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.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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