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For example, below we have a simplified example of Frequency Shift Keying (FSK) where we having the following coding for '1' and '0':

Frequency Shift Keying for '1' and '0'.

Based on the above coding, we can create digital signals based on 0's and 1's by putting together the above two"codes" in an infinite number of ways. For this example we will transmit a basic 3-bit number, 101, which isdisplayed in [link] :

The bit stream "101" coded with the above FSK.

Now, the signal picture above represents our original signal that will be transmitted over some communicationsystem, which will inevitably pass through the "communications channel," the part of the system that willdistort and alter our signal. As long as the noise is not too great, our matched filter should keep us from havingto worry about these changes to our transmitted signal. Once this signal has been received, we will pass the noisysignal through a simple system, similar to the simplified version shown in [link] :

Block diagram of matched filter detector.

[link] basically shows that our noisy signal will be passed in (we will assume that it passes inone "bit" at a time) and this signal will be split and passed to two different matched filter detectors. Eachone will compare the noisy, received signal to one of the two codes we defined for '1' and '0.' Then this valuewill be passed on and whichever value is higher ( i.e. whichever FSK code signal the noisy signal most resembles) will be the value that thereceiver takes. For example, the first bit that will be sent through will be a '1' so the upper level of the blockdiagram will have a higher value, thus denoting that a '1' was sent by the signal, even though the signal may appearvery noisy and distorted.

The interactive example below supposes that our transmitter sends 1000 bits, plotting how many of those bits are received and interpreted correctly as either 1s and 0s, and also keeps a tally of how many are accidentally misinterpreted. You can play around with the distance between the energy of the "1" and the "0" (discriminability), the degree of noise present in the channel, and the location of the criterion (threshold) to get a feel for the basics of signal detection theory.

Let's use a matched filter to find the "0" bits in a simple signal.

Let's use the signal s 1 ( t ) from example 1 to represent the bits. s 1 ( t ) represents 0, while - s 1 ( t ) represents 1.

0 b 1 s 1 t s t for 0 t T

1 b -1 s 2 t s t for 0 t T

X t i P P b i s t i T

The matched filter output clearly shows the location of the "0" bits.

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One of the first, and more intriguing forms of communication that used the matched filter concept was radar. A known electromagnetic signal is sent out by a transmitter at a target and reflected off of the target back to the sender with a time delay proportional to the distance between target and sender. This scaled, time-shifted signal is then convolved with the original template signal, and the time at which the output of this convolution is highest is noted.

This technology proved vital in the 1940s for the powers that possessed it. A short set of videos below shows the basics of how the technology works, its applications, and its impact in World War 2.

History of radar

See the video in [link] for an analysis of the same basic principle being applied to adaptive cruise control systems for the modern car.

Video on radar-based adaptive cruise control from The Science Channel.

Matched filter demonstration

Interact (when online) with a Mathematica CDF demonstrating the Matched Filter. To Download, right-click and save target as .cdf.

Matched filter summary

As can be seen, the matched filter detector is an important signal processing application, rich both in theoretical concepts and in practical applications. The matched filter supports a wide array of uses related to pattern recognition, including image detection, frequency shift keying demodulation, and radar signal interpretation. Despite this diversity of purpose, all matched filter applications operate in essentially the same way. Every member of some set of signals is compared to a target signal by evaluating the absolute value of the inner product of the the two signals after normalization. However, the signal sets and result interpretations are application specific.

Questions & Answers

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
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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
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
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
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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