Chapter 2: Creating Digital Music
Frequently asked questions
1. What is the difference between a spectrogram and frequency
spectrum?
A sound spectrogram is a visual representation of sound. As
in musical notation, the horizontal dimension corresponds to
time, and the vertical dimension corresponds to frequency (or
pitch), with higher sounds shown higher on the display. Frequency
is measured in Hertz, or cycles per second. The relative intensity
of the sound at any particular time and frequency is indicated
by the darkness of the spectrogram at that point. Since a spectrogram
is based on actual
measurements of the changing frequency content of a sound over
time, it provides more complete and precise information.
A frequency spectrum refers to a range of frequencies, which
the spectrum shows as a set of lines. It represents the frequency
content at a fixed moment in time.
As a spectrogram typically has time along the horizontal dimension,
frequency along the vertical dimension and relative intensity
represented as darkness, a frequency spectrum represents the
same information as a vertical slice of a spectrogram (the frequency
content at a fixed time). To make this information more comprehensible
it is reformatted with frequency content along the horizontal
dimension and relative intensity along the vertical dimension.
2. Why can dogs hear sounds that people can not
hear?
Most people can hear sounds between a low frequency cutoff of
20 Hz and a high frequency cutoff which ranges from 15KHz to
20KHz depending on age and hearing damage of the person. The
structure of our ears makes us responsive to sounds in this
frequency range. Other animals respond different frequency ranges.
A whistle at a frequency above 20 KHz would not be heard by
a person, but it might be in the range of hearing for a dog
because the dog can hear up to 40-45 KHz. Bats, whales, and
porpoises can hear sounds above 100 KHz while ferrets and elephants
can hear lower frequencies than humans. See more at http://www.lsu.edu/deafness/HearingRange.html
.
3. Why do people's voices sound different on the
telephone than they do when you are talking to them in the same
room?
When you are talking to people in the same room, you hear all
the frequencies in their speech that fall within the frequency
range over which your ears respond.
Normally this range is 20 Hz to 20,000 Hz. The telephone circuit
greatly reduces or eliminates all frequencies above about 3800Hz
so when you listen to a person's voice on the telephone you
do not hear all the frequencies you would hear if the person
were standing next to you while talking. This is particularly
noticeable for children's voices because their voices have a
higher pitch and more of their speech
will be above the cutoff frequency of the telephone. This limited
frequency response is very noticeable when trying to differentiate
between the letters “f” and “s” on the phone.
4. How are sines and cosine different?
A sine and a cosine signal with the same frequency and same
amplitude will be exactly the same except that they will be
shifted in time by one fourth of a period.
We know that for any angle ., cos(.) = sin(. + p/2) when . is
measured in radians. We could also write this as cos(. - p/2)
= sin(.) as we did in Equation 2.6
For the signal s(t) = A × cos( 2pf ( t+d
) ) = A × cos( 2pf t + 2pf d ) from Equation 2.12 , we
would call it a cosine signal if the time delay d is 0. If 2pf
d = - p/2, then we could call it a sine signal. This would correspond
to d = - p/( 4pf ) = - 1/( 4f ) = - ./4, which is one quarter
of a period. The value d measured in units of time is called
a time delay or a time offset while the radian value 2pf d is
called a phase delay or a phase offset.
5. Are sines and cosines only useful for digital music?
We learned in Chapter 1 that we can build very complex things
out of simple building blocks (block diagrams). In engineering
we often design and analyze systems based on how they respond
to sines and cosines. Even in the most complicated engineering
analysis sines and cosines appear as they are fundamentally
the building blocks of complex signals.
6. When I download MP3s from the web they have different bit
rates. How does this correspond to frequency?
This issue is addressed in detail in Chapters 5 and 6. It revolves
around how often you must sample a signal and how many bits
per sample you require to reliably reproduce the signal.
Chapter 1: The World of Modern Engineering
Frequently asked questions
1. How do I become an engineer?
If you ask “why?”, if you ask “how?” and
if you ask “what can I create today?” engineering
is for you! Take a broad, wide range of courses in high school
- meaning take courses that cover a broad range of topics (math,
English, history, government, computer programming, science,
psychology, etc) AND take a "deep" set of classes
in Math, Science, and English. By deep, we mean take as
many as possible (usually 4 years worth in high school). For
math, strive for calculus; and for science, strive to take at
least one class in biology, one in chemistry, and one in physics.
AND, realize that a degree in engineering offers opportunities
even beyond traditional engineering fields. An engineering degree
is a strong starting point for a career in medicine, law, and
business, to name just a few.
