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Data and Signals
Hello, we will be continuing our discussion on Computer Networks and InternetProtocols. We were discussing on Physical Layer phenomenons. As I mentioned earlierthat physical layer is the lowest layer in the OSI and TCP/IP protocol suite. In some ofthe cases in physical layers are kept apart from the actual network protocols suitebecause of the reason that, that it is primarily more concerned about the communicationbetween the devices or underlining media right. And as we understand that there can bedifferent sort of consideration that can be wireless and wired and type of things and Ineed finally, I need a media to transfer the data from one system to another right.Now, incidentally the mostly the mediums are mostly are carry signals throughelectromagnetic waves so to say and those are analog. So, is our digital thing needs to beconverted to analog to convert that to transmit right. We have also seen that, thepredominant connectivity because, this requires a physical infrastructure to be in placeright, if I want to communicate across the world or across India also then I require aphysical infrastructure which will work at the back bone right.And typically the physical infrastructure which is somewhat readily available with us isour telephone network right; though the bandwidth may not be that high, butnevertheless these days with the fiber etcetera you can get higher bandwidth but, that thetelephone our telephone network is the basic framework of the things.And there are several service providers which able to which give services. So, our oneconsideration that if I can hook this telephone network then I can travel using thisnetwork and then at the other end get the data out of it right. So, again we are talkingabout the physical connects, physical layer consideration right, now in order to have thisto push it to this telephone network and type of things, we have seen there is a we requirea device called modulator at the at our end at that the source end. And a demodulator atthe other end if the communication is this way or in other way or rather we requiremodem or modems at the at the devices devices right.
Also we have seen that we the network interface card which comes with every system tosupport the network connectivity is primarily have both physical and data link layerproperties right. So, they have a physical layer consideration; that means, the you canconnect RJ45 like our standard ethernet cables or wireless connectivity or fiberconnectivity or in some cases coax connectivity etcetera right. So, these are the physicalconnectivity, so in other sense there should be a data link layer should be converting inthem into appropriate signals to travel push the data across through the media right.And when it travels to the media that the whatever the means consideration from themedia medium comes into play it will be there right, like there could be attenuation dueto noise and type of things or transmitting to a larger area a larger distance and so and soforth. So, those things will be there. So those will be there and those are consideration, itvaries from medium to medium.The things which is true for fiber are not true for not always true that particular true forcable or wireless and type of things right. So, again I just to reiterate that when we aretalking about physical layer, we are considering the other layers are as there in theirplace. The same thing like the routing protocols works the TCP that transport layerprotocols works at the suppose to work application works at they are suppose to work.So, when you open a your email or a some network application at the upper layer thespeed may vary right, due to the different type of physical wired connection, wirelessconnection, fiber connection and type of things speed may vary, but nevertheless theapplication for the application it is a communication path which is available right. So,this physical layer connectivity is the what we say that the last mile or not only that thatbottom most layer of the connectivity etcetera and it dictates heavily that what should bethe bandwidth, what should be the throughput, to some extent reliability and so and soforth.So, this lectures what we are trying to do we are trying to look at different physical layerproperties which may affect our networking capacity right. And also little bit of try to notthat go into deep into the communication, but little bit of consideration of thecommunications which may help us understanding our systems right, so that is ourconsideration. So, today also we will look at some of the features and maybe in next
lecture we will see some of or few more features, where the physical layer phenomenoncome into picture.(Refer Slide Time: 06:12)
So, as we are discussing now, so 2 things coming now and then is the data and signalright. So, analog and data and signal so what is data, what is signal and how things aregoing on.So, whatever we are generating in our systems are or working with is the data which hasprimarily to manifestation 1 or 0 right. So, that is a binary representation of the thingsand I generate the data for my purpose and I do not care that how it things to be there;whereas, at the backbone as you are telling at the backbone it is primarilyelectromagnetic wave need to be converted to some signal. So, data can be analog ordigital, analog data are continuous, take continuous values, digital data whereas adiscrete state and take discrete values right. So, to be to transmit data must betransformed to electromagnetic signals as the media is can carry that electromagneticsignal primarily.So, data can be as I told data analog or digital, signals also can be analog or digital rightand analog signals can have infinite number of values in the range, a digital signal canhave only a limited number of values within a particular range. In a data communicationwe commonly use periodic analog signals and non periodic digital signals right. So, it isthe periodic analog signals and non periodic digital signals; that is the things which we
