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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

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.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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