Show that the simple binary coding is
inefficient.
Find an unequal-length codebook for this sequence
that satisfies the Source Coding Theorem. Does yourcode achieve the entropy limit?
How much more efficient is this code than the
simple binary code?
Source compression
Consider the following 5-letter source.
Letter
Probability
a
0.4
b
0.2
c
0.15
d
0.15
e
0.1
Find this source's entropy.
Show that the simple binary coding is
inefficient.
Find the Huffman code for this source.
What is its average code length?
Speech compression
When we sample a signal, such as
speech, we quantize the signal's amplitude to a set ofintegers. For a
-bit
converter, signal amplitudes are represented by
integers. Although these integers could be represented
by a binary code for digital transmission, we shouldconsider whether a Huffman coding would be more
efficient.
Load into Matlab the segment of speech contained
in
y.mat . Its sampled values lie in the
interval (-1, 1). To simulate a 3-bit converter, we useMatlab's round function to create quantized amplitudes
corresponding to the integers
[0 1 2 3 4 5 6
7] .
y_quant = round(3.5*y + 3.5);
Find the relative frequency of occurrence of quantized
amplitude values. The following Matlab program computesthe number of times each quantized value occurs.
for n=0:7;
count(n+1) = sum(y_quant == n);end;
Find the entropy of this source.
Find the Huffman code for this source. How
would you characterize this source code inwords?
How many fewer bits would be used in
transmitting this speech segment with your Huffmancode in comparison to simple binary coding?
Digital communication
In a digital cellular system, a signal bandlimited to 5
kHz is sampled with a two-bit A/D converter at itsNyquist frequency. The sample values are found to have
the shown relative frequencies.
Sample
Value
Probability
0
0.15
1
0.35
2
0.3
3
0.2
We send the bit stream consisting of
Huffman-coded samples using one of the two
depicted signal sets .
What is the datarate of the compressed
source?
Which choice of signal set maximizes the
communication system's performance?
With no error-correcting coding, what
signal-to-noise ratio would be needed for your chosensignal set to guarantee that the bit error probability
will not exceed
?
If the receiver moves twice as far from the transmitter(relative to the distance at which the
error rate was obtained), how does the performance change?
Signal compression
Letters drawn from a four-symbol alphabet have the
indicated probabilities.
Letter
Probability
a
1/3
b
1/3
c
1/4
d
1/12
What is the average number of bits necessary to
represent this alphabet?
Using a simple binary code for this alphabet, a
two-bit block of data bits naturally emerges. Find anerror correcting code for two-bit data blocks that
corrects all single-bit errors.
How would you modify your code so that the
probability of the letter
being confused with the
letter
is minimized? If
so, what is your new code; if not, demonstrate that thisgoal cannot be achieved.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?