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.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product