Lecture 11 Representing Sound Mark Horowitz Stanford University horowitz@ee.stanford.edu Copyright © 2015 by Mark Horowitz M. Horowitz E40M Lecture 11 1 Learning Objectives M. Horowitz E40M Lecture 11 2 PREVIOUSLY IN E40M M. Horowitz E40M Lecture 11 3 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 M. Horowitz E40M Lecture 11 4 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 M. Horowitz E40M Lecture 11 5 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 M. Horowitz E40M Lecture 11 6 REPRESENTING SOUND M. Horowitz E40M Lecture 11 7 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 M. Horowitz E40M Lecture 11 8 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 M. Horowitz E40M Lecture 11 9 Seeing Sound (Demo) M. Horowitz E40M Lecture 11 10 Equalizers • I think we have all seen this type of display • What information does it represent? M. Horowitz E40M Lecture 11 11 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. M. Horowitz E40M Lecture 11 12 FREQUENCY SPECTRUM M. Horowitz E40M Lecture 11 13 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 M. Horowitz E40M Lecture 11 14 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 M. Horowitz E40M Lecture 11 15 Relating Voltage to Sinewaves M. Horowitz E40M Lecture 11 16 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 M. Horowitz E40M Lecture 11 17 FOURIER SERIES M. Horowitz E40M Lecture 11 18 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 M. Horowitz E40M Lecture 11 19 Formal Definition • M. Horowitz E40M Lecture 11 20 Equation For A Square Wave • M. Horowitz E40M Lecture 11 21 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 M. Horowitz E40M Lecture 11 22