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Project 1:
Sampling
(v1.1)
Common Sense Caveat:
If you need to modify a problem in order to obtain a meaningful
outcome, do so but do so using common sense.
The object of the Project 1 is to provide an inquirybased experience in exploring sampling and
sampling limitations.
The study makes direct use of Shannon’s Sampling Theorem but requires
that you properly interpret this important signal processing tool.
Part 1.a:
Implement, observe, quantify, and qualify the composite sinusoidal signal.
Construct the audio signal x[k] defined below, sampled at f
s
= 44,100Sa/s, with a signal duration
around 5 seconds (choose a signal length N to be a radix2 number).
The signal x[k] consists of
5 distinct sinusoidal components satisfying:
(
29
(
29
(
29
(
29
)
(
]
14700
,
441
[
;
)
/
2
cos
]
[
689
64
/
;
)
/
2
cos
]
[
amplitude
decreasing
;
]
[
1
/
1
]
[
]
[
0
0
0
4
1
0
random
uniformly
Hz
f
f
k
f
k
x
Hz
f
f
f
k
f
k
x
k
x
i
k
x
k
x
i
s
i
i
s
s
i
i
∈
=
=
=
=
+
+
=
∑
=
π
Analyze each individual signal spectrum and listen to x[k] (MATLAB SOUND).
MATLAB Code Snippet
» nn=0:1:1023;
» fs=44100; f0=fs/64;
%
689 Hz
» x=cos(2*pi*f0*nn/fs);
%
cosine
» [X,w]=freqz(x); %
generate spectrum  could also have used X=abs(fft(x))
» plot(nn,x); plot(w,abs(X));
Figure 1: 1024point cosine sampled at f
s
= 44100 Sa/s centered at
ϖ
0
= 2
π
f
0
where
f
0
= 689 Hz (f
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This note was uploaded on 09/18/2011 for the course EEL 5718 taught by Professor Janisemcnair during the Fall '11 term at University of Florida.
 Fall '11
 janisemcnair
 Computer Networks

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