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(a) The frequency response of the channel. (b) The spectrum of the signal. (c) The product of (a) and (b) which is the spectrum of the received signal. (d) A BPF filter that has been shaped to undo the effect of the channel. (e) The product of (c) and (d), which combine to give a clean representation of the original spectrum of the signal.
(a) The frequency response of the channel. (b) The spectrum of the signal. (c) The product of (a) and (b)which is the spectrum of the received signal. (d) A BPF filter that has been shaped to undo the effectof the channel. (e) The product of (c) and (d), which combine to give a clean representation of the originalspectrum of the signal.

Thus, filtering in the receiver can be used to reshape the received signal within the frequency band of the transmissionas well as to remove unwanted out-of-band frequencies.


Another kind of corruption that a signal may encounter on its journey from the transmitter to the receiver is called“fading,” where the frequency response of the channel changes slowly over time. This may be caused because the transmission pathchanges. For instance, a reflection from a cloud might disappear when the cloud dissipates, an additional reflection mightappear when a truck moves into a narrow city street, or in a mobile device such as a cell phone the operatormight turn a corner and cause a large change in the local geometry of reflections. Fading may also occurwhen the transmitter and/or the receiver are moving. The Doppler effect shifts the frequencies slightly,causing interferences that may slowly change.

Such time-varying problems cannot be fixed by a single fixed filter; rather, the filter must somehow compensatedifferently at different times. This is an ideal application for the adaptive elements of [link] , though results from the study of linear filters will becrucial in understanding how the time variations in the frequency response can be represented as time-varyingcoefficients in the filter that represents the channel.

Linear systems: linear filters

Linear systems appear in many places in communication systems. The transmission channel is often modeled as a linear systemas in [link] . The bandpass filters used in the front end toremove other users (and to remove noises) are linear. Lowpass filters are crucial to the operation of the demodulatorsof Chapter  [link] . The equalizers of Chapter  [link] are linear filters that are designed during the operation of the receiveron the basis of certain characteristics of the received signal.

Time invariant linear systems can be described in any one of three equivalent ways:

  • The impulse response h ( t ) is a function of time that defines the output of a linear system when the input is an impulse (or δ ) function. When the input to the linear system is more complicated than a single impulse, the output can becalculated from the impulse response via the convolution operator.
  • The frequency response H ( f ) is a function of frequency that defines how the spectrum of the input is changed into the spectrum of the output. The frequency responseand the impulse response are intimately related: H ( f ) is the Fourier transform of h ( t ) .
  • A linear difference equation with constant coefficients (such as [link] ) shows explicitly how the linear system can be implemented and canbe useful in assessing stability and performance.

This chapter describes the three representations of linear systems and shows how they interrelate. The discussion beginsby exploring the δ -function, and then showing how it is used to define the impulse response. The convolution property of theFourier transform then shows that the transform of the impulse response describes how the system behaves in termsof the input and output spectra, and so it is called the frequency response. The final step is to show how the action of the linear system can be redescribedin the time domain as a difference (or as a differential) equation. This is postponed to Chapter  [link] .

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
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
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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.
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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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