# 0.9 Logarithms  (Page 2/4)

 Page 2 / 4
$\text{SNR}=\text{10}{\text{log}}_{\text{10}}\left(\frac{{P}_{\text{signal}}}{{P}_{\text{noise}}}\right)\text{dB}$

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)

$\text{SNR}=\text{10}{\text{log}}_{\text{10}}\left(\frac{{P}_{\text{signal}}}{{P}_{\text{noise}}}\right)=\text{10}{\text{log}}_{\text{10}}\left(\frac{\text{30}W}{5W}\right)=\text{10}{\text{log}}_{\text{10}}\left(6\right)=7\text{.}\text{78}\text{dB}$

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

$\text{SNR}=\text{10}{\text{log}}_{\text{10}}\left(\frac{\text{27}W}{0\text{.}\text{25}W}\right)=\text{10}{\text{log}}_{\text{10}}\left(\text{108}\right)=\text{10}\cdot 2\text{.}\text{03}=\text{20}\text{.}\text{33}\text{dB}$

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

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.

what is variations in raman spectra for nanomaterials
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
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
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
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution  By By By By  By   By