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One common application of multirate processing arises in multirate, multi-channel filter banks ( [link] ).

One application is separating frequency-division-multiplexed channels. If the filters are narrowband, the output channelscan be decimated without significant aliasing.

Such structures are especially attractive when they can be implemented efficiently. For example, if the filters are simplyfrequency modulated (by 2 k L n ) versions of each other, they can be efficiently implemented using FFTs!

Furthermore, there are classes of filters called perfect reconstruction filters which are of finite length but from which the signal can be reconstructed exactly (using all M channels), even though the output of each channel experiences aliasing in the decimation step. These types of filterbankshave received a lot of research attention, culminating in wavelet theory and techniques.

Uniform dft filter banks

Suppose we wish to split a digital input signal into N frequency bands, uniformly spaced at center frequencies ω k 2 k N , for 0 k N 1 . Consider also a lowpass filter h n , H ω 1 ω N 0 . Bandpass filters can be constructed which have the frequency response H k ω H ω 2 k N from h k n h n 2 k n N The output of the k th bandpass filter is simply (assume h n are FIR)

x n h k n m 0 M 1 x n m h m 2 k m N y k n
This looks suspiciously like a DFT, except that M N , in general. However, if we fix M N , then we can compute all y k n outputs simultaneously using an FFT of x n m h m : The kth FFT frequency output y k n ! So the cost of computing all of these filter banks outputs is O N N , rather than N 2 , per a given n . This is very useful for efficient implementation of transmultiplexors (FDM to TDM).

How would we implement this efficiently if we wanted to decimate the individual channels y k n by a factor of N , to their approximate Nyquist bandwidth?

Simply step by N time samples between FFTs.

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Do you expect significant aliasing? If so, how do you propose to combat it? Efficiently?

Aliasing should be expected. There are two ways to reduce it:

  1. Decimate by less ("oversample" the individual channels) such as decimating by a factor of N 2 . This is efficiently done by time-stepping by the appropriate factor.
  2. Design better (and thus longer) filters, say of length L N . These can be efficiently computed by producing only N (every L th) FFT outputs using simplified FFTs.

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How might one convert from N input channels into an FDM signal efficiently? ( [link] )

Such systems are used throughout the telephone system, satellite communication links, etc.

Use an FFT and an inverse FFT for the modulation (TDM to FDM) and demodulation (FDM to TDM), respectively.

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
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
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Source:  OpenStax, Digital signal processing: a user's guide. OpenStax CNX. Aug 29, 2006 Download for free at http://cnx.org/content/col10372/1.2
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