<< Chapter < Page Chapter >> Page >
SNR = 10 log 10 P signal P noise dB size 12{ ital "SNR"="10"`"log" rSub { size 8{"10"} } left ( { {P rSub { size 8{ ital "signal"} } } over {P rSub { size 8{ ital "noise"} } } } right )~ ital "dB"} {}

where P signal and P noise represent the values for the signal power and noise power respectively.

At the receiver, the original signal arrives with an added noise component. Communication engineers use signal processing algorithms in the form of filters to minimize the power of the noise that is present in the received noisy signal while seeking to retain as much of the power of the original signal as possible. Such algorithms are based on the premise that although random, noise may well fall into different regions of angular frequency in the electromagnetic spectrum than the signal itself. Thus, frequency selective filters can be utilized to increase the signal-to-noise ratio.

Suppose that we represent the signal-to-noise ratio at the input to the signal processing algorithm as SNR in and that at its output as SNR out . For a good designs, SNR out will be significantly higher that that of SNR in . This increase in signal-to-noise ratio results in superior performance and more reliable communication of information.

Question: A signal with power 30 W is sent through a noisy communication channel. The noise introduced by the communication channel has an associated power of 5 W. What is the signal-to-noise ratio of the noisy signal that is received from the communication channel in decibels?

Solution: We can find the SNR by substituting the appropriate values for the parameters into equation (4)

SNR = 10 log 10 P signal P noise = 10 log 10 30 W 5 W = 10 log 10 ( 6 ) = 7 . 78 dB size 12{ ital "SNR"="10"`"log" rSub { size 8{"10"} } left ( { {P rSub { size 8{ ital "signal"} } } over {P rSub { size 8{ ital "noise"} } } } right )="10"`"log" rSub { size 8{"10"} } left ( { {"30"~W} over {5~W} } right )="10"`"log" rSub { size 8{"10"} } \( 6 \) =7 "." "78"~ ital "dB"} {}

Question: Consider the noisy signal described in Example 2. Suppose that a signal processing filter is applied to it. The filter reduces the noise power by 95% while it reduces the signal power by only 10%. What is the signal-to-noise ratio of the filtered output?

Solution: The amount of signal power present in the filtered output is 30 W – 0.1 (30 W) or 27 W. The amount of noise power present in the filtered output is 5 W – 0.95 (5 W) or 0.25 W.

The signal-to-noise ratio of the filtered output is

SNR = 10 log 10 27 W 0 . 25 W = 10 log 10 ( 108 ) = 10 2 . 03 = 20 . 33 dB size 12{ ital "SNR"="10"`"log" rSub { size 8{"10"} } left ( { {"27"~W} over {0 "." "25"~W} } right )="10"`"log" rSub { size 8{"10"} } \( "108" \) ="10" cdot 2 "." "03"="20" "." "33"~ ital "dB"} {}

We see that the primary result obtained by the application of the signal processing filter is to raise the signal to noise ratio from 7.78 dB to 20.33 dB . This represents an increase in SNR of 20.33 – 7.78 dB = 12.55 dB . Along with this increase in SNR, one would observe an increase in reliable communication of information.

Transient response (exponential decay)

The transient response of a circuit is response of a circuit that is expressed as a function of time. Determining the transient response of a circuits is important in that knowledge of the transient response reveals how a circuit will behave whenever perturbations arise, such as the opening or closing of a switch.

Let us examine the RC circuit present in the figure below

Switched RC circuit.

This circuit is called an RC circuit in that it contains a resistor and a capacitor.

The switch is open for values of time ( t ) less than 0. Thus for negative values of time there is no current flow. Because there is no current flow, the voltage across the resistor ( v ( t )) is zero. The capacitor is initially charged. The initial voltage across the capacitor (V 0 ) is 10 V.

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
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
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
Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Math 1508 (laboratory) engineering applications of precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11337/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Math 1508 (laboratory) engineering applications of precalculus' conversation and receive update notifications?