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Wavelets are an alternative tool for signal decomposition using orthogonal functions. Unlike basic Fourier analysis, wavelets do not lose completely time information, a feature that makes the technique suitable for applications where the temporal location of the signal’s frequency content is important.One of the fields where wavelets have been successfully applied is data analysis. In particular, it has been demonstrated that wavelets produce excellent results in signal denoising i.e. the removal of noise from an unknown signal. Shrinkage methods for noise removal, first introduced by Donoho in 1993, have led to a variety of approaches combining wavelets with probabilistic concepts leading to new efficient denoising procedures. This work presents a summary of basic methods for noise removal. Their main features and limitations are discussed and a comparison study is developed. A signal contaminated with Gaussian additivenoise is used as testbed for the methods. Conclusions on the performance of the methods, based upon computational efficiency and number of terms used for decomposition, are presented.

Signal Denoising using Wavelets-based Methods Ioannis Kougioumtzoglou, Isaac Hernandez-Fajardo, Georgios Evangelatos

and Xin Ming.

George R. Brown School of Engineering, Rice University

Houston, TX - USA

Introduction

The basic idea which lies behind wavelets is the representation of an arbitrary function as a combination of simpler functions, generated as scaled and dilated versions of a particular oscillatory “mother” function.

Late Jean Morlet, a geophysical engineer, introduced the term “wavelet” while attempting to analyze signals related to seismic data. The mathematical formulation of the wavelet transform and its inverse was rigorouslyestablished by Grossman and Morlet citep( ). Since then, ideas from diverse scientific fields have resulted in developing wavelets into a powerful analysis tool.

The term wavelet is often used to denote a signal located in time with a concentrated amount of energy citep( ). This “mother” wavelet is used to generate a set of “daughter”functions through the operations of scaling and dilation applied to the mother wavelet. This set forms an orthogonal basis that allows, using inner products,to decompose any given signal much like in the case of Fourier analysis. Wavelets, however, are superior to Fourier analysis for time information is not lost when moving to the frequency domain. This property makes them suitable forapplications from diverse fields where the frequency content of a signal as well as the energy's temporal location is valuable.

The wavelets application of interest for this work is their use for data analysis, specifically for signals denoising. Denoising stands for the process of removing noise, i.e unwanted information, present in an unknown signal.The use of wavelets for noise removal was first introduced by Donoho and Johnstone citep( ). The shrinkage methods for noise removal, first introduced by Donoho citep( ), have led to a variety of approaches to signal denoising.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Elec 301 projects fall 2008. OpenStax CNX. Jan 22, 2009 Download for free at http://cnx.org/content/col10633/1.1
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