Analyzing Sound

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Analyzing Sound
JUNE 2002 WPI Mathematics in Industry
Institute

• Mary Ellen Connor
• Kathy Crowley
• Judith Doherty
• Ginny Giordano
• Cat MacDonald

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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

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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.
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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.

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Fouriers 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.

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Steps to Analyzing the Data

• Recorded sounds
• Ahhs and eees of each individual

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Say Ahhh!
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MatLab wouldnt work on Tuesday.
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Got MatLab?
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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 individuals voice.

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Graphs of Amp vs Time
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Graphs of Amp vs Time
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Zoom in
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Zoom in
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Spectrum of eee graphs
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Spectrum of eee graphs
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Peaks are at n?
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Peaks are at n?
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Filter out all but fundamental fs
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Zoom in
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Group ahhh and Cat ahhh