# 0.6 Digital filtering and the dft  (Page 12/13)

 Page 12 / 13

## Filter design

This section gives an extended explanation of how to use M atlab to design a bandpass filter to fit a specified frequency response with a flat passband. The same procedure(with suitable modification) also works for the design of other basic filter types.

A bandpass filter is intended to scale, but not distort, signals with frequencies that fall within the passband, and to rejectsignals with frequencies in the stopband. An ideal, distortionless response for the passbandwould be perfectly flat in magnitude, and would have linear phase (corresponding to a delay).The transition band from the passband to the stopband should be as narrow as possible.In the stopband, the frequency response magnitude should be sufficiently small and the phase is of no concern.These objectives are captured in [link] . Recall (from [link] ) for a real $w\left(t\right)$ that $|W\left(f\right)|$ is even and $\angle W\left(f\right)$ is odd, as illustrated in [link] .

M atlab has several commands that carry out filter design. The firpm command Some early versions of M atlab use remez instead of firpm . provides a linear phase impulse response (with real, symmetric coefficients $h\left[k\right]$ ) that has the best approximation of a specified (piecewise flat) frequencyresponse. There are many possible meanings of the word “best”; for the firpm algorithm, “best” is defined in terms of maintaining an equal ripple in the flat portions. The syntax of the firpm command for the design of a bandpass filter as in [link] is     b = firpm(fl,fbe,damps) which has inputs fl , fbe , and damps , and output b .

• fl specifies (one less than) the number of terms in the impulse response of the desired filter. Generally, more is betterin terms of meeting the design specifications. However, larger fl are also more costly in terms of computation and in terms ofthe total throughput delay, so a compromise is usually made.
• fbe is a vector of frequency band edge values as a fraction of the prevailing Nyquist frequency.For example, the filter specified in [link] needs six values: the bottom of the stopband (presumably zero), the top edge of the lower stopband(which is also the lower edge of the lower transition band), the lower edge of the passband, the upper edge of the passband,the lower edge of the upper stopband, and the upper edge of the upper stopband (generally the last value will be 1).The transition bands must have some nonzero width (the upper edge of the lower stopband cannot equalthe lower passband edge) or M atlab produces an error message.
• damps is the vector of desired amplitudes of the frequency response at each band edge. The length of damps must match the length of fbe .
• b is the output vector containing the impulse response of the specified filter.

The following M atlab script designs a filter that mimics [link] : fbe=[0 0.24 0.26 0.74 0.76 1];  % frequency band edges as a%   fraction of the Nyquist frequency damps=[0 0 1 1 0 0];            % desired amplitudes at band edges fl=30;                          % filter sizeb=firpm(fl,fbe,damps);          % b is the designed impulse response freqz(b)                        % plot frequency response to check design 

  [link] . Observe that the stopband is about 14 dB lower than thepassband, a marginal improvement over the naive lowpass filter of [link] , but the design is much flatter in the pass band. The “equiripple” nature of this filteris apparent in the slow undulations of the magnitude in the passband.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!