2. What can I do after I get an engineering degree?
Anything you want! Engineers solve problems. They make devices
or products or processes that satisfy human needs and wants.
Some engineers design products, some test products, and some
work with customers to find what they need and help them make
a clear specification. (A specification is a written document
that engineers use to “specify” the goals, constraints,
and other attributes of an item
which is being designed.) Some engineers work with other companies
to find parts and tools needed for their own products. Some
engineers work in marketing and some make repairs to things
that are broken or do not function correctly.
Some engineers never travel and some travel all over the world
to do their jobs. Some engineers live in the same town all their
lives and others move to a new town every few years. Some engineers
work with a small group most of the time and others are constantly
meeting new people and working with new teams. Some engineers
manage groups of engineers on large undertakings in any of these
areas. During a career, one engineer may have several different
types of jobs.
Engineers can also move on to other professions after they get
their engineering degree. There are innumerable examples of
engineers migrating to the field of medicine, law, politics,
and finance and so on! The amazing part is they all vouch that
their knowledge of engineering has helped them in their new
endeavors.
3. How much do engineers earn?
Engineering salaries depend on the specific type of engineering
work, the years of work experience the engineer has, and to
some extent on the geographical location. Average salary data
over time shows that engineers earn a good professional salary.
4. How are women and minorities represented in the field of
engineering?
The representation of women and minorities in engineering has
increased over the past thirty years. The graphs below demonstrate
the steady increase in the numbers of women and minorities receiving
bachelor degrees in science and engineering.
5. Is there another way to convert decimal numbers
into binary numbers?
In a word, yes. The scope of the text required omitting many
of the relationships between binary arithmetic and decimal arithmetic.
One popular method for binary conversion which is not covered
in the text is presented in Appendix A of this manual. Instead
of memorizing the powers of 2 and subtracting them from
the decimal number to be converted, it repeatedly divides the
number by 2 and records the remainder. Many students find this
method easier as it does not required knowing the powers of
2 and the repeated division by 2 is less prone to errors than
subtraction.
6. What is a transistor?
A transistor is an electronic device that can be used as a switch
or as an amplifier. The "transistor radios" introduced
in the 1950's allowed people to have small pocket-sized portable
battery operated radios for the first time. Transistors in these
radios were being used as amplifiers. A simple analogy of using
a transistor as an amplifier is to consider it as a “dimmer”
switch. In addition to a dimmer switch being “off”
or “on” it has a number of partially “on”
states in which the output “brightness of the light”
increases as you turn the dial. In digital circuits transistors
are used as a switch that is either on or off. A computer or
a digital signal processing microprocessor uses transistors
as switches.
Transistor technology is often characterized by the linear size
of the part of the transistor that does the switching. Thus
when people talk about 0.18 micron technology, they are talking
about the dimension of the active region of the transistor.
However, this does not tell you the total size of the transistor.
Room must be left for the connections to other parts of the
circuit, and the perpendicular dimension is usually 3 or 4 times
the length of the active region of the transistor.
Refer to the answer to homework Exercises 1.3, Problem 20 for
some specific values.
7. Do digital computers have to use transistors?
Digital computers use switching elements, and since the 1950's
the switching element used has been the transistor because of
its small size, low power usage, and its use in integrated circuits.
Before transistors, vacuum tubes were used as switching elements.
Before that small computers were designed using electromechanical
switching elements called relays that were heavily used in telephone
switching networks or purely mechanical switches.
Digital computers of the future will probably be built of other
switching elements such as molecular switches which will be
much smaller than transistors or perhaps with optical switches.
8. Can Moore’s Law hold forever?
Gordon Moore made his remarkable observation in 1965, just four
years after the first planar integrated circuit was demonstrated.
Ever since then, this observation has been dubbed as “Moore’s
Law”. This law predicts the rate of development of technology
and is not tied to basic laws of physics. The semiconductor
industry, to date, has been able to overcome every hurdle in
the way of Moore’s law and thus has kept pace with the
prediction of exponential growth in the number of transistors
per integrated circuit. The table below shows the trend in the
number of transistors per processor chip released over a period
of years.
