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ECE 3250
HOMEWORK ASSIGNMENT IX
Fall 2009
1.
Let
x
1
be a 1024point signal and
x
2
be a 1025point signal. Note that
x
1
*
x
2
is a
2048point signal.
(a) Show that it takes a worstcase 512
.
5
×
2
11
multiplications to compute
x
1
*
x
2
directly. (Suggestion: it takes one multiplication to compute
x
1
*
x
2
(0), two
multiplications to compute
x
1
*
x
2
(1), etc. You may use the fact that
P
n
k
=1
k
=
n
(
n
+ 1)
/
2.)
(b) Suppose you use
N
point DFTs to compute
x
1
*
x
2
. First of all, what is
N
?
Second, assuming you use the standard decimationintime FFT to compute the
DFTs, ﬁnd how many multiplications it takes to compute
x
1
*
x
1
. You may
assume that it takes the same number of multiplications to compute an inverse
DFT as it takes to compute a DFT when you use the FFT.
2.
Find the
z
transform (formula for
X
(
z
) along with (ROC)
X
), if the transform exists,
for each signal
x
speciﬁed below. If the transform fails to exist, explain why.
(a)
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This note was uploaded on 03/26/2010 for the course ECE 3250 at Cornell University (Engineering School).
 '07
 DELCHAMPS

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