±
6.003
Homework
8
Please
do
the
following
problems
by
Wednesday,
April
7,
2010
.
You
need
not
submit
your
answers:
they
will
NOT
be
graded.
Solutions
will
be
posted.
Problems
1.
Fourier
Series
Determine
the
Fourier
series
coeﬃcients
for
each
of
the
following
periodic
CT
signals.
x
1
(
t
)=
x
1
(
t
+ 10)
t
1
1
10
x
2
(
t
)=
x
2
(
t
+ 10)
t
1
2
10
x
3
(
t
)=
x
3
(
t
+ 10)
t
1
−
1
1
2 3
10
x
4
(
t
)=
x
4
(
t
+ 10)
t
1
1 2 3
10
2.
Inverse
Fourier
series
Determine
the
CT
signals
with
the
following
Fourier
series
coeﬃcients.
Assume
that
the
signals
are
periodic
in
T
= 4.
a.
a
k
=
î
jk
;

k

<
3
0
otherwise
b.
b
k
=
1;
k
odd
0;
k
even
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2
6.003
Homework
8
/
Spring
2010
3.
Matching
Consider
the
following
sets
of
Fourier
series
coeﬃcients.
1
k
a
k
1
k
b
k
=
³
3
j
2
k
k
=
±
1
,
±
2
,
±
4
,
±
5
,
±
7
,...
0
k
= 0
,
±
3
,
±
6
,
···
1
k
c
k
1
k
d
k
1
k
e
k
1
k
f
k
a.
Which
(if
any)
set
corresponds
to
the
following
periodic
signal?
2
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 Spring '11
 DennisM.Freeman
 Digital Signal Processing, Periodic function, LTI system theory

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