# 0.10 Wavelet-based signal processing and applications  (Page 12/13)

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Energy concentration is one of the most important properties for low bitrate transform coding. Suppose for the sample quantization step size $T$ , we have a second set of basis that generate less significant coefficients. The distribution of the significant map indicators is moreskewed, thus require less bits to code. Also, we need to code less number of significant values, thus it may require less bits. In the mean time, asmaller $M$ reduces the second error term as in  [link] . Overall, it is very likely that the new basis improves the rate-distortionperformance. Wavelets have better energy concentration property than theFourier transform for signals with discontinuities. This is one of the main reasons that wavelet based compression methods usually out perform DCTbased JPEG, especially at low bitrate.

## Improved wavelet based compression algorithms

The above prototype algorithm works well [link] , [link] , but can be further improved for its various building blocks [link] . As we can see from [link] , the significant map still has considerable structure, which could be exploited.Modifications and improvements use the following ideas:

• Insignificant coefficients are often clustered together. Especially, they often cluster around the same location across severalscales. Since the distance between nearby coefficients doubles for every scale, the insignificant coefficients often form a tree shape, as we cansee from Figure: Discrete Wavelet Transform of the Houston Skyline, using ${\psi }_{D{8}^{\text{'}}}$ with a Gain of $\sqrt{2}$ for Each Higher Scale . These so called zero-trees can be exploited [link] , [link] to achieve excellent results.
• The choice of basis is very important. Methods have been developed to adaptively choose the basis for the signal [link] , [link] . Although they could be computationally very intensive, substantial improvement canbe realized.
• Special run-length codes could be used to code significant map and values [link] , [link] .
• Advanced quantization methods could be used to replace the simple scalar quantizer [link] .
• Method based on statistical analysis like classification, modeling, estimation,and prediction also produces impressive result [link] .
• Instead of using one fixed quantization step size, we can successively refine the quantization by using smaller and smaller stepsizes. These embedded schemes allow both the encoder and the decoder to stop at any bit rate [link] , [link] .
• The wavelet transform could be replaced by an integer-to-integer wavelet transform, no quantization is necessary, and the compression islossless [link] .

## Why are wavelets so useful?

The basic wavelet in wavelet analysis can be chosen so that it is smooth , where smoothness is measured in a variety of ways [link] . To represent $f\left(t\right)$ with $K$ derivatives, one can choose a wavelet $\psi \left(t\right)$ that is $K$ (or more) times continuously differentiable; the penalty for imposing greater smoothness in this senseis that the supports of the basis functions, the filter lengths and hence the computational complexity all increase. Besides, smooth wavelet basesare also the “best bases” for representing signals with arbitrarily many singularities [link] , a remarkable property.

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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