consider mostly we will see that what are the things. So, this is a typical example of aanalog signals and this is a typical scenario of a digital signal. So, we have digital things.So, I can consider that the positive has some positive voltage negative voltage, I can havedifferent level at the positive or negative type of things.(Refer Slide Time: 08:09)
So, signals if you see what they have? They have a amplitude primarily periodic signalthey have a amplitude. They have some frequency and they have a phase right. So,frequency means how what is the after what time period is returns repeats the signalwhereas, the amplitude is the highest value it attains on the on the positive side or the onthe negative side the minimum value it attains and the things that dictates (Refer Time:08:45) the amplitude of the things. And phase we will see that how much it is driftedfrom the origin so to say later on we will see that how things will be there, so at whattime it is static.So, signals with same phase and frequency, but different amplitudes. So, this is starting atthe same time that is 0 and 0, having same frequency repeatability this and this whereas,they have different amplitude right. So, frequency and periodicity or periods areinversely proportional. So, frequency equal to 1 by T. So, it repeats f every T timedurations of frequency will be 1 by T or T equal to 1 f. Signals with same amplitude andphase, but different frequency may or happens. Like this signal as repeatability is higher
than this like here 6 periods in 1 second, here 12 periods in 1 second, so here frequencyis typically 12 hertz here 6 hertz right, so hertz is the unit of frequency you know.(Refer Slide Time: 09:54)
So, sine in this case, sine of the wave with same amplitude frequency, but with differentphase, so it is (Refer Time: 10:01) different at start time right. So, it is a sine wave is atdifferent, so this is say amplitude and frequency on these 3 waves are same, but theyhave different start time. So, these are the 3 thing. Now one interesting thing you seefrom here, so if I some way add this 3 sine wave to make a composite wave right, I have3 waves, I have a adder or which adds. So, what does add means, that any point of timeyou see that what is the signal strength at 0, here it is say plus 5 or plus 10, here it is also0, so the I in my output here I put this as a 10 if this value I if we consider as 10.Again at this particular junction or some junction, I can basically put this vertical linesand calculate that how much value etcetera there and then some of the things and say thisis my output signal because, this composite added signal right. Had it been all in thephase, same phase same amplitude etcetera the things could have gone little higher at thething because, the same repeatability.
(Refer Slide Time: 11:17)
Now this way, I can have a composite signal type of things like time domain ascomposite signal like it may generate end up in making a composite periodic signal right,so we will see that.(Refer Slide Time: 11:24)
Now, we see there are 2 type of representation; the time domain and frequency domainplots of the sine wave like in this case, it is a time domain plots with time it is changingthis peak value is 5 volt 5. Whereas, we can have a frequency domain thing, how many
frequencies are there in here, only one frequency 6 giga 6 hertz, so it is repeatability is 6hertz.So, here also it is one frequency and I know that what is amplitude of the thing right, sohere the amplitude of the thing. Now if I have 2 sine wave, one with a rather here we arehaving 3 waves, 1 with frequency 0; that is flat, one with frequency 8 and one withfrequency 16, so blue, then this pink and green and then I can represent them into 3things right like if it is a 0 frequency, there is no repeatability, so it is a dc thing, it is nonot repeatable it is a constant thing and that is at 15. Whereas, frequency with 8 is thatpink is at 10 and frequency with 16 that is a green is at this right.Now, in this case again if I want to make them composite, so any point of time I go onadding what are the different values and do the composite signal right like typically I canI may have a some sort of a composite signal like this and which is again repeatable, itmay not be repeatable also means it may be non periodic. But in this case periodicsignals we are having because there is a inherent periodicity in the whole thing right.So, there are in this typically if that is some half if you do in a graph paper also you cancalculate. So, typically how many frequencies are there, there are 3 frequencies, if it is asum we made it so 0 8 and 16 hertz right. So, there are a techniques like using Fouriertransforms like that and we can basically (Refer Time: 13:35) composite signal is there,we can deduce it to this signal right ok. So, that is a way of representation of the thingsok.
(Refer Slide Time: 13:51)
So, so now we see that non periodic composite signal. It can be the signal created by amicrophone or a telephone set, where the when a word or two are pronounced like, so itis I am doing analog talking with a in a microphone or telephone set. So, those things canbe composite can be so, when 2 words are pronounced in this case the composite signalcannot be periodic otherwise, it is repeatability of the whole things will come up usuallythe conversation is a in information action. So, repeatability is much less and things arethey are not periodic they are non periodic. So, bandwidth of a composite frequencydifference between the highest and the lowest frequency obtained from the things.Now, if I look at that composite frequency, it may vary from 0 that is not no signal to 4kilohertz that is our range of vocal and type of things also that what we see that range ofour telephone plane or pots telephone line is also typically in this range. So, that is thething and I can have any frequency within this range right. So, these are this is more of athis sort of a structure I can have different frequencies at this range and it is a compositefrequency.
