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where H 1 is ( M + 1 ) by ( N + 1 ) , h 1 is length- ( L - M ) , and H 2 is ( L - M ) by N . The lower ( L - M ) equations are written

0 = h 1 + H 2 a *

or

h 1 = - H 2 a *

which must be solved for a * . The upper M + 1 equations of [link] are written

b = H 1 a

which allows the calculation of b .

If L = N + M , H 2 is square. If H 2 is nonsingular, [link] can be solved exactly for the denominator coefficients in a * , which are augmented by the unity term to give a . From [link] , the numerator coefficients in b are found. If H 2 is singular [link] and there are multiple solutions, a lower order problem can be posed. Ifthere are no solutions, the approximation methods must be used.

Note that any order numerator and denominator can be prescribed. If the filter is in fact an FIR filter, a is unity and a * does not exist. Under these conditions, [link] states that b n = h n , which is one of the cases of FIR frequency sampling covered [link] . Also note that there is no control over the stability of the filter designed by this method.

Summary

In this section, an interpolation design method was developed and analyzed. Use of the DFT converted the frequency- domainspecifications to the time domain. A matrix partitioning allowed uncoupling the solution for the numerator from the solution of thedenominator coefficients. The use of the DFT prevents the possibility of unequally spaced frequency samples as was possiblefor FIR filter design. The solution of simultaneous equations would allow unequal spacing which is not as troublesome as with the FIRfilter because IIR filters are usually of lower order.

The frequency-sampling design of IIR filters is somewhat more complicated than for FIR filters because of the requirement that H 2 be nonsingular. As for the FIR filter, the samples of the desired frequency response must satisfy the conditions to insurethat h n are real. The power of this method is its ability to interpolate arbitrary magnitude and phase specification. In contrastto most direct IIR design methods, this method does not require any iterative optimization with the accompanying convergence problems.

As with the FIR version, because this design approach is an interpolation method rather than an approximation method, theresults may be poor between the interpolation points. This usually happens when the desired frequency-response samples are notconsistent with what an IIR filter can achieve. One solution to this problem is the same as for the FIR case [link] , the use of more frequency samples than the number of filter coefficients and the definition of an approximation errorfunction that can be minimized. There is no simple restriction that will guarantee stable filters. If the frequency-response samplesare consistent with an unstable filter, that is what will be designed.

Discrete least-squared equation-error iir filter design

In order to obtain better practical filter designs, the interpolation scheme of the previous section is extended to give anapproximation design method [link] . It should be noted at the outset that the method developed in this section minimizes anequation-error measure and not the usual frequency-response error measure.

Questions & Answers

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
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Digital signal processing and digital filter design (draft). OpenStax CNX. Nov 17, 2012 Download for free at http://cnx.org/content/col10598/1.6
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