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M 10/3/05
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HW due:
Show that NAND gates, all by themselves, are capable of creating any digital
logic circuit. In class we showed that an inverter (Ø gate) is easily created. All you have left to do is
to show that Ù and Ú gates can also be formed from NANDs.
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T 10/4/05
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HW due:
Attempt all of the following questions. Depending on how adept you are with
Web browsing, this assignment may take you anywhere between 5 minutes and 3
hours.
1. Perform an Internet search to locate the most expensive high-end diamond
phonograph cartridge that you can find available for sale.
2. Calculate the byte rate (Kbytes per second) required for CD-quality stereo
audio, using 40,500 quantizations per second, 16 bits per sample, and 2
channels.
3. What Beethoven symphony was used as the standard for setting the capacity
for CDs when the format was originally introduced?
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W 10/5/05
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HW due:
Read this
article about endianness and answer the following questions.
1. Are Windows machines big-endian or little-endian?
2. What about Macintoshes?
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Th 10/6/05
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Unit Quiz
on “What’s So Great About Digital?” (topics 0x21–0x2F,
excluding endianness). As you prepare for the quiz, you may find this discussion of digital vs. analog to be
helpful.
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F 10/7/05
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No school.
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M 10/10/05
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No school.
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T 10/11/05
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HW due:
Work through the entire tutorial on
exponential and logarithmic functions and take the quiz at the bottom of
the page. You may need to work through the topic several times to understand
what is going on. Then, after you understand (more or less) how logarithms
work, read the article
on decibels so that you will be familiar with some of the terminology
regarding electronics that we will discuss in class.
Warning: This material is quite
difficult. You will probably need to work through it several times before it
makes any sense at all. Even on the third pass, you may find that you are not
getting everything. Be sure to keep a list of your questions so that we have
something to start from in class.
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W 10/12/05
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HW due:
Fill in the following chart:
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Power
ratio
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dB change
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Power ratio
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dB change
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2 (doubled)
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+3 dB
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1500
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__________
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3 (tripled)
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+5 dB
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3000
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__________
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4 (double double)
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+6 dB
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8000
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__________
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6 (double triple)
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+8 dB
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10 thousand
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__________
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8
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__________
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30 thousand
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__________
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10
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+10 dB
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80 thousand
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__________
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15
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__________
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1 million
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__________
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20
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__________
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2 million
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__________
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30
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__________
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3 million
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__________
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40
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__________
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6 million
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__________
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60
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__________
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60 million
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__________
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80
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__________
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600 million
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__________
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100
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+20 dB
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6 billion
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__________
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150
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__________
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600 billion
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__________
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200
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__________
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6 trillion
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__________
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300
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__________
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6 quintillion
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__________
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400
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__________
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8 quintillion
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__________
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600
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__________
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10 sextillion
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__________
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800
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__________
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100 sextillion
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__________
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1000
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+30 dB
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1 septillion
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__________
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Th 10/13/05
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HW due:
1. Which is more dangerous, 10,000 volts passing through a person wearing
gloves providing 300 KW of resistance, or 12 volts passing through a person whose resistance
has been lowered to 20W? Show your work.
2. Compute the power dissipated in each case in #1.
3. Compute the S/N ratio if a signal is at 30 watts and total noise is at 20
microwatts. Give your answer in dB.
4. Human hearing is such that a sound volume increase of 10 dB sounds to most
people like a doubling of sound. In addition, most people view doubling as an
additive effect; in other words, two doublings sounds like “2 notches louder”
to most people. Explain why human hearing is called logarithmic.
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F 10/14/05
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HW due:
1. Name something other than human hearing that is logarithmic. Choose an
example from real life, perhaps something that has been in the news during
the past week.
2. Compute the S/N ratio if a signal is at 40 watts and total noise is 20
milliwatts. Do not use your calculator.
3. If data/information/signal can be thought of as something that has the
capacity to show change (i.e., modulation), explain how an audio signal can
be transmitted (a) using analog AM technology, (b) using analog FM
technology, and (c) using digital versions of each.
4. Devise a method for sending a secret message of several thousand
characters using nothing more than the text from the King James version of
the Bible. In other words, anyone who intercepted the message would think it
was simply a word processing file of the Bible and would ignore it. Be
creative!
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M 10/17/05
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HW due:
Two reading assignments as described below. Reading notes and questions from
both are required.
First, read this
article concerning digital audio and PCM. Most of this is a review of
topics already discussed in class. You should be able to understand 80% or
90% of this article. Take a few reading notes and prepare questions for
Monday’s class discussion.
OK, so now we understand (mostly) how digital audio can be encoded as digital
data. But how do we transmit it wirelessly? In other words, how do we use the
1’s and 0’s of our data to modulate
a carrier wave so that it can be transmitted and then demodulated at the receiver’s end to recreate a stream of 1’s and
0’s?
There are 3 answers. Two of them we have already discussed in class: ASK
(amplitude-shift keying) uses AM technology, and FSK (frequency-shift keying)
uses FM technology. However, neither of these techniques is used much in
practice. The third method is called PSK (phase-shift keying).
