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6.450
Principles
of
Digital
Communication
Wednesday,
October
17,
2002
MIT,
Fall
2002
Handout
#24
Due:
Wednesday,
October
24,
2001
Problem
Set
7
Problem
7.1
Prove
the
following
statement
using
the
theorems
about
linear
vector
spaces
in
lecture
10:
Every
set
of
n
vectors
that
spans
an
n
dimensional
vector
space
V
is
a
linearly
independent
set
and
is
a
basis
of
V
.
Problem
7.2
Prove
that
if
a
set
of
n
vectors
uniquely
spans
a
vector
space
V
,
in
the
sense
that
every
v
∈ V
can
only
be
represented
in
one
way
as
a
linear
combination
of
the
n
vectors,
then
those
n
vectors
are
linearly
independent
and
V
is
an
n
dimensional
space.
Problem
7.3
A
discrete
memoryless
source
emits
binary
equiprobable
symbols
at
a
rate
of
1000
symbols
per
second.
The
symbols
from
a
one
second
interval
are
grouped
into
pairs
and
sent
over
a
bandlimited
channel
using
4PAM
modulation.
In
particular,
the
transmitted
signal
U
(
t
)
is
given
by
U
(
t
) =
500
k
=1
A
k
sinc
t
T
−
k
(1)
where
T
= 0
.
002,
A
k
takes
values
in
{−
3
d/
2
,
−
d/
2
, d/
2
,
3
d/
2
}
and
we
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 Spring '08
 DanielLee

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