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  1. Perfect Reconstruction (i.e., y ( n ) = x ( n ) ).
  2. Usefulness . Clearly this depends on the application. For the subband coding application, the filter frequency responses mightapproximate the ideal responses in [link] . In other applications the filters may have to satisfy other constraints orapproximate other frequency responses.

If the signals and filters are multidimensional in [link] , we have the multidimensional filter bank design problem.

Ideal Frequency Responses in an L-band Filter Bank
Ideal Frequency Responses in an L -band Filter Bank


A transmultiplexer is a structure that combines a collection of signals into a single signal at a higher rate; i.e., it is the dual of a filterbank. If the combined signal depends linearly on the constituent signal, we have a linear transmultiplexer. Transmultiplexers were originally studied in the context of converting time-domain-multiplexed (TDM) signalsinto frequency domain multiplexed (FDM) signals with the goal of converting back to time-domain-multiplexed signals at some later point.A key point to remember is that the constituent signals should be recoverable from the combined signal. [link] shows the structure of a transmultiplexer. The input signals y i ( n ) were upsampled, filtered, and combined (by a synthesis bank of filters)to give a composite signal d ( n ) . The signal d ( n ) can be filtered (by an analysis bank of filters) and downsampled to give a set of signals x i ( n ) . The goal in transmultiplexer design is a choice of filters that ensures perfect reconstruction (i.e., for all i , x i ( n ) = y i ( n ) ). This imposes bilinear constraints on the synthesis and analysis filters. Also,the upsampling factor must be at least the number of constituent input signals, say L . Moreover, in classical TDM-FDM conversion the analysis and synthesis filters must approximate the ideal frequency responses in [link] . If the input signals, analysis filters and synthesis filters are multidimensional, we havea multidimensional transmultiplexer.

Perfect reconstruction—a closer look

We now take a closer look at the set of bilinear constraints on the analysis and synthesis filters of a filter bank and/or transmultiplexerthat ensures perfect reconstruction (PR). Assume that there are L analysis filters and L synthesis filters and that downsampling/upsampling is by some integer M . These constraints, broadly speaking, canbe viewed in three useful ways, each applicable in specific situations.

  1. Direct characterization - which is useful in wavelet theory (to characterize orthonormality and frame properties),in the study of a powerful class of filter banks (modulated filter banks), etc.
  2. Matrix characterization - which is useful in the study of time-varying filter banks.
  3. z-transform-domain (or polyphase-representation) characterization - which is useful in the design and implementation of (unitary) filter banks and wavelets.

Direct characterization of pr

We will first consider the direct characterization of PR, which, for both filter banks and transmultiplexers, follows from an elementary superpositionargument.

Theorem 38 A filter bank is PR if and only if, for all integers n 1 and n 2 ,

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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