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Say that the DWT for a particular choice of wavelet yields an efficient representation of a particular signal class. Inother words, signals in the class are well-described using a few large transform coefficients.

Now consider unstructured noise , which cannot be eifficiently represented by any transform, includingthe DWT. Due to the orthogonality of the DWT, such noise sequences make, on average, equal contributions to alltransform coefficients. Any given noise sequence is expected to yield many small-valued transform coefficients.

Together, these two ideas suggest a means of de-noising a signal. Say that we perform a DWT on a signal from our well-matched signal class that has been corrupted by additive noise. We expect thatlarge transform coefficients are composed mostly of signal content, while small transform coefficients should be composedmostly of noise content. Hence, throwing away the transform coefficients whose magnitude is less than some small thresholdshould improve the signal-to-noise ratio. The de-noising procedure is illustrated in .

Now we give an example of denoising a step-like waveform using the Haar DWT. In , the top right subplot shows the noisy signal and the top left shows itDWT coefficients. Note the presence of a few large DWT coefficients, expected to contain mostly signal components, aswell as the presence of many small-valued coefficients, expected to contain noise. (The bottom left subplot shows theDWT for the original signal before any noise was added, which confirms that all signal energy is contained within a fewlarge coefficients.) If we throw away all DWT coefficients whose magnitude is less than 0.1, we are left with only thelarge coefficients (shown in the middle left plot) which correspond to the de-noised time-domain signal shown in themiddle right plot. The difference between the de-noised signal and the original noiseless signal is shown in the bottom right. Non-zero error results from noise contributions to the large coefficients; there isno way of distinguishing these noise components from signal components.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Digital signal processing (ohio state ee700). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10144/1.8
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