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

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

3. Projects Sounds  Music  Birds  Dolphins EKG-ECG-EEG Ocean Waves

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

5. Cool Edit

6. Gold Wave

7. Addition of Sines

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

9. Theory Fourier Series  Sum of Sines Fourier Analysis  Spectrum Analysis  Harmonic Analysis + =

10. Fourier Series

12. Reconstruction

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

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

15. Example #1 - Birds

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

17. 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)

18. Vibrating Beams