2. Analyzing Sound Mary Ellen Connor Kathy Crowley Judith Doherty Ginny Giordano Cat MacDonald JUNE 2002 WPI Mathematics in Industry Institute

3. The Problem DEKA is working on algorithms for intelligent hearing aids. The problems: How do you measure speech intelligibility? What is a phoneme? The mathematics: Addition of trigonometric functions The software: MatLab

4. Getting Started We began by doing research in books and online concerning Fourier series Fourier transforms and MatLab. A phoneme is a single component of sound.

5. Steps to Understanding Read Who is Fourier? Jean Baptiste Joseph, Baron de Fourier French mathematical physicist (1768-1830) Sound Vibrations of air The graph is periodic. Loudness affects amplitude. Pitch affects the frequency.

6. Fourier’s Big Discovery “No matter how complicated it is, a wave that is periodic - with a pattern that repeats itself - consists of the sum of many simple waves.”

7. Steps to Analyzing the Data Recorded sounds Ahhs and eees of each individual

8. Say Ahhh!

9. MatLab wouldn’t work on Tuesday.

10. Got MatLab?

11. Working with the software Imported sounds to MatLab Plotted amplitude vs time Used FFT to plot the spectra of the sounds Determined the peaks and noticed the peaks occur at equal intervals These intervals are multiples of the fundamental frequencies of each individual’s voice.

12. Graphs of Amp vs Time

14. Zoom in

16. Spectrum of eee graphs

18. Peaks are at nω

20. Filter out all but fundamental f’s

21. Zoom in

22. Group ahhh and Cat ahhh