# 0.9 Logarithms  (Page 2/4)

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

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
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LITNING
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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 .?
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Kyle
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why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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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
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Good
Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution