EXPLORATIONS OF SIGNAL ANALYSIS IN HIGH SCHOOL AND BEYOND

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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 Waves
Birds\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 Series
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Reconstruction
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Reconstruction
Fourier Expansion
Power Spectrum
Comparison between f(x)and F(x)
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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\firstbird.wav
Birds\Recbird.wav
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More Birds
Birds\owl2.wav
Birds\newowl.wav
-0.025991cos(2pi1327.0833t)0.033382cos(2pi
1329.8423t)-0.043522cos(2pi1332.6014t)
0.061318cos(2pi1335.3604t)-0.081395cos(2pi
1338.1194t)0.09432cos(2pi1340.8784t)
-0.096081cos(2pi1343.6374t)0.090427cos(2pi
1346.3964t)-0.058718cos(2pi1349.1554t)
0.047292cos(2pi1354.6734t)-0.090452cos(2pi
1357.4324t)0.091498cos(2pi1360.1914t)
-0.044081cos(2pi1362.9505t)-0.03472cos(2pi
1365.7095t)0.075536cos(2pi1368.4685t)
-0.039251cos(2pi1371.2275t)-0.058875cos(2pi
1373.9865t)0.12712cos(2pi1376.7455t) -0.07
7859cos(2pi1379.5045t)-0.062965cos(2pi1382
.2635t)0.13712cos(2pi1385.0225t)
0.12768cos(2pi1390.5405t)0.081571cos(2pi13
93.2995t)0.070206cos(2pi1396.0586t)
-0.022393cos(2pi1398.8176t)-0.11979cos(2pi
1401.5766t)0.094213cos(2pi1407.0946t)
0.06029cos(2pi1409.8536t)-0.076122cos(2pi1
412.6126t)-0.13165cos(2pi1415.3716t)
-0.043479cos(2pi1418.1306t)0.074439cos(2pi
1420.8896t)0.13719cos(2pi1423.6486t)
0.08474cos(2pi1426.4077t)-0.060982cos(2pi1
431.9257t)-0.049597cos(2pi1434.6847t)
-0.036721cos(2pi1445.7207t)-0.024337cos(2pi
1448.4797t)0.032224cos(2pi1456.7568t)
.033543cos(2pi1459.5158t)0.024255cos(2pi14
65.0338t)
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Vibrating Beams