Digital Sound as Computer Science
Jennifer Burg
CPATH Workshop Series:
“Revitalizing Computer Science Education
Through the Science of Digital Media”
Workshop 2, July 28 and 29, 2008
Wake Forest University
This work was funded by National Science Foundation CPATH grant CCF 0722261, Jennifer Burg PI, Conrad Gleber Co-PI
National Science Foundation CPATH
Grant

“Revitalizing Computer Science Education through the
Science of Digital Media”




Jennifer Burg, PI, Wake Forest University
Conrad Gleber, Co-PI, La Salle University
Three years (Aug. 2007 – July 2010), seven workshops
Each workshop
A special digital media topic
 One speaker from a related academic discipline
 One speaker from a related business or industry
 What would they like to see in a computer science major working for or
with them?

Workshop Series
Host
Location
Topic
Date
Conrad Gleber, Dir. of Digital Arts and
Multimedia Design, Dept. of Math.
and Computer Science
La Salle University,
Philadelphia, PA
Algorithms, scripting, and
programming for visual art
May 29 and 30,
2008
Jennifer Burg, Associate Professor of
Computer Science
Wake Forest University,
Winston-Salem, NC
Digital sound
July 28 and 29,
2008
Gail Rubini, Prof. of Design, College
of Visual Arts, Theatre, and Dance
and Ken Balfauf, Dir. Program for
Interdisciplinary Computing
Florida State University,
Tallahassee, FL
Visualization
April 2009
Michael Mateas, Assistant Prof. of
Computer Science
University of California
Santa Cruz
TBA
Tentatively May
2009
Michael Niederman, Chair, Television
Department
Columbia College, Chicago,
IL
Digital media in television
production
Tentatively August
2009
Cher Cornett, Dir. Digital Media
Center
East Tennessee State
University, Johnson City, TN
Game programming
Tentatively May
2010
Gerald Gannod, Assoc. Prof. of
Comp. Sci. and Systems Analysis
Miami University, Oxford,
OH
TBA
Tentatively August
2010
Digital Sound Production Workshop
 June 2
to July 25, 2008
 Students of music and computer science working
together
 Interdisciplinary collaborative projects
 Funded by National Science Foundation CCLI grant
“Linking Science, Art, and Practice through Digital
Sound,” Jennifer Burg, PI; Jason Romney, Co-PI
Goals in this workshop from the PIs’
perspective
 Consider in
what ways digital sound is legitimately
part of the computer science curriculum
 Explore concepts, assignments, experiments, and
exercises that are interesting to students because
they bring together science, art, and practice
 Figure out where these can be plugged into the
computer science curriculum
Goals in this workshop from the
participants’ perspective
 Consider how
these ideas shed light on your own
work
 Make contacts with colleagues who share your
interests
 Eat well
What does the study of digital sound
entail?

Physics


Engineering and digital signal processing (DSP)


Trigonometry, logarithms, complex numbers, summations, integrals, transforms
Music


Sound card, microphones, speakers, hardware sound processors, cables
Mathematics


sound waves, acoustics, resonance
Fundamental frequencies, harmonics, octaves
Algorithms

Transforms, filters, compression
What makes digital sound a suitable
topic within computer science?
 It’s based on
digital encoding and manipulation of
digital data.
 It’s “applied” computer science, which is what
makes it interesting.
Topics in Digital Sound as Computer Science
Sound waves and acoustics
 Analog vs. digital representations, digital encoding,
sampling and quantization
 Decibels for measuring amplitude
 Frequencies related to pitch, complex waveforms
 Implications of sampling rate: the Nyquist theorem and
aliasing
 Implications of bit depth: quantization error, SQNR,
dynamic range, dithering, noise shaping, dynamic
compression and expansion

Topics in Digital Sound as Computer Science
 MIDI compared to
digital audio
 MIDI message formats and protocols
 MIDI samplers vs. synthesizers
 Sound wave synthesis
Topics in Digital Sound as Computer Science
 Hardware
for sound processing
 Sound
cards; ADCs and DACs; connection types;
cables; microphones, speakers and monitors; frequency
response of microphones, speakers, and monitors
 Software for
sound processing
 Audition, Audacity,
Sound Forge, Logic, Pro Tools,
Reason, Cakewalk Music Creator and Sonar, etc.
 MATLAB
 Chuck
Topics in Digital Sound as Computer Science
 Fourier analysis, frequency components, the
Fourier transform, windowing functions
 Filters (FIR and IIR), EQ, types of filters (shelf, lowpass, high-pass, bandpass, bandstop)
 Special effects, e.g. reverb, autotuning, vocoding
 Data rate, data compression, psychoacoustical
models for compression, frequency masking
As is true with most topics in computer
science, you can approach digital sound at
different levels of abstraction
 Mathematical/algorithmic –
pencil and paper,
chalkboard, and calculator
 Low-level programming (e.g. C under Linux)
 Chuck
 MATLAB
 Audition, Audacity, Sound Forge, Logic, Pro Tools,
Reason, various plugins, etc.
 Sample
editor vs. track editor
 Combining digital audio and MIDI
Frequency Components of
Sound Waves

