Analyzing Sound

Mary Ellen ConnorKathy CrowleyJudith DohertyGinny GiordanoCat MacDonald

JUNE 2002 WPIMathematics in Industry Institute

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

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.

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.

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.”

Steps to Analyzing the Data

Recorded soundsAhhs and eees of each individual

Say Ahhh!

MatLab wouldn’t work on Tuesday.

Got MatLab?

Working with the software

Imported sounds to MatLabPlotted amplitude vs timeUsed FFT to plot the spectra of the soundsDetermined the peaks and noticed the

peaks occur at equal intervalsThese intervals are multiples of the fundamental

frequencies of each individual’s voice.

Graphs of Amp vs Time

Graphs of Amp vs Time

Zoom in

Zoom in

Spectrum of eee graphs

Spectrum of eee graphs

Peaks are at nω

Peaks are at nω

Filter out all but fundamental f’s

Zoom in

Group ahhh and Cat ahhh