# Introduction

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Introduction to Information and Entropy

In this and the following modules the basic concepts of information theory will be introduced. For simplicity we assume that the signalsare time discrete. Time discrete signals often arise from sampling a time continous signal. The assumption of time discrete signal is valid becausewe will only be looking at bandlimited signals . (Which can, as we know , be perfectly reconstructed).

In treating time discrete signal and their information content we have to distinguish between two types of signals:

• signals have amplitude levels belonging to a finite set
• signals that have amplitudes taken from the real line
In the first case we can measure the information content in terms of entropy , while in the second case the entropy is infinte and we must resort to characterise the source by means of differential entropy .

## Examples of information sources

The signals treated are mainly of a stochastic nature, i.e. the signal is unknown to us.Since the signal is not known to the destination (because of it's stochastic nature), it is then bestmodeled as a random process, discrete-time or continuous time. Examples of information sources that we model as random processes are:

• Digital data source (e.g. a text) can be modeled as a random process.
• Video signals can be modeled as a random process. Such signals are mainly bandlimited toaround 5 MHz (the value depends on the standards used to raster the frames of image).
• Audio signals can be modeled as a random process. Speech is typically between 300 Hz and3400 Hz, see .

Video and speech are analog information signals are bandlimited. Therefore, if sampled faster than two times the highest fequency component, they can be reconstructedfrom their sample values.

A speech signal with bandwidth of 3100 Hz can be sampled at the rate of 6.2 KHz. If the samples are quantized with a 8level quantizer then the speech signal can be represented with a binary sequence with bit rate

$6200\log_{2}8=18600\mathrm{bits/sec}$

The sampled real values can be quantized to create a discrete-time discrete-valued random process.

## The core of information theory

The key observation from the discussion above is that for a reveiver the signals are unknown . It is exact this uncertainty that enables the signalto transmit information. This is the core of information theory:

Information transfer happens when the receiver is unable to know or predict at message before it isreceived.

## Some statistics

Here we present some statistics with the intent of reviewing a few basic concepts and to introduce the notation.

Let X be a stochastic variable. Let $X={x}_{i}$ and $X={x}_{j}$ denote two outcomes of X.

• Dependent outcomes implies: $(X={x}_{i}, X={x}_{j})=(X={x}_{i})({x}_{i}, X={x}_{j})=(X={x}_{j})({x}_{j}, X={x}_{i})$
• Independent outcomes implies $(X={x}_{i}, X={x}_{j})=(X={x}_{i})(X={x}_{j})$
• Bayes' rule: $({x}_{i}, X={x}_{j})=\frac{({x}_{j}, X={x}_{i})(X={x}_{j})}{(X={x}_{i})}$
More about basic probability theory and a derivation of Bayes' rule can be found here .

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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