# 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.

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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?
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
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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