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Rate-changing appears expensive computationally, since for both decimation and interpolation the lowpass filter is implementedat the higher rate. However, this is not necessary.

Interpolation

For the interpolator, most of the samples in the upsampled signal are zero, and thus require no computation. ( [link] )

For m L m L m L and p m L ,
x 1 m m N 1 N 2 h L p m y m k N 1 L N 2 L g p k x 0 m L k
g p n h L n p Pictorially, this can be represented as in [link] .
These are called polyphase structures , and the g p n are called polyphase filters .

Computational cost

If h m is a length- N filter:
  • No simplification: N T 1 L N T 0 computations sec
  • Polyphase structure: L L N 1 T 0 o computations sec N T 0 where L is the number of filters, N L is the taps/filter, and 1 T 0 is the rate.
Thus we save a factor of L by not being dumb.
For a given precision, N is proportional to L , (why?), so the computational cost does increase with the interpolationrate.
Can similar computational savings be obtained with IIR structures?

Efficient decimation structures

We only want every M th output, so we compute only the outputs of interest. ( [link] ) x 1 m k N 1 N 2 x 0 L m k h k

Polyphase decimation structure

The decimation structures are flow-graph reversals of the interpolation structure. Although direct implementation ofthe full filter for every M th sample is obvious and straightforward, these polyphasestructures give some idea as to how one might evenly partition the computation over M cycles.

Efficient l/m rate changers

Interpolate by L and decimate by M ( [link] ).

Combine the lowpass filters ( [link] ).
We can couple the lowpass filter either to the interpolator or the decimator to implement it efficiently ( [link] ).
Of course we only compute the polyphase filter output selected by the decimator.

Computational cost

Every T 1 M L T 0 seconds , compute one polyphase filter of length N L , or N L T 1 N L M L T 0 N M T 0 multiplies second However, note that N is proportional to L M .

Questions & Answers

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
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
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
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
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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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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