# 13.3 Matched filter detector  (Page 4/4)

 Page 4 / 4

For example, below we have a simplified example of Frequency Shift Keying (FSK) where we having the following coding 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] :

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] :

[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 ${s}_{1}\left(t\right)$ from example 1 to represent the bits. ${s}_{1}\left(t\right)$ represents 0, while $-{s}_{1}\left(t\right)$ represents 1.

$0\implies (b=1)\implies ({s}_{1}(t)=s(t))$ for $0\le t\le T$

$1\implies (b=-1)\implies ({s}_{2}(t)=-s(t))$ for $0\le t\le T$

${X}_{t}=\sum_{i=-P}^{P} {b}_{i}s(t-iT)$

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

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.

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

## 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.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!