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For problems where the signal and noise spectra are such that a specific frequency ω o that separates the desired passband from the desired stopband can be specified but specific separate transition band edges, ω p < ω s , cannot, we formulate [link] a design method where the pass and stop band ripple sizes, δ p and δ s are specified along with the separation frequency, ω o . The algorithm described below will interpolate the specified ripple sizes exactly (asthe HOS algorithm does) but will allow exact control over the location of ω o by not requiring maximum ripple. Although not set up to be an optimization procedure, it seems to minimize the transition band width.This formulation suits problems where there is no obvious transition band (“don't care band") having no signal or noise energy to be passed orrejected.

The optimal Chebyshev filter designed with this new algorithm is generally not extra ripple and, therefore, will have an extremalfrequency at ω = 0 or ω = π as the Parks-McClellan formulation does. Because we are trying to minimizing the transition bandwidth, we do not specify both the edges, ω p and ω s , but only one of them or, perhaps, the center of the transition band, ω o . This results in R equations which are used to find the R coefficients a ( n ) . The equations are formulated by adding the alternating peak pass and stop band ripples to the A d in [link] and not having the special last column of C nor the unknown δ appended to a as was done by Parks and McClellan in [link] . The resulting equation to be iterated in our new exchange algorithm has theform

A d ( ω 0 ) A d ( ω 1 ) A d ( ω o ) A d ( ω s + 1 ) A d ( ω R - 1 ) + δ p - δ p 0 δ s ± δ s = cos ( ω 0 0 ) cos ( ω 0 1 ) cos ( ω 0 ( R - 1 ) ) cos ( ω 1 0 ) cos ( ω 1 1 ) cos ( ω 1 ( R - 1 ) ) cos ( ω o ) cos ( ω o 1 ) cos ( ω o ( R - 1 ) ) cos ( ω s + 1 0 ) cos ( ω s + 1 1 ) cos ( ω s + 1 ( R - 1 ) ) cos ( ω R - 1 0 ) cos ( ω R - 1 1 ) cos ( ω R - 1 ( R - 1 ) ) a ( 0 ) a ( 1 ) a ( 2 ) a ( ( R - 1 ) ) .

The exchange algorithm is done as by Parks and McClellan finding new extremal frequencies at each iteration, but with fixed ripple sizes in bothpass and stop bands. This new algorithm reduces the transition band width as done by the Hofstetter, Oppenheim, and Siegel method but with thetransition band location controlled and without requiring the extra ripple solution. Note that any transition band frequency could be fixed. Itcould be A d ( ω o ) = 1 / 2 to fix the half-power point. It could be A d ( ω p ) = 1 - δ p to fix the pass band edge. Or it could be A d ( ω s ) = δ s to fix the stop band edge.

Extending this formulation and algorithm to the multiple transition band case complicates the problem as the solution may not be unique or may haveanomalous behavior in one of the transition bands. Details of the solution to this problem are given in [link] .

Estimations of, the length of optimal chebyshev fir filters

All of the design methods discussed so far have assumed that N ,the length of the filter, is given as part of the secifications. In many cases,perhaps even most, N is a parameter that we would like to minimize. Often specifications are to meet certain pass and stopband ripplespecifications with given pass and stopband edges and with the shortest possible filter. None of our methods will do that. Indeed, it is notclear how to do that kind of optimization other than by some sort of search. In other words, design a set of filters of different lengthsand choose the one that meet the specifications with minimum length.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
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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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