Microprocessor Year of introduction Transistors
Intel 4004 1971 2,250
Intel 8008 1972 2,500
Motorola 6800 1974 4,000
Intel 8080 1974 5,000
Zilog Z 80 1975 8,500
Intel 8086 1978 29,000
Motorola 68000 1979 68,000
Intel 286 1982 120,000
Intel 386™ processor 1985 275,000
Intel 486™ DX processor 1989 1,180,000
Intel Pentium® processor 1993 3,100,000
Intel Pentium II processor 1997 7,500,000
IBM Power 3 1998 23,000,000
Intel Pentium III processor 1999 24,000,000
Intel Pentium 4 processor 2000 42,000,000
IBM Power PC 970 2002 52,000,000
But can this trend continue forever?
Obviously it can not if it is interpreted literally
and restricted to predictions about transistor densities. A
transistor requires many atoms to function and at some point
in the not so distant future the
predicted density would not allow enough room for these atoms.
However, new research on molecular switching elements is very
promising. When these new devices are used in circuits instead
of transistors, we may have a new law that predicts technological
advances in the density of switching elements.
9. Who are some famous engineers?
It is unusual for an individual engineer to be famous in the
way that a sports figure or movie star may become a household
word for a period of time. Engineers are know by their work
and their creations and may be very well known by reputation
among other engineers. Some engineers however have become quite
famous.
• Scott Adams - cartoonist and creator of "Dilbert"
- read an interview with him in Prism Magazine - http://www.asee.org/publications/dilbert.cfm
• Yasser Arafat - Palestinian leader and Nobel Peace Prize
Laureate. Graduated as a civil engineer from the University
of Cairo.
• Neil Alden Armstrong - became the first man to walk on
the moon on July 20, 1969, at 10:56 p.m. EDT. Armstrong received
his B.S. in aeronautical engineering from Purdue University
and an M.S. in aerospace engineering from the University of
Southern California.
• Jimmy Carter - 39th President of the United States. Attended
Georgia Southwestern College and the Georgia Institute of Technology
and received a B.S. degree from the United States Naval Academy
in 1946.
• Leonardo Da Vinci - Florentine artist, one of the great
masters of the High Renaissance, celebrated as a painter, sculptor,
architect, engineer, and scientist.
• Alfred Hitchcock - British-born American director and
producer of many brilliantly contrived films, most of them psychological
thrillers including "Psycho", "The Birds",
"Rear Window", and "North by Northwest."
He was born in London and trained there as an engineer at Saint
Ignatius College.
• Tom Landry - former Dallas Cowboys coach.
• Jair Lynch - 1992 and 1996 Olympic gymnast. Civil Engineering
degree from Stanford University.
• Jack Kilby – Nobel Prize winner, inventor of the
integrated circuit.
• Herbert Hoover - civil engineer, 31st President of the
United States
• Thomas Edison - Edison patented 1,093 inventions in his
lifetime, earning him the nickname "The Wizard of Menlo
Park." The most famous of his inventions was an incandescent
light bulb. Besides the light bulb, Edison developed the phonograph
and the kinetoscope, a small box for viewing moving films. He
also improved upon the original design of the stock ticker,
the telegraph, and Alexander Graham Bell's telephone. Edison
was quoted as saying, "Genius is one percent inspiration
and 99 percent perspiration."
• Grace Murray Hopper, a computer engineer and Rear Admiral
in the U.S. Navy, developed the first computer compiler in 1952
and the computer program language COBOL. Upon discovering that
a moth had jammed the works of an early computer, Hopper popularized
the term "bug.” She was one of the first women to
be elevated to the rank of Rear Admiral. Hopper received numerous
honors over the course of her lifetime. In 1969, the Data Processing
Management Association awarded her the first Computer Science
Man-of-the-Year Award. She became the first person from the
United States and the first woman to be made a Distinguished
Fellow of the British Computer Society in 1973. She also received
multiple honorary doctorates from universities across the nation.
The Navy christened a ship in her honor. In September 1991,
she was awarded the National Medal of Technology, the nation's
highest honor in engineering and technology.
See http://www.asee.org/precollege/famous.cfm
for profiles of even more interesting engineers.
10. Block Diagrams seem boring. Is there a way
to make them fun?
As described in the text a block diagram abstracts everything
in a design to a function along with its inputs and outputs.
Engineers use block diagrams to simplify complex designs and
clearly show how different parts of a design interact. Since
block diagrams make complex things appear simple, an interesting
exercise is to make block diagrams of systems which were designed
to make simple things be complex. Rube Goldberg was a famous
cartoonist who depicted exceedingly complex ways to perform
simple tasks. Descriptions of his works along with many examples
can be found at http://www.rubegoldberg.com/html/gallery.htm.
A fine modern day example of a Rube Goldberg machine is the
subject of a 2-minute advertisement for Honda which can be found
on the web at http://multimedia.honda-eu.com/accord/.
