EXPLORATIONS OF SIGNAL ANALYSIS IN HIGH SCHOOL AND BEYOND

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Presentation transcript:

EXPLORATIONS OF SIGNAL ANALYSIS IN HIGH SCHOOL AND BEYOND Russell Herman Gabriel Lugo University of North Carolina at Wilmington

Outline Projects – High School through College Tools Theory Typical Project Examples

Projects Sounds Music Birds Dolphins EKG-ECG-EEG Ocean Waves

Tools Sound Editors Theory Support Cool Edit Gold Wave Audacity PPC Applications Theory Support Mathcad, Maple, Matlab VB Modules Web Applets

Cool Edit

Gold Wave

Addition of Sines

Adding Sine Waves Birds\Untitled (8.2).wav Birds\tone.wav Birds\pt.wav

Theory Fourier Series Fourier Analysis Sum of Sines Spectrum Analysis Harmonic Analysis = +

Fourier Series

Fourier Series

Reconstruction

Reconstruction Fourier Expansion: Power Spectrum Comparison between f(x)and F(x)

Typical Project Addition of Sinusoidal Functions Explorations Using Sound Editors Picking Out Dominant Frequencies Reconstruction and Fine Tuning

Example #1 - Birds

Birds: Reconstruction Birds\firstbird.wav Birds\Recbird.wav

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)

Vibrating Beams