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Practical filtering

Filtering can be viewed as the process of emphasizing or attenuating certain frequencies within a signal. Linear time-invariant filtersare common because they are easy to understand and straightforward to implement. Whether in discreteor continuous time, a LTI filter is characterized by its impulse response (i.e., its output whenthe input is an impulse). The process of convolution aggregates the impulse responses from all theinput instants into a formula for the output. It is hard to visualize the action of convolution directlyin the time domain, making analysis in the frequency domain an important conceptual tool.The Fourier transform (or the DFT in discrete time) of the impulse response gives the frequency response,which is easily interpreted as a plot that shows how much gain or attenuation (or phase shift) each frequency undergoesby the filtering operation. Thus, while implementing the filter in the time domainas a convolution, it is normal to specify, design, and understand it in the frequency domain as a point-by-pointmultiplication of the spectrum of the input and the frequency response of the filter.

In principle, this provides a method not only of understanding the action of a filter, but also of designinga filter. Suppose that a particular frequency response is desired, say one that removes certain frequencies, while leaving othersunchanged. For example, if the noise is known to lie in one frequencyband while the important signal lies in another frequency band, then it is natural to design a filter that removes thenoisy frequencies and passes the signal frequencies. This intuitive notion translates directly into amathematical specification for the frequency response. The impulse response can then be calculated directlyby taking the inverse transform, and this impulse response defines the desired filter.While this is the basic principle of filter design, there are a number of subtleties that can arise, and sophisticated routines areavailable in M atlab that make the filter design process flexible, even if they are not foolproof.

Filters are classified in several ways:

  • Lowpass filters (LPF) try to pass all frequencies below some cutoff frequency and remove all frequencies above.
  • Highpass filters try to pass all frequencies above some specified value and remove all frequencies below.
  • Notch (or bandstop) filters try to remove particular frequencies (usually in a narrow band) and to pass all others.
  • Bandpass filters try to pass all frequencies in a particular range and to reject all others.

The region of frequencies allowed to pass through a filter is called the passband , while the region of frequencies removed is called the stopband . Sometimes there is a region between where it is relativelyless important what happens, and this is called the transition band .

By linearity, more complex filter specifications can be implemented as sums and concatenations of the above basic filter types.For instance, if h 1 [ k ] is the impulse response of a bandpass filter that passes only frequencies between100 and 200 Hz, and h 2 [ k ] is the impulse response of a bandpass filter that passes only frequencies between500 and 600 Hz, then h [ k ] = h 1 [ k ] + h 2 [ k ] passes only frequencies between 100 and 200 Hz or between 500 and 600 Hz.Similarly, if h l [ k ] is the impulse response of a lowpass filter that passes all frequencies below 600 Hz, and h h [ k ] is the impulse response of a highpass filter that passes all frequencies above 500 Hz, then h [ k ] = h l [ k ] * h h [ k ] is a bandpass filter that passes only frequencies between 500 and 600 Hz, where * represents convolution.

Questions & Answers

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 to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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