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UCSB
Fall 2007
ECE 130A:
Problem Set 6
Assigned:
Wednesday, November 14
Due:
Wednesday, November 21 (and
then
enjoy your Thanksgiving!)
Reading:
4.14.5, 9.19.3
Problem 1:
Find and sketch the magnitude

X
(
j
2
πf
)

of the Fourier transform for the following
signals. State for each waveform whether it is a
baseband
or
bandpass
signal (the de±nitions are to be
applied loosely, with most of the frequency content being in a band around DC for a baseband signal,
and most of the frequency content being in a band away from DC for a bandpass signal):
(a)
x
(
t
) = sinc(4
t
)sinc(2
t
)
(b)
x
(
t
) = sin 12
πt
(c)
x
(
t
) = sinc(4
t
)sinc(2
t
) sin 12
πt
.
(d)
x
(
t
) =
e

2

t

.
(e)
x
(
t
) =
e

2

t

cos 12
πt
Problem 2:
Use Matlab for the following plots and computations, comparing the result against what
you get by analytical computations in Problem 1.
(a) Plot
x
(
t
) = sinc(4
t
)sinc(2
t
) versus
t
for

4
≤
t
≤
4.
(b) Using the DFT (as in Problem 6, Problem Set 5), ±nd

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This note was uploaded on 08/06/2008 for the course ECE 130A taught by Professor Madhow during the Fall '07 term at UCSB.
 Fall '07
 MADHOW

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