
)
(
)
(
π
b.
(1pt)
∑
∞
−∞
=
−
−
=
m
mp
x
a
e
x
f


)
(,
a
>
0
II.
(see Exercise 4.10) Let f be a suitably regular 1periodic function, let
0<x
0
<1
,
and let
m
be a positive integer
m=1,2,3,
…
What can you infer about the
Fourier coefficients (
c
n
)
n
of
f
if you know that:
a.
(1pt)
)
(
)
(
x
f
x
f
=
b.
(1pt)
)
(
)
(
x
f
x
f
−
=
c.
(1pt)
)
(
1
x
f
m
x
f
=
⎟
⎠
⎞
⎜
⎝
⎛
+
d.
(1pt)
)
(
2
1
x
f
x
f
−
=
⎟
⎠
⎞
⎜
⎝
⎛
+
e.
(1pt)
()
)
(
0
0
x
x
f
x
x
f
−
=
+
f.
(1pt)
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 Spring '08
 staff
 matlab, Fourier Series, Continuous function, Haar wavelet, following pperiodic functions, coarser scale approximation

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