explorations of signal analysis in high school and beyond russell herman gabriel lugo university of...
DESCRIPTION
Projects Sounds Music Birds Dolphins EKG-ECG-EEG Ocean WavesTRANSCRIPT
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EXPLORATIONS OF SIGNAL ANALYSIS IN HIGH SCHOOL AND BEYOND
Russell Herman Gabriel LugoUniversity of North Carolina at Wilmington
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Outline
Projects – High School through College Tools Theory Typical Project Examples
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Projects
Sounds Music Birds Dolphins
EKG-ECG-EEG Ocean Waves
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Tools
Sound Editors Cool Edit Gold Wave Audacity PPC Applications
Theory Support Mathcad, Maple, Matlab VB Modules Web Applets
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Cool Edit
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Gold Wave
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Addition of Sines
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Adding Sine WavesBirds\Untitled (8.2).wav
Birds\tone.wav
Birds\pt.wav
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Theory
Fourier Series Sum of Sines
Fourier Analysis Spectrum Analysis Harmonic Analysis
+ =
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Fourier Series
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Fourier SeriesFourier Series
Eigenfunctions:
L 2 c x n( ) cosn xL
s x n( ) sinn xL
Function: f x( ) sin x( ) 2 cos 2x( ) x 0 .1 L
Fourier Coefficients:
a012L L
Lxf x( )
dN 8 n 1 N
a n( )1L L
Lxf x( ) c x n( )
d
b n( )1L L
Lxf x( ) s x n( )
d
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Reconstruction
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Reconstruction
2
0
a n( )
81 n
2
0
b n( )
81 n
2
0
a n( )2 b n( )2
81 n
F x( ) a 0n
a n( ) c x n( ) b n( ) s x n( )( )Fourier Expansion:
3
3
f x( )
F x( )
2 0 x
Comparison between f(x)and F(x)
Power Spectrum
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Typical Project
Addition of Sinusoidal Functions Explorations Using Sound Editors Picking Out Dominant Frequencies Reconstruction and Fine Tuning
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Example #1 - Birds
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Birds: Reconstruction
Birds\Recbird.wav
Birds\firstbird.wav
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More Birds
Birds\owl2.wav
Birds\newowl.wav
-0.025991*cos(2*pi*1327.0833*t)+0.033382*cos(2*pi*1329.8423*t)+-0.043522*cos(2*pi*1332.6014*t)+ 0.061318*cos(2*pi*1335.3604*t)+-0.081395*cos(2*pi*1338.1194*t)+0.09432*cos(2*pi*1340.8784*t)+ -0.096081*cos(2*pi*1343.6374*t)+0.090427*cos(2*pi*1346.3964*t)+-0.058718*cos(2*pi*1349.1554*t)+ 0.047292*cos(2*pi*1354.6734*t)+-0.090452*cos(2*pi*1357.4324*t)+0.091498*cos(2*pi*1360.1914*t)+ -0.044081*cos(2*pi*1362.9505*t)+-0.03472*cos(2*pi*1365.7095*t)+0.075536*cos(2*pi*1368.4685*t)+ -0.039251*cos(2*pi*1371.2275*t)+-0.058875*cos(2*pi*1373.9865*t)+0.12712*cos(2*pi*1376.7455*t)+-0.077859*cos(2*pi*1379.5045*t)+-0.062965*cos(2*pi*1382.2635*t)+0.13712*cos(2*pi*1385.0225*t)+ 0.12768*cos(2*pi*1390.5405*t)+0.081571*cos(2*pi*1393.2995*t)+0.070206*cos(2*pi*1396.0586*t)+ -0.022393*cos(2*pi*1398.8176*t)+-0.11979*cos(2*pi*1401.5766*t)+0.094213*cos(2*pi*1407.0946*t)+ 0.06029*cos(2*pi*1409.8536*t)+-0.076122*cos(2*pi*1412.6126*t)+-0.13165*cos(2*pi*1415.3716*t)+ -0.043479*cos(2*pi*1418.1306*t)+0.074439*cos(2*pi*1420.8896*t)+0.13719*cos(2*pi*1423.6486*t)+ 0.08474*cos(2*pi*1426.4077*t)+-0.060982*cos(2*pi*1431.9257*t)+-0.049597*cos(2*pi*1434.6847*t)+ -0.036721*cos(2*pi*1445.7207*t)+-0.024337*cos(2*pi*1448.4797*t)+0.032224*cos(2*pi*1456.7568*t)+ .033543*cos(2*pi*1459.5158*t)+0.024255*cos(2*pi*1465.0338*t)
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Vibrating Beams
0 20 40 60 80 100 120 140-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 140
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Frequency
Pow
er
Periodogram