# 0.6 Digital filtering and the dft  (Page 8/13)

 Page 8 / 13

## 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 ${h}_{1}\left[k\right]$ is the impulse response of a bandpass filter that passes only frequencies between100 and 200 Hz, and ${h}_{2}\left[k\right]$ is the impulse response of a bandpass filter that passes only frequencies between500 and 600 Hz, then $h\left[k\right]={h}_{1}\left[k\right]+{h}_{2}\left[k\right]$ passes only frequencies between 100 and 200 Hz or between 500 and 600 Hz.Similarly, if ${h}_{l}\left[k\right]$ is the impulse response of a lowpass filter that passes all frequencies below 600 Hz, and ${h}_{h}\left[k\right]$ is the impulse response of a highpass filter that passes all frequencies above 500 Hz, then $h\left[k\right]={h}_{l}\left[k\right]*{h}_{h}\left[k\right]$ is a bandpass filter that passes only frequencies between 500 and 600 Hz, where $*$ represents convolution.

#### Questions & Answers

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
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
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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
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 did you get the value of 2000N.What calculations are needed to arrive at it
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