The second part of your assignment is to read this difficult article
concerning PSK. Most of this article will probably be incomprehensible to
you, which means that you will have to skim it, looking for recognizable
parts. Do not simply give up and say, “Forget this!” Part of my duty as a
teacher is to prepare you for college, where you will frequently be forced to
read textbooks and journal articles that are way over your head. You might as
well start practicing now.
Pay special attention to the first two paragraphs (total of 5 bulleted items)
under the heading “Introduction.” Read those paragraphs very carefully, over
and over if necessary. The rest of the article you may read more casually.
Don’t worry; you are not expected to understand all the higher math contained
therein.
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T 10/18/05
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Because Form VI is on
retreat today, there is no additional HW due. However, the rest of the class
will meet today to review all topics in Unit 0x30, plus endianness, in
preparation for tomorrow’s quiz.
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W 10/19/05
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HW due:
Please read the first half of this chapter
on MP3. There is much fascinating information here, although much of it will
not be tested until we get to the unit on compression. Reading notes are
required, as always.
The unit quiz originally scheduled for today has been postponed until
Thursday because of the need for an additional day of review.
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Th 10/20/05
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Unit Quiz
on Audio (topics 0x31–0x3E, plus
endianness). Note that HDR, high definition radio, has not been covered yet.
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F 10/21/05
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HW due:
Read this
article on data compression. You should find most it to be readable. Make
a list of specific questions as part of your reading notes. [Note: The original
link I posted seems to be a bit flaky. The text is essentially the same
in both places.]
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M 10/24/05
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HW due:
Read this additional article
on data compression. Focus most closely on §§1.1 and 1.2. Read those two
sections very carefully. You may read §1.3, §1.5, and §1.6 rather quickly,
and you may skip §1.4 altogether. Then answer the following questions:
1. Which is better, lossy or lossless compression?
2. What does LZW stand for?
3. What does data compression remove? (You may wish to refer to Friday’s
reading assignment also.)
In class: Data compression preliminaries. Correction: I accidentally stated
that 0x1A is the ESC character. Actually, 0x1B is the ESC character. Sorry
for the confusion.
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T 10/25/05
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HW due:
1. Skim this
article about the Unicode standard and pp. 111-112 in the textbook. Write
at least one sentence of reading notes from each.
2. Design a scheme for RLE compression of a short all-uppercase Unicode text
file. Assume that the original file is stored in Unicode format (2 bytes per
character, where the first byte is always 0x00 for simple English text
files). Refer to the table on p. 110, which gives the first 256 Unicode
characters. In Unicode, capital A is 0x0041, capital B is 0x0042, and so on.
In your scheme, you must clearly define the following:
(a) how you will store “normal” characters (for example, as 6 bits, 8 bits,
16 bits, or whatever)
(b) the escape character or escape code you will use
(c) how you will indicate a repeat count
(d) how you will indicate the character to be repeated, if different from
part (a)
(e) how you will indicate the escape code if it should happen to occur as
text within your file
Because uppercase text characters come from the ASCII codes 0x20 through 0x5F
only (see table on p. 110), you may choose to represent a normal or repeated
character—questions (a) and (d) above—as a 6-bit code instead of a full byte.
This will allow you to achieve a substantially better compression ratio.
However, if you do this, you will need to figure out how to adapt your 6-bit
code so that the conversion between Unicode/ASCII and your 6-bit code is
straightforward. Also, in parts (b) and (c), you would simplify matters
considerably if you used an escape code and a repeat count that were sized to
match. In other words, do not use a full 8-bit escape code and an 8-bit or a
16-bit repeat count if your character codes are 6 bits.
3. Use your scheme to practice compressing and decompressing your text file.
4. How many bytes did you save?
5. Compute the compression ratio. Show your work.
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W 10/26/05
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HW due: Do
a better job on the assignment that was due yesterday. In other words, make
the reading notes that were required, and when you design your RLE scheme,
you must answer all of the questions posed. Compression ratio is generally
defined as (original size – compressed size)/(original size), expressed as a
percentage.
I have updated the course outline in
order to reduce the scope of the course somewhat.
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Th 10/27/05
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HW due:
Read this article about faxes
in general and this
article about CCITT (ITU) protocols. Then answer the following questions.
1. How old is the basic technology behind faxing?
2. Why do fax machines scan quickly when a page is blank or nearly blank, and
much more slowly when a page is crowded with text or densely packed
illustrations?
3. What is a protocol?
4. What was the CCITT? What is it called today?
5. What protocols does the ITU define other than fax protocols?
6. What fax protocol(s) are currently in use?
7. What is meant by the baud rate of a protocol? Is it the same as a bit
rate? (You will have to follow one of the links in the second article to
answer this question.)
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F 10/28/05
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HW due:
Read this
article concerning the “psychoacoustic” compression used by MP3. Then
answer the following questions.
1. Are the tradeoffs made in MP3 compression worth it?
2. Which of the various tradeoffs in MP3 are least audible to you personally?
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F 10/28/05
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HW due:
Read this
article concerning the “psychoacoustic” compression used by MP3. Then
answer the following questions.
