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In signal processing, a filter removes unwanted parts of the signal, such as random noise, or extracts the useful parts of the signal, such as the components lying within a certain frequency range.

In signal processing, there are many instances in which an input signal to a system contains extra unnecessary content or additional noise which can degrade the quality of the desired portion. In such cases we may remove or filter out the useless samples. For example, in the case of the telephone system, there is no reason to transmit very high frequencies since most speech falls within the band of 400 to 3,400 Hz. Therefore, in this case, all frequencies above and below that band are filtered out. The frequency band between 400 and 3,400 Hz, which isn’t filtered out, is known as the passband, and the frequency band that is blocked out is known as the stopband.

FIR, Finite Impulse Response, filters are one of the primary types of filters used in Digital Signal Processing. FIR filters are said to be finite because they do not have any feedback. Therefore, if you send an impulse through the system (a single spike) then the output will invariably become zero as soon as the impulse runs through the filter.

How to characterize digital fir filters

There are a few terms used to describe the behavior and performance of FIR filter including the following:

  • Filter Coefficients - The set of constants, also called tap weights, used to multiply against delayed sample values. For an FIR filter, the filter coefficients are, by definition, the impulse response of the filter.
  • Impulse Response – A filter’s time domain output sequence when the input is an impulse. An impulse is a single unity-valued sample followed and preceded by zero-valued samples. For an FIR filter the impulse response of a FIR filter is the set of filter coefficients.
  • Tap – The number of FIR taps, typically N, tells us a couple things about the filter. Most importantly it tells us the amount of memory needed, the number of calculations required, and the amount of"filtering"that it can do. Basically, the more taps in a filter results in better stopband attenuation (less of the part we want filtered out), less rippling (less variations in the passband), and steeper rolloff (a shorter transition between the passband and the stopband).
  • Multiply-Accumulate (MAC) – In the context of FIR Filters, a"MAC"is the operation of multiplying a coefficient by the corresponding delayed data sample and accumulating the result. There is usually one MAC per tap.

General types of filter

There are a couple different basic filter responses. Each will have a unique frequency response based on its cut-off frequency, the number of taps used, its roll off, and amount of ripple. The various attributes describing a filter may be seen in the following diagram:

This figure demonstrates an FIR low pass filter with 40 taps.
Reducing the number of taps used in the filter will reduce the number of calculations to process in the signal, however, the quality of the filtering will suffer. Rippling will become more sever, the rolloff will be less steep, and the passband will be less accurate. This may be seen in the following diagram where fewer number of taps were used.
Using only 11 taps has degraded the filter from figure 1.
All filters may be categorized by the section of the frequency spectrum that they alter. The following figures depict some of the basic types of digital filters:
High pass filters remove low frequency content.
Bandpass filters allow a section in the middle of the spectrum to remain.
Stopband filters remove a section in the middle of the spectum.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
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
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Microcontroller and embedded systems laboratory. OpenStax CNX. Feb 11, 2006 Download for free at http://cnx.org/content/col10215/1.29
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