<< Chapter < Page Chapter >> Page >

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

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing and digital filter design (draft)' conversation and receive update notifications?

Ask