# 0.10 Wavelet-based signal processing and applications  (Page 6/13)

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## Noise reduction capacity

It has been shown that the thresholding of wavelet coefficients has near optimal noise reduction property for many classes of signals [link] . The thresholding scheme used in the approximation in the proposed FAFT algorithm is exactly the hard thresholding schemeused to denoise the data. Soft thresholding can also be easily embedded in the FAFT. Thus the proposed algorithm also reduces the noise whiledoing approximation. If we need to compute the DFT of noisy signals, the proposed algorithm not only can reduce the numerical complexity but alsocan produce cleaner results.

## Summary

In the past, the FFT has been used to calculate the DWT [link] , [link] , [link] , which leads to an efficient algorithm when filters are infinite impulse response (IIR). Inthis chapter, we did just the opposite – using DWT to calculate FFT. We have shown that when no intermediate coefficients are dropped and noapproximations are made, the proposed algorithm computes the exact result, and its computational complexity is on the same order of the FFT; i.e., $O\left(N{log}_{2}N\right)$ . The advantage of our algorithm is two fold. From the input data side, the signals are made sparse by the wavelet transform, thusapproximation can be made to speed up the algorithm by dropping the insignificant data. From the transform side, since the twiddle factors of the new algorithm have decreasingmagnitudes, approximation can be made to speed up the algorithm by pruning the section of the algorithm which corresponds to the insignificant twiddle factors. Since wavelets are an unconditionalbasis for many classes of signals [link] , [link] , [link] , the algorithm is very efficient and has built-in denoising capacity.An alternative approach has been developed by Shentov, Mitra, Heute, and Hossen [link] , [link] using subband filter banks.

## Nonlinear filtering or denoising with the dwt

These methods are based on taking the discrete wavelet transform (DWT) of a signal, passing this transform through a threshold, which removes thecoefficients below a certain value, then taking the inverse DWT, as illustrated in [link] . They are able to remove noise and achieve high compression ratios because of the “concentrating" ability ofthe wavelet transform. If a signal has its energy concentrated in a small number of wavelet dimensions, its coefficients will be relatively largecompared to any other signal or noise that has its energy spread over a large number of coefficients. This means that thresholding or shrinkingthe wavelet transform will remove the low amplitude noise or undesired signal in the wavelet domain, and an inverse wavelet transform will thenretrieve the desired signal with little loss of detail. In traditional Fourier-based signal processing, we arrange our signals such that thesignals and any noise overlap as little as possible in the frequency domain and linear time-invariant filtering will approximately separatethem. Where their Fourier spectra overlap, they cannot be separated. Using linear wavelet or other time-frequency or time-scale methods, onecan try to choose basis systems such that in that coordinate system, the signals overlap as little as possible, and separation is possible.

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
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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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