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This module covers the fundamentals of Filterbanks and explains why the are very useful in filter design.

Why filterbanks?

Sub-band processing

There exist many applications in modern signal processing where it is advantageous to separate a signal into differentfrequency ranges called sub-bands . The spectrum might be partitioned in the uniform mannerillustrated in , where the sub-band width Δ k 2 M is identical for each sub-band and the band centers areuniformly spaced at intervals of 2 M .

Alternatively, the sub-bands might have a logarithmic spacing like that shown in .

For most of our discussion, we will focus on uniformly spaced sub-bands.

The separation into sub-band components is intended to make further processing more convenient. Some of the mostpopular applications for sub-band decomposition are audio and video source coding (with the goal of efficient storageand/or transmission).

illustrates the use of sub-band processing in MPEG audio coding. There apsychoacoustic model is used to decide how much quantization error can be tolerated in each sub-band while remainingbelow the hearing threshold of a human listener. In the sub-bands that can tolerate more error, less bits are usedfor coding. The quantized sub-band signals can then be decoded and recombined to reconstruct (an approximateversion of) the input signal. Such processing allows, on average, a 12-to-1 reduction in bit rate while stillmaintaining "CD quality" audio. The psychoacoustic model takes into account the spectral masking phenomenon of the human ear, which says that high energy in one spectral region will limit the ear's ability to heardetails in nearby spectral regions. Therefore, when the energy in one sub-band is high, nearby sub-bands can becoded with less bits without degrading the perceived quality of the audio signal. The MPEG standard specifies32-channels of sub-band filtering. Some psychoacoustic models also take into account "temporal masking" propertiesof the human ear, which say that a loud burst of sound will temporarily overload the ear for short time durations,making it possible to hide quantization noise in the time interval after a loud sound burst.

In typical applications, non-trivial signal processing takes place between the bank of analysis filters and the bank ofsynthesis filters, as shown in . We will focus, however, on filterbank design rather than on the processing that occurs between thefilterbanks.

Our goals in filter design are:

  • Good sub-band frequency separation ( i.e. , good "frequency selectivity").
  • Good reconstruction ( i.e. , y n x n d for some integer delay d ) when the sub-band processing is lossless.

The first goal is driven by the assumption that the sub-band processing works best when it is given access to cleanly separated sub-band signals, while thesecond goal is motivated by the idea that the sub-band filtering should not limit the reconstruction performancewhen the sub-band processing ( e.g. , the coding/decoding) is lossless or nearly lossless.

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
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absolutely yes
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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
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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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