1. Are the tradeoffs made in MP3 compression worth it?
2. Which of the various tradeoffs in MP3 are least audible to you personally?
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M 10/31/05
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Unit Quiz
on Compression (topics 0x41-0x4F),
excluding 0x48 and 0x4E. We will cover those two topics during the next unit
on digital video. Note: Because
people had so much trouble with endianness on the last quiz, topic 0x29 will
be re-quizzed. Also, be sure that you can compute compression ratios
accurately. With regard to the formula (original – compressed)/original, you
should either memorize it or store it in your calculator. Some sample
problems and answers are shown below.
1. Write the number 0x0005234FC0AB in (a) big-endian format and (b)
little-endian format.
2. Uncompressed digital audio (WAV format) uses 16 bits per sample and a
sampling rate of 44.1 KHz. Calculate the data requirement per minute, in MB.
3. As described in the Friday
10/28 assigned reading, there are several different MP3 bit rates that
provide tradeoffs between file size and quality. For each of the standard MP3
bit rates (160 kbps, 128 kbps, 96 kbps, and 64 kbps), compute the compression
ratio in (a) in XX:1 ratio style and (b) percentage style.
4. Consult p. 5 from the Friday
10/28 assigned reading. Suppose that a 3 KHz tone (the frequency where
human hearing is most acute) is just barely audible at a power level of 1.75
microwatts. That power level will be different for different people, of
course, but suppose for the sake of this question that our test subject needs
1.75 microwatts under certain test conditions. According to the chart, what
would the power requirement be for a 12 KHz tone to be just barely audible to
our test subject?
Solutions
1.(a) 0005234FC0AB [no change!] (b)
ABC04F230500 [first byte last, last byte first]
2. sampling rate · bit depth = 44,100 · 16 bits per sample = 44,100 · 2 bytes
per sample = 88,200 bytes
Divide by 1024 to get 86.133 KB/second.
Double (since 2 channels) to get 172.266 KB/second.
Multiply by 60 (since 60 seconds in a
minute) to get 10,336 KB/minute, rounded to nearest KB.
Divide by 1024 (since 1024 KB in a MB) to
get approximately 10.09 MB/minute as the answer.
3.(a) Note: Throughout this
problem, we use the figure of 10.09 MB/min. obtained in question #2.
160 kbps format: 160 kbps = 20,000
bytes/second (since 8 bits to a byte) = 1,200,000 bytes/min.
Divide
by 1024 to get 1171.875 KB/min.
Divide
by 1024 (since 1024 KB in a MB) to get 1.1444 MB per minute.
Compression
ratio » 10.09/1.1444 » 8.8:1.
[In
the article, this figure was rounded to 9:1.]
128 kbps format: Scale everything from
previous example by the factor 128/160.
Data
rate » .91552 MB per minute.
(This is 1.1444 · 128/160.)
Compression
ratio » 10.09/.91552 » 11.02:1.
[In
the article, this figure was rounded to 11:1.]
96 kbps format: Scale everything from 160
kbps example by the factor 96/160.
Data
rate » .68664 MB per minute.
(This is 1.1444 · 96/160.)
Compression
ratio » 10.09/.68664 » 14.7:1.
[In
the article, this figure was rounded to 15:1.]
64 kbps format: Scale everything from
previous example by the factor 64/96, or simply 2/3.
Data
rate » .45776 MB per minute.
(This is .68664 · 2/3.)
Compression
ratio » 10.09/.45776 » 22.04:1.
[In
the article, this figure was rounded to 22:1.]
(b)
160 kbps format: 160 kbps = 20,000
bytes/second (since there are 8 bits to a byte)
Uncompressed
stereo audio: 44,100 samples · 2 bytes/sample · 2 channels.
Uncompressed
data requirement = 44,100 · 2 · 2 = 176,400 bytes/second.
Compression
= (original – compressed)/original
=
(176,400 – 20,000)/176,400
» .8866
» 89%.
128 kbps format: 128 kbps = 16,000
bytes/second (since there are 8 bits to a byte)
Compression
= (original – compressed)/original
=
(176,400 – 16,000)/176,400
» .909297
» 91%.
96 kbps format: 96 kbps = 12,000
bytes/second (since there are 8 bits to a byte)
Compression
= (original – compressed)/original
=
(176,400 – 12,000)/176,400
» .93197
» 93%.
64 kbps format: 64 kbps = 8,000
bytes/second (since there are 8 bits to a byte)
Compression
= (original – compressed)/original
=
(176,400 – 8,000)/176,400
» .9546
» 95.5%.
4. According to the chart, the threshold of audibility for a 12 KHz tone is
up 20 dB from the 0 dB reference level. Since 20 dB means a power factor of
100, the 12 KHz tone must be at 175 microwatts. (The abbreviation is
175 mW.)
Incidentally, 3 KHz is near the upper end of a piano keyboard, and 12 KHz is
2 octaves higher, beyond the range of the piano. There is no note on the
piano exactly at 3 KHz, which is a frequency about halfway between F-sharp
and G in the piano’s highest octave.
It is no accident that babies scream in the 3 KHz range, since that is where
their parents’ hearing is most sensitive!
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