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Multipath interference

In some situations, an electromagnetic wave can propagate directly from one place to another. For instance, when aradio signal from a spacecraft is transmitted back to Earth, the vacuum of space guarantees that the wave will arrivemore or less intact (though greatly attenuated by distance). Often, however, the wave reflects, refracts, or diffracts,and the signal arriving is quite different from the one that was sent.

These distortions can be thought of as a combination of scaled and delayed reflections of the transmitted signal, which occurwhen there are different propagation paths from the transmitter to the receiver. Between two transmission towers, for instance, the paths may include one alongthe line-of-sight, reflections from the atmosphere, reflections from nearby hills, and bounces from a field or lake betweenthe towers. For indoor digital TV reception, there are many (local)time-varying reflectors, including people in the receiving room, nearby vehicles, and the buildings of an urban environment. [link] , for instance, shows multiple reflections that arrive after bouncing off a cloud, after bouncing offa mountain, and others that are scattered by multiple bounces from nearby buildings.

The received signal may be a combination of several copies of the original transmitted signal, each with a different attenuation and delay.
The received signal may be a combination of several copies of the original transmitted signal, eachwith a different attenuation and delay.

The strength of the reflections depends on the physical properties of the reflecting surface, while the delay of thereflections is primarily determined by the length of the transmission path. Let s ( t ) be the transmitted signal. If N delays are represented by Δ 1 , Δ 2 , ... , Δ N , and the strengths of the reflections are h 1 , h 2 , ... , h N , then the received signal r ( t ) is

r ( t ) = h 1 s ( t - Δ 1 ) + h 2 s ( t - Δ 2 ) + ... + h N s ( t - Δ N ) .

As will become clear in "Convolution in Time: It's What Linear Systems Do" , this model of the channel has the form of a linear filter(since the expression on the right hand side is a convolution of the transmitted signal and the h i 's). This is shown in part (a) of [link] . Since this channel model is a linear filter,it can also be viewed in the frequency domain, and part (b) shows its frequency response.When this is combined with the BPF and the spectrum of the signal (shown in (c)), the result is the distorted spectrumshown in (d).

(a) The channel model Equation 4 as a filter. (b) The frequency response of the filter. (c) An idealized BPF and the spectrum of the signal. The product of (b) and (c) gives (d), the distorted spectrum at the receiver.
(a) The channel model [link] as a filter. (b) The frequency response of the filter. (c) An idealized BPF andthe spectrum of the signal. The product of (b) and (c) gives (d), the distorted spectrum at the receiver.

What can be done?

If the kinds of distortions introduced by the channel are known (or can somehow be determined), then thebandpass filter at the receiver can be modified in order to undo the effects of the channel. This can beseen most clearly in the frequency domain, as in [link] . Observe that the BPF is shaped (part (d)) to approximately invert the debilitatingeffects of the channel (part (a)) in the frequency band of the signal and to remove all the out-of-band frequencies.The resulting received signal spectrum (part (e)) is again a close copy of the transmitted signal spectrum, in stark contrast tothe received signal spectrum in [link] where no shaping was attempted.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
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Crow Reply
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RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
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Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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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
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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
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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biomolecules are e building blocks of every organics and inorganic materials.
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sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian 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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