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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

what is variations in raman spectra for nanomaterials
Jyoti Reply
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
yes that's correct
Professor
I think
Professor
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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