This ad depicts a long
chain of events containing precision engineered Honda parts
cascading into one another culminating in the unveiling of their
new car. The process is complicated enough to inspire awe in
almost anyone. Yet if broken down into simple blocks where a
person need only concern themselves with the action of 1 part
and how it
interacts with the part before and after it, then one can readily
see how their individual part of the process can be accomplished.
11. When I read about Moore's law on the web, some references
say the doubling occurs every year, some say every 18 months,
and some say every 2 years. Which is correct?
Moore's law is a predictor of the rate of technological advances
or a "rule of thumb", not a physical law of nature.
All of those rates have been correct for some time interval.
The originally predicted doubling interval was one year in 1965.
It was 17 months in 1975, 22 months in 1985, and 32 months in
1995. In 2004 is has gone back to 22 months. The article "5
Commandments" (IEEE Spectrum, December 2003, p30) describes
this history in a very readable manner and
includes economic context.
Chapter 2: Creating Digital Music
Frequently asked questions
1. What is the difference between a spectrogram and frequency
spectrum?
A sound spectrogram is a visual representation of sound. As
in musical notation, the horizontal dimension corresponds to
time, and the vertical dimension corresponds to frequency (or
pitch), with higher sounds shown higher on the display. Frequency
is measured in Hertz, or cycles per second. The relative intensity
of the sound at any particular time and frequency is indicated
by the darkness of the spectrogram at that point. Since a spectrogram
is based on actual
measurements of the changing frequency content of a sound over
time, it provides more complete and precise information.
A frequency spectrum refers to a range of frequencies, which
the spectrum shows as a set of lines. It represents the frequency
content at a fixed moment in time.
As a spectrogram typically has time along the horizontal dimension,
frequency along the vertical dimension and relative intensity
represented as darkness, a frequency spectrum represents the
same information as a vertical slice of a spectrogram (the frequency
content at a fixed time). To make this information more comprehensible
it is reformatted with frequency content along the horizontal
dimension and relative intensity along the vertical dimension.
2. Why can dogs hear sounds that people can not
hear?
Most people can hear sounds between a low frequency cutoff of
20 Hz and a high frequency cutoff which ranges from 15KHz to
20KHz depending on age and hearing damage of the person. The
structure of our ears makes us responsive to sounds in this
frequency range. Other animals respond different frequency ranges.
A whistle at a frequency above 20 KHz would not be heard by
a person, but it might be in the range of hearing for a dog
because the dog can hear up to 40-45 KHz. Bats, whales, and
porpoises can hear sounds above 100 KHz while ferrets and elephants
can hear lower frequencies than humans. See more at http://www.lsu.edu/deafness/HearingRange.html
.
3. Why do people's voices sound different on the
telephone than they do when you are talking to them in the same
room?
When you are talking to people in the same room, you hear all
the frequencies in their speech that fall within the frequency
range over which your ears respond.
Normally this range is 20 Hz to 20,000 Hz. The telephone circuit
greatly reduces or eliminates all frequencies above about 3800Hz
so when you listen to a person's voice on the telephone you
do not hear all the frequencies you would hear if the person
were standing next to you while talking. This is particularly
noticeable for children's voices because their voices have a
higher pitch and more of their speech
will be above the cutoff frequency of the telephone. This limited
frequency response is very noticeable when trying to differentiate
between the letters “f” and “s” on the phone.
4. How are sines and cosine different?
A sine and a cosine signal with the same frequency and same
amplitude will be exactly the same except that they will be
shifted in time by one fourth of a period.
We know that for any angle ., cos(.) = sin(. + p/2) when . is
measured in radians. We could also write this as cos(. - p/2)
= sin(.) as we did in Equation 2.6
For the signal s(t) = A × cos( 2pf ( t+d
) ) = A × cos( 2pf t + 2pf d ) from Equation 2.12 , we
would call it a cosine signal if the time delay d is 0. If 2pf
d = - p/2, then we could call it a sine signal. This would correspond
to d = - p/( 4pf ) = - 1/( 4f ) = - ./4, which is one quarter
of a period. The value d measured in units of time is called
a time delay or a time offset while the radian value 2pf d is
called a phase delay or a phase offset.
5. Are sines and cosines only useful for digital music?
We learned in Chapter 1 that we can build very complex things
out of simple building blocks (block diagrams). In engineering
we often design and analyze systems based on how they respond
to sines and cosines. Even in the most complicated engineering
analysis sines and cosines appear as they are fundamentally
the building blocks of complex signals.