Generate notes C4, E4, and G4. Add the waves and look
at the result.


In Audition
In MATLAB
A single-frequency wave is a single pitch.
 Voices and instruments don’t produce single pitches.
They have harmonics.
 Sound in music and nature are complex waveforms with
frequency components.

Notes, Octaves, and Frequencies
Let f1 and f2 be the frequencies of two notes where the
second is an octave above the first. Then f2 = 2*f1.
 There are 12 notes in an octave. Find x such that
 f2 =2*f1 = ((((((((((((f1*x)*x)*x)*x)*x)*x)*x)*x)*x)*x)*x)*x)
 2*f1= f1*x12
 2 = x12
12
 x = 2  1.0595
 Thus if fa and fb are the frequencies of two consecutive
notes, then fb = 1.0595 * fa.

Nyquist Theorem and Aliasing
 The sampling
rate must be more than twice the
frequency of the highest frequency component of
the sound being sampled.
 Otherwise
you can have aliasing.
 A frequency component comes out lower than it should
be.
 Demonstrated in Audition
How is amplitude measured?
Decibelsbased on sound pressure :
 air pressure of sound being measured 

dbSPL  20 log10 
 air pressure of the threshold of hearing 
In Audition
Decibels full scale :
 sample value
dBFS  20 log10 
n-1
2

where n is the bit depth




The Effect of Bit Depth in Quantization
 Rounding
to discrete quantization levels causes
error. The error is itself a wave.
 In MATLAB
 Signal to quantization noise ratio (SQNR) and
dynamic range are also measured in decibels.
SQNR  20 log10 (2n )
where n is the bit depth
Audio Dithering
 Add
a random amount between -1 and 1 (scaled to
the bit depth of the audio file) to each sample before
quantizing.
 There will be fewer consecutive samples that round
to the same amount. Rounding to 0 is the worst
thing, causing breaks.
 Demonstration
 In Audition
 In
MATLAB
Noise Shaping
Raise error wave above the Nyquist frequency.
 Do this by making the error go up if it was previously
down and down if it was previously up. This raises the
error wave’s frequency.
 The amount added to a sample depends on the error in
previous sample.

