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Quantization errors in an IIR filter structure are filtered by portions of the structure before reaching the output. The total quantization noise variance at the output is the sum of the variances of the individual filtered quantizer noises as seen at the filter output.

Finite-precision effects are much more of a concern with IIR filters than with FIR filters, since the effects are more difficult to analyze andminimize, coefficient quantization errors can cause the filters to become unstable, and disastrous things like large-scale limit cycles can occur.

Roundoff noise analysis in iir filters

Suppose there are several quantization points in an IIR filter structure. By our simplifying assumptions about quantization errorand Parseval's theorem, the quantization noise variance y,i 2 at the output of the filter from the i th quantizer is

y,i 2 1 2 w H i w 2 S S n i w n i 2 2 w H i w 2 n i 2 n h i n 2
where n i 2 is the variance of the quantization error at the i th quantizer, S S n i w is the power spectral density of that quantization error, and H H i w is the transfer function from the i th quantizer to the output point.Thus for P independent quantizers in the structure, the total quantization noise variance is y 2 1 2 i P 1 n i 2 w H i w 2 Note that in general, each H i w , and thus the variance at the output due to each quantizer, is different; for example, the system as seen by a quantizer at theinput to the first delay state in the Direct-Form II IIR filter structure to the output, call it n 4 , is
with a transfer function H 4 z z -2 1 a 1 z a 2 z -2 which can be evaluated at z w to obtain the frequency response.

A general approach to find H i w is to write state equations for the equivalent structure as seen by n i , and to determine the transfer function according to H z C z I A B d .

The above figure illustrates the quantization points in a typical implementation of a Direct-Form II IIRsecond-order section. What is the total variance of the output error due to all of thequantizers in the system?

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By making the assumption that each Q i represents a noise source that is white, independent of the other sources, and additive,

the variance at the output is the sum of the variances atthe output due to each noise source: y 2 i 1 4 y , i 2 The variance due to each noise source at the outputcan be determined from 1 2 w H i w 2 S n i w ; note that S n i w n i 2 by our assumptions, and H i w is the transfer function from the noise source to the output .

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
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
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How can I make nanorobot?
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
how can I make nanorobot?
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.
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