engr101: lecture 7 · engr101: lecture 7 march 201915/25. what is the goal of the project? (2)...

ENGR101: Lecture 7Signals, siganal processing basics

March 2019

ENGR101: Lecture 7 March 2019 1 / 25

What we cover today?

• Signals - analog and digital

• C++: branching and cycles

• Working with files

• Project 1 introduction


Project

• You write a software which produces audio files

• Play the files and visualize air pressure (there is a software for that)

• We made it easier for you - you don’t have to follow all the bells andwhistles of audio format. All you have to do is to generate array ofintegers.

• This software has to generate the signal.

You will need:

• Make new C++ project

• include library functions into your project

• Make some parts of code run repeatedly (cycles)

• Make code perform different actions depending upon some condition


What is the signal?

• Anything that carries information can be called a signal.

• Information in most basic form is a measure of surprise. Thereshould be a change otherwise there is no new information.

• Any kind of changing physical variable can be a signal. Sound is asignal – changing air pressure as sensed by an ear.Image is a signal – light intensity and colours are perceived by the eye.


Signal

Question: Which statement contains more information?

1 It is snowing in Sahara today

2 Today is windy day inWellington


Analog signal

• Analog signal is continuous - nomatter how much you zoom inyou will see smooth curve

• We perceive everything as ananalog signals - if changes arenot too fast

• But computers work withnumbers and they do steps intime.


Sampling

• First step is to measure signal atfixed moments of time.

• A sample is a value at a point intime.

• Samples are taken every Tseconds

• The sampling frequency fs orsampling rate, fs, is the averagenumber of samples obtained inone second (samples persecond), thus fs = 1/T.

• If samples are taken at rate 10per second (T=0.1 sec), forexample, frequency is 10 Hz.


Sampling rate

• How fast samples should be taken?

• Music examples: 1024 samples per second and 44 100 sps (samplesper second)

• Human ear can hear acoustic signals up to 20 000 Hz

• NYQUIST THEOREM:To detect a signal at frequency f, you must digitize at a rate of fasterthan 2f. To detect 1000 Hz, must digitize at > 2000 samples persecond (minimum).

Music: Courtesy http://music.columbia.edu/cmc/musicandcomputers/chapter2/02 03.php

Why we hear low tones?


Nyquist theorem

• Sampling frequencyshould be high enoughso that samples followoriginal signal

• If sampling frequency isnot high enoughdigitized signal isdistorted

• It will lose all higherfrequencies

• Output will have lowfrequency signals whichare not in original signal


Analog to Digital Conversion (ADC)

• Process we went through isAnalog-to-Digital-Conversion

• ADC converts continuous(analog) input signal intostream of binary numbers

• Usually it does sampling andquantization

• Output is distorted signal(quantization noise) becausebinary output do not representinput signal exactly


Another way around - Digital To Analog conversion

Figure:

Simple sequence of numbers (rawdata) is not enough. You have toexplain to DAC what is time intervalbetween samples.


Audio file formats

http://soundfile.sapp.org/

doc/WaveFormat/

To restore waveform from set ofnumber we need to know more:

• Sampling rate

• For music - is it mono or stereo

• How many bytes per sample

• and what not...

All this information is contained inheader (it is not h file as in C++).First lines in the file contain thisinformation.


http://soundfile.sapp.org/doc/WaveFormat/

http://soundfile.sapp.org/doc/WaveFormat/

Open wav file in text editor

Good news is that youdon’t have to writethis part.


Reminder - what you may need to complete the project?

• Working with arrays

• Reserving memory for the arrays (initializing)

• Traversing (cycles)

• Working with files (challenge part)


What is the goal of the project? (1)

• Software should generate arrayof samples (red in picture).Hardware(speaker) will smoothit (can not move very fast) andair pressure will follow blue line(can call it envelope)

• First of all we need to decidewhat is time interval betweensamples (dt). Good qualitysound can be produced if we use44100 samples per second.



• 44100 samples per secondmeans that samples shouldfollow every dt = 1/44100seconds

• Select duration of the sound T

• If duration is T seconds andsamples should be dt secondsapart then total number ofsamples is:

N = T/dt (1)



• We know now how manysamples we should have - N

• Now we calculate amplitude(volume) of each sample

• What is time of sample i?OK, it is sample number i,samples are dt apart, so it is

ti = i ∗ dt (2)

• Volume at this moment oftime? Say, we want simpletone:

a(t) = A · sin(ωt) (3)


Array of samples

There is an equation which describes waveform:

a(t) = A · sin(ωt) (4)

, where A is an amplitude (volume) of the sound,ω is the frequency. ω = 2 · π · f and f is frequency [Hz].t is time calculated by:

ti = i ∗ dt (5)

and i is changing from 0 to N Putting it all together:Array of samples is:

a[i ] = A ∗ sin(2 ∗ π ∗ f ∗ i ∗ dt) (6)

To use sin and π you have to include math.h. We have to do calculationsfor i changing from 0 to N. How?


Iterations

Sometimes we need to repeat calculations several times.Say, we want to print numbers from 1 to 6.

Figure:

There is shortcut for it:

for (int i = 1 ; i < 6 ; i= i+1)

{

cout <<i<<endl;

}

// carry on

All shown in green logic is implemented byone line:

for (int i = 1 ; i < 6 ; i= i+1)


Question?

#include <iostream >

using namespace std;

int main (){

for (int i = 0 ; i < 6 ; i=i+2){

cout <<i<<" ";

}

}

1 0 2 4

2 0 1 2 3 4 5

3 0 1 2 3 4 5 6


Question, again?



int main (){

for (int i = 10 ; i < 6 ; i=i+2){

cout <<i<<" ";

}

}

1 0 2 4

2

3 10 8 6 4 2 0


Question, again?



int main (){

for (int i = 0 ; i < 6 ; i=i+1){

if ( i > 2 ){

cout <<i<<" ";

}

}

}

1 0 2 4

2 3 4 5

3 0 1 2 3 4 5


How to to work with an array of ints?

Usually you use for() to work with arrays.



int main (){

int a[5];

for ( int i = 0 ; i < 5;i = i + 1){

a[i] = i*2;

}

for ( int i = 0 ; i < 5;i = i + 1){

cout <<a[i]<<" ";

}

return 0;

}

1 0 2 4 6 8

2 3 4 5

3 0 1 2 3 4 5


Working with files


#include <fstream >


int main (){

string line;

ifstream myfile;

myfile.open("file.txt");

while(getline(myfile , line)) {

cout <<"From file="<<line <<endl;

}

}

• We used iostream -input/output fromkeyboard/display

• fstream class to performinput/output ofcharacters from file

• You open the file first


Questions?


engr101: lecture 7 · engr101: lecture 7 march 201915/25. what is the goal of the project? (2)...

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