F _ ini  F _ ini  Di  cEi 1
F _ out i  F _ ini 
E i  F _ ini  F _ out i
Digital Filters
 Infinite impulse
response (IIR) vs. finite impulse
response (FIR) filters
 Filtering in the time domain by means of convolution
Click to animate
Digital Filters
 Filtering in
the frequency domain by means of the
Fourier transform
Digital Filters
Creating Filters
frequency response graph
Creating Filters
frequency
response
graphs
Creating a Low-Pass Filter
Frequency
Response
(frequency
domain)
Impulse
Response
(time
Domain)
Creating a Low-Pass Filter
Creating a Low-Pass Filter
 You
can do it yourself in MATLAB:
 Create
the filter using the given function, sin(2fc)/n
 Read in an audio clip
 Since this is a filter in the time domain, convolve audio
clip with the filter
 Listen to the result
 Graph the frequencies of filtered clip against the
unfiltered clip. (Do this by taking the Fourier transform
of each first.)
 See the demonstration and worksheet for details.
Creating FIR and IIR Filters with MATLAB’s Digital
Signal Processing Toolbox
>> lowA = wavread('440.wav');
>> highA = wavread('880.wav');
>> highest = wavread('2000.wav');
>> mixed = (lowA+highA+highest) / 3;
>> [a,b] = butter(6,1000/4000);
>> output = filter(a,b,mixed);
>> ideal = (lowA+highA) / 2;
>> wavplay(ideal,8000);
>> wavplay(output,8000);
>> hold on
>> plot(ideal);
>> plot(output,'red');
>> axis([1 50 -1 1])
Demonstration
Filter Visualization Tool in MATLAB
 MATLAB also
has a Filter Visualization Tool that lets
you set zeros and poles for a filter and see the
frequency, phase, and impulse responses.
Demonstration
C Programs for Digital Sound and MIDI
Reading Messages from dev/midi
#include <stdio.h>
#include <string.h>
#include <linux/soundcard.h>
#include <unistd.h>
#include <fcntl.h>
/*CTRL-Break out of program*/
int main()
{
char* device00 = "/dev/midi" ;
unsigned char data[3];
unsigned char byte1, byte2, byte3;
int fd
fd = open(device00, O_RDONLY, 0);
if (fd < 0) {
printf("Error: cannot open %s\n", device00);
}
else printf("Opened dev/midi00\n");
byte1 = byte2 = byte3 = -1;
while (1) {
read(fd, data, sizeof(data));
if (!(data[0] == byte1 && data[1] == byte2 && data[2]
== byte3) {
printf("%d ", data[0]);
printf("%d ", data[1]);
printf("%d\n", data[2]);
byte1 = data[0];
byte2 = data[1];
byte3 = data[2];
}
}
return 0;
}
Reading from and
Writing to
the Sound Card
#include <unistd.h>
#include <fcntl.h>
#include <sys/types.h>
#include <sys/ioctl.h>
#include <stdlib.h>
#include <stdio.h>
#include <linux/soundcard.h>
#define LENGTH 3
#define RATE 8000
#define SIZE 8
#define CHANNELS 1
unsigned char buf[4*LENGTH*RATE*SIZE*CHANNELS/8];
int main(){
int fd, arg, status;
int i, j, k, begin, end, bufEnd;
char temp;
printf("Size of buffer is %d\n", sizeof(buf));
fd = open("/dev/dsp", O_RDWR, 0);
if (fd < 0) {
perror("Opening /dev/dsp failed\n");
exit(1);
}
arg = SIZE;
status = ioctl(fd, SOUND_PCM_WRITE_BITS, &arg);
if (status == -1)
perror("Unable to set sample size\n");
Reading from and
Writing to
the Sound Card
arg = CHANNELS;
status = ioctl(fd, SOUND_PCM_WRITE_CHANNELS, &arg);
if (status == -1)
perror("Unable to set number of channels\n");
arg = RATE;
status = ioctl(fd, SOUND_PCM_WRITE_RATE, &arg);
if (status == -1)
perror("Unable to set sampling rate\n");
status = read(fd, buf, 1);
while (buf[0] >= 125 && buf[0] <= 131) {
status = read(fd, buf, 1);
}
printf("%d ",buf[0]);
printf("broke the silence\n");
for (i = 0; i <= 3; i++) {
//printf("Say something\n");
status = read(fd, buf+(24000*i), 24000);
if (status != 24000)
perror("Read wrong number of bytes\n");
begin = 24000*i;
end = begin + 12000;
bufEnd = begin + 24000 - 1;
for (j = begin, k = 0; j < end; j++, k++) {
temp = *(buf+j);
*(buf+j) = *(buf + bufEnd - k);
*(buf+j) = temp;
}
}
status = ioctl(fd, SOUND_PCM_SYNC, 0);
if (status == -1)
perror("SOUND_PCM_SYNC failed\n");
printf("You said \n");
status = write(fd, buf, sizeof(buf));
if (status != sizeof(buf))
perror("Wrote wrong number of bytes\n");
Reading from and
Writing to
the Sound Card
}
Creating a Vocoder in MATLAB
From http://www.paia.com/ProdArticles/vocodwrk.htm
Creating a Vocoder in MATLAB
function output = vocoder(input1, input2, s, window)
h = hanning(window)';
input1 = input1';
input2 = input2';
q=(s-window);
output = zeros(1,s);
fftdata = zeros(1,s);
input1fft = zeros(1,s);
input2fft = zeros(1,s);
for i=1:window/4:q
b = i+window-1;
input1partfft = fft(input1(i:b).*h);
input2partfft = fft(input2(i:b).*h);
input1fft(i:b) = input1fft(i:b) + abs(input1partfft);
input2fft(i:b) = input2fft(i:b) + abs(input2partfft);
mult = input1partfft.*input2partfft;
fftdata(i:b) = fftdata(i:b)+ abs(fft(mult));
output(i:b) = output(i:b)+ifft(mult);
end
output = output/max(output);
Demonstration
Questions for this workshop
 How
do we relate the science to art and practice?
 How much science does the artist/practitioner
need?
 Where are the points where knowing the science
results in better work?
 How do we change the computer science
curriculum to retain the science but relate it more
interestingly to art and practice?