6. When I download MP3s from the web they have different bit
rates. How does this correspond to frequency?
This issue is addressed in detail in Chapters 5 and 6. It revolves
around how often you must sample a signal and how many bits
per sample you require to reliably reproduce the signal.
Chapter 3: Making Digital Images
Frequently asked questions
1. While working on the labs for this chapter, the monitor seems
to show incorrectcolors.
One option:
Place your mouse on the background of windows.
Right click on your mouse.
Select properties.
Go to settings.
Make sure that you have selected
True Color (32 bit) Use most numbers of bits.
This should help.
2. What does the megapixel value on a digital camera signify?
The resolution of the image sensor is usually specified in terms
of megapixels.
For example, if a digital camera is advertised as having a 3
megapixel CCD sensor, what it means is the following. We have
seen that the aspect ratio for screens and monitors is typically
4:3 and so is the case for the digital light sensor used in
these cameras, which is called as the Charge Coupled Device
or CCD for short. For N = 3,000,000 total number of pixels,
and a width to height ratio of 4:3,
the sensor elements (or pixels) along the row and column are
2000 and 1500 respectively. Obviously, the higher the resolution,
the better the picture quality. But as we have seen from the
text, more storage space is required. Check out
http://electronics.howstuffworks.com/digital-camera.htm
for a good description of how a digital camera works.
3. Why do we use red, green and blue to define color images
when the primary colors we use for mixing paint and food coloring
are really red, blue and yellow?
For pigments which absorb light, the colors red, blue and yellow
are often used as primary colors. By just mixing them you can
get almost any color you want, although it is very hard to make
black. Ideally white is no pigment and black is a mixture of
all three pigments. See the Interesting fact on the text page
139.
But a monitor creates color by mixing light, not pigment. This
additive mixing effect for light creates the colors out of red,
green and blue. When no colors are present, we have black. When
all three colors are present we have white. Red light and green
light together make yellow light. Red, blue and yellow (or more
accurately magenta, cyan and yellow) are indeed primary colors,
as far as subtractive mixing is concerned. If you mix 3 inks
or paints of these respective colors in equal proportions, ideally
you get black,
because each ink roughly absorbs its third of the visible spectrum,
and no light is left.For ink jet printers and most quality color
printing, black is added as a fourth color because it is so
hard to make black by mixing pigments.
This site http://www.engr.csulb.edu/~jewett/colors/index.html
has some great description of various color schemes and formats
used for displaying color images on monitors and screens. Check
out this paper about using color in imaging and printing http://www.gain.net/PIA_GATF/PDF/GATF/info005.pdf
(you will need Adobe’s PDF reader to view this paper –
download a free reader from http://www.adobe.com/products/acrobat/readstep2.html)
4. It seems like digital cameras were developed after the first
spy satellite. How is that possible?
The first US spy satellite was called Corona. Between 1960 and
1972 Corona missions captured over 800,000 photographs. Getting
the pictures back to earth was as much an engineering challenge
as getting the photos in the first place. It took pictures on
film and released a canister containing the film to plummet
back to earth. The canister was retrieved during its descent
by a plane specially equipped to “catch” the falling
canister. Details of the design of the system and how it operated
can be found at
http://www.nasm.si.edu/exhibitions/gal114/SpaceRace/sec400/sec420.htm
5. If most video we see ranges from 30 to 60 frames per second
why would anyone ever build a digital video camera with any
other frame rate?
Cameras exist with frame rates that vary from 1 frame every
30-60 minutes (1/1800 to 1/3600 frames per second) to several
1000 frames per second. Most of these non-standard frame rate
camera’s are for scientific use. See text page 157-158.
The very high frame rate cameras are utilized to capture extremely
fast moving objects. For instance, certain breeds of hummingbirds
can flap their wings 200 times a second. If you used a standard
camera to capture a
hummingbird in flight it would flap its wings 6.66 times in
a single frame of your video. The wings would be a blur. With
a camera with a 1000 frames/sec frame rate, you would have 5
frames for each flapping of the wing, thereby allowing you a
much better chance to observe the detail of the wings. On the
other end of the spectrum are cameras with frame rates approaching
1 frame per hour. These
cameras are typically used in astronomy where extremely faint
celestial objects are being observed. So little light from these
objects reaches earth that a digital camera must collect the
light for nearly an hour before it has enough to differentiate
the object from the darkness of space. These cameras are typically
cooled to make them very low noise; otherwise the noise of the
camera would
overwhelm the image.
