# 7.16 Dwt application - de-noising

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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.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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