Lecture 11
Representing Sound
Mark Horowitz
Stanford University
horowitz@ee.stanford.edu
Copyright © 2015 by Mark Horowitz
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Learning Objectives
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PREVIOUSLY IN E40M
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We Constructed Our Plane
•  We have an 6 x 6 array
–  Logically looks like:
–  Physically it is different
•  Need to drive it
–  To light up the lights
•  For independent light control
–  Either only one + wire high
–  Or only one - wire low
–  Max of 6 LEDs on at once
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What is Sound Anyway?
•  It is a pressure wave that moves in air
–  Created by voice, instruments, speakers
http://www.mediacollege.com/audio/01/sound-waves.html
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How Does a Speaker Create Sound?
•  All speakers (and headphones) create sound the same way
•  http://electronics.howstuffworks.com/speaker6.htm
•  Power
–  100W stereo, Speakers are 8 Ω
•  Vi =100; i=V/R V2 = 800
•  V swing > +/- 30V
•  So we represent sound by voltage
–  Which varies in time
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REPRESENTING SOUND
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Natural Way To Represent Sound
•  We create pressure waves by moving a speaker
–  Larger voltage causes more deflection
•  Sound both pushes and pulls the speaker cone
–  Voltages are both + and –
•  Represent sound by voltage vs. time
•  On computers
–  Sample voltage at 44K/sec
–  Digitize the voltage
•  Into 15 bit integer (signed)
–  Raw = .wav; compressed .mp3
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Analog Input into Arduino
•  Connecting a voltage to an analog input to Arduino
•  Arduino converter 0-5V signal into 10-bit digital value
•  Value ranges from 0-1023
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Seeing Sound (Demo)
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Equalizers
•  I think we have all seen this type of display
•  What information does it represent?
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Setting An Equalizer
•  You might have even played with setting levels
•  Ever think about what you are really doing here?
–  The music is a set of voltages vs. time.
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FREQUENCY SPECTRUM
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Representing Signals In Different Ways
•  While we can represent sound as a string of numbers
–  Which represent voltage at different times
–  Our brain doesn’t process sound that way
•  We think and talk about sound/music as combinations of tones
–  Summation of different sinewaves
–  And you can represent sound this way too
•  All signals can be represented in two ways
–  Voltages in time
–  Sum of tones of different amplitudes and frequencies
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Demo
•  Java applet from:
–  http://www.falstad.com/fourier/index.htm
–  But most browsers won’t run it any more (security issues)
–  So it is posted with lecture notes fourier.jar
•  Allows you to create waveform and see tones
–  Or add tones and see waveform
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Relating Voltage to Sinewaves
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Viewed In Terms of Sine-waves
•  So you can take the music and look sinewaves in a block of time
–  Then repeat that for another block of time
–  This analysis plots frequency vs. time – a spectrogram
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FOURIER SERIES
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Fourier Series
•  The formal name for this alternative representation
•  Officially it only works for repetitive signals
–  Since sine-waves repeat
•  There is an extension for non repetitive signals
–  It is called the Fourier Transform
•  Many people use Fourier series for a block of data
–  And just assume that the block of data repeats
–  That is what the java demo does
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Formal Definition
•
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Equation For A Square Wave
•
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Why Worry About Frequency Domain Analysis?
•  Sure it can make interesting light displays
–  But really …
•  Turns out it will be very helpful to understand circuits
–  With Capacitors and Inductors in them
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