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Announcements Take textbook to lab.

» Be sure to read Chapter 13 before lab– MATLAB tutorial

– Can skip Section 13.4

Bring your transmitter and receiver to lab.» 8 AA batteries» 2 9V batteries» Earphones

First Professional Memo Due TODAY!

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Today’s Topics

Digital signals

Introduction to MATLAB

Generating audio signals with MATLAB

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Digital Music - Recording

Sampler

-0.0364-0.1884-0.6928-1.7398-2.7642-2.2378 0.1711 1.8333 …

10110101010

byteCD

Analog signal Digital signal

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Digital Music - Playback

D/AConverter

-0.0364-0.1884-0.6928-1.7398-2.7642-2.2378 0.1711 1.8333 …

CD

Analog signalDigital signal

AudioAmplifier

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Computer-Generated Signals

MATLAB Sound Card

D/AConverter

AudioAmplifier

0.0000 0.5878 0.9511 0.9511 0.5878 0.0000-0.5878 …

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Audio Signal

Sound generated by a PC originates as a sequence of numbers (a discrete signal).

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What we want What we can generate

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MATLAB

MATLAB® allows us to generate sequences easily.» The basic data structure in MATLAB is a

vector.» A vector is a convenient way to store a

sequence. We can also play sounds from within

MATLAB.

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MATLAB Basics

Assign a value to a variable>> a=3

a =

3

>> a=3;>> a

a =

3>>

Semicolon suppresses echo

Typing a variable name displays the value

Be careful!!

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MATLAB Basics Vectors

>> v=[1,3]v = 1 3

>> v=[1;3]v = 1 3

>> v'ans = 1 3

>> v=1:0.5:3v = 1.0000 1.5000 2.0000 2.5000 3.0000

Comma delimits columns

Semicolon delimits rows

Apostrophe means transpose(turn rows into columns andvice versa)

start value : increment : end value

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We have been considering sine waves:

is the frequency of the sine wave. Sample the waveform every T seconds.

» Let » We get a sequence » Let n=0,…,N to get sequence corresponding to a

duration of NT seconds.

Generating Sine Waves

tftx 02sin)( 0f

nTt Tnfnx 02sin)(

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Continuous Sine Wave

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Time in seconds

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Sampling Operation

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Time in seconds

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Sampled Signal

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Time in seconds

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Discrete Array

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Index (n)

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MATLAB

>> f0=100;>> T=.0008;>> n=0:62;>> x=sin(2*pi*f0*T*n);>> stem(n,x)

Tnfnx 02sin)(

start value : end value (assumes increment of 1)

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stem(n,x) plot(n,x)

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Good Programming Habits

>> f0=100;>> T=.0008;>> n=0:62;>> x=sin(2*pi*f0*T*n);>> stem(n,x)

>> x=sin(2*pi*100*.0008*(0:62));>> stem(n,x)

GOOD

BAD!

Do not Repeat Yourself!!

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MATLAB vs. C C code to create a sine wave:#include <stdio.h>

#include <math.h>

main(argc,argv)

int argc;

char *argv[];

{

int i,n;

double *sv, f0;

n=5000;

f0=100;

sv = (char *) calloc(n, double);

for (i = 0; i < 50000; i++) {

sv(i) = sin(2*3.1415927*f0*I/44100);

}

}

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Other MATLAB Abilities

Many built-in functions Can easily add your own functions Immediate results without compiling Can solve systems of equations easily All kinds of plotting methods Simulink Maple Symbolic Math Toolbox

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Sampling Period

If we sample too slowly (T too large), we can get a misleading sequence.

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Sampled Signal

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Is this the true signal?

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Or, is this the true signal?

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Aliasing

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Sampling Rate Too Low

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“Wagon Wheel Effect”

Correct Sampling

Aliasing

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Avoiding Aliasing

To avoid aliasing, sample at least twice as fast as the highest frequency in the signal.» Minimum of two samples per period» Shannon’s Sampling Theorem

Example:» A 40 Hz sine wave should be sampled at 80 Hz

or more

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Playing Sounds in MATLAB

Can play sounds directly from MATLAB:» sound(x,44100)

– x is the sequence of values in a vector

– 44100 is the output sampling rate

» soundsc(x,44100)– Same as sound() but auto-levels before playing

– Each sound played at the same level

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Playing Sounds in MATLAB

Can read or write WAV files:» y = wavread(‘fast.wav’);

– y is the sound sequence read in as a vector

– fast.wav is the name of the file to be read.

» wavwrite(y,44100,’fast.wav’)

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Stereo in MATLAB

If x is an Nx2 vector, the left column will be played as the left channel, and the right column will be played as the right channel.» fl=200;» fr=300;» t=[0:1/44100:8];» xl = sin(2*pi*fl*t);» xr = sin(2*pi*fr*t);

sound([xl’ xr’],44100)

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Quiz 8

1. Long calculations or detailed specifications should be included in the main text of the a report. (True or False)

2. Contractions are acceptable in an engineering report. (True or False)