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2.161 Signal Processing: Continuous and Discrete
Fall 2008
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View Full Document MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
DEPARTMENT
OF
MECHANICAL
ENGINEERING
2.161
Signal
Processing
 Continuous
and
Discrete
Fall
Term,
2007
Quiz
#1
—
October
18,
2007
Notes:
•
The
quiz
is
openbook.
•
The
time
allowed
is
ninety
minutes.
•
There
are
six
problems,
answer
them
all.
•
Partial
credit
will
be
given.
1
Problem
1:
(15
points)
Show
that
to
interpolate
a
value
to
the
midpoint
of
a
sampling
interval
in
the
sample
set
{
f
n
}
,
n
= 0
...N
−
1,
where
f
n
=
f
(
n
Δ
T
),
the
cardinal
(Whittaker)
reconstructor
may
be
written
1
N
−
1
f
(
n
Δ
T
+ Δ
T/
2)
=
f
k
(
−
1)
k
π
(
n
−
k
+ 1
/
2)
k
=0
Problem
2:
(20
points)
(a)
Design
(ﬁnd
the
transfer
function
of)
a
unitygain
3rdorder
lowpass
Butterworth
analog
ﬁlter
with
a
3dB
cutoﬀ
frequency
of
10
rad/s.
(b)
Make
a
polezero
plot
for
your
ﬁlter.
(c)
Convert
your
design
to
a
highpass
ﬁlter
with
the
same
cutoﬀ
frequency.
(d)
If
(do
not
do
it)
you
were
to
convert
your
design
to
a
bandpass
ﬁlter,
what
would
be
the
order
of
the
ﬁlter,
how
many
zeros
would
be
created,
and
where
in
the
s
plane
would
the
zeros
lie?
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.161 taught by Professor Derekrowell during the Fall '08 term at MIT.
 Fall '08
 DerekRowell

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