(Refer Slide Time: 15:08)
So, bandwidth of a composite signal is the difference between the highest and the lowestfrequency of the thing right. So, it is bandwidth is given by the highest and the lowestfrequency for that matter in a signal the highest frequency and lowest frequency is themagnitude of the things right. Why we are breaking our heads on this, because yourcommunication channel may not allow all frequency batch right. So, it has a ownproperty right, it has own materialistic material property and then based on that allfrequencies may not be allowed. So, it may allow a set of frequency, if it is some of thechannels may allow in wider range, it may be allowing this range of frequencies in thethings.So, your data signal or the data which you are generating at the at the end points, shouldbe able to put through this channel only right or I need to know that how much thechannel can allow and capacity type of things right. So, that is why we need to study thathow is this type of bandwidth consideration those are coming up in terms of thissignaling or communication.
Data and Signals - Part 2
Now, if you come to the digital signal it addition to being represented by a analog signal,information can all be also be represented by a digital signal; for example, one canencoded as a positive voltage, 0 can be encoded as a means as a 0 voltage, so I can have0 and 1 digital signal can have more than 2 levels, even it can have 2 levels, 1 is here it isonly 2 levels right with 1 and 0. It can have more than more than two levels rightdifferent levels, so I can have 1 1 1 0 0 1 1 0 0 0 and type of things right.So, this is more than 2 levels that the more data is packed within the thing right. So, in aeffectively I can make more data communicate within that pack thing. So, it gives us abetter output right, but not always feasible we will see.
(Refer Slide Time: 17:22)
So, a digital signal has 8 level, how many bits are needed per level. We can calculate thebits as with a formula that log 2 8 equal to 3 bits. So, if it is eight level so I can have 3bits 2 to the power 3 is 8 right. Each signal level is represented by 3 bits. So, bit rate isthe number of bits, since in one second expressed in bits per second right. So, assume weneed to download the text documents at the rate 100 pages per minute. So, if that is myconsideration what is the required bit rate of the channel so, if the page is an average of24 lines with 80 characters each line, we assume that one character requires 8 bitrepresentation. The bit rate is 100 into 8 into 80 into 8 equal to 1 point so that is 1.63mbps. So, that is the bit rate for this type of things right.So, it is a very flat way of calculation, there will be lot of other consideration, butnevertheless we can have a come to a thing.
(Refer Slide Time: 18:33)
Similarly, a digitized voice as we see in somewhere it is digitized at a 4 kilohertz and weneed to sample the twice the highest frequency then we can have a bit rate. Similarlywhat is the bit rate of HTTP, we can calculate with the rate of what is the reference timeand so and so forth.(Refer Slide Time: 18:50)
So, this way I can calculate the bit rate. There is a concept of bit length, the bit length isthe distance of 1 bit occupies in the transmission medium right. So, bit length is thedistance 1 bit occupies in a transmission medium. So, bit length equal to propagation
delay into bit duration, so how much duration is there along with the propagation speedis give me the bit length.(Refer Slide Time: 18:15)
So, time and frequency domain periodic and non periodic digital signal, so this is therepresentation of this if I have a periodic signal and if you have a non periodic digitalsignal then the frequencies are both actually, both cases it goes to infinity right, so end ofthe things. But in order to reconstruction I may not require those frequencies whichcontribute very less into the things right. So, there are different consideration from thecommunication point of view, there are consideration like take that which harmonics ofthe things will be there or harmonics and type of thing, how many you can go to gaveeffective reconstruction. So, both bandwidths are infinite, but the periodic signals hasdiscrete frequencies, which referred as the non periodic signal has continuous frequencyright.
(Refer Slide Time: 20:02)
So, there is another consideration comes out when we try to transmit data over a channelright, what we say it is a transmission impairment right. Signal travel throughtransmission media which are not perfect, the imperfection cause signal impairmentright. This means that the signal at the beginning of the media is not at the same otherthings. So, you send something and it is something got in not the same thing. Thetypically 3 categories of things are there, one is the attenuation, one is distortion, anotheris the noise. So, this type of 3 type of situations which causes this term impairment.(Refer Slide Time: 20:42)
In case of attenuation loss of energy, when the signal and the simple or composite travelthrough the media, it losses some of its energy in the in overcoming the resistance of themedia. To compensate this loss the amplifier are used to or signal regenerator I used tosay instead of amplifier are used to regenerate the signal right, so it has the degrader aregenerator.Suppose a signal travels through a transmission media and its power is reduced to half.So, it was P and now it is P by 2 or sorry P1 and now P2 is half of P1. In this case, theattenuation loss power can be calculated as like this right. So, a loss of 3 db or minus 3db is equivalent of losing half of the power. That is why that that 3 db loss etcetera wecoming to play that is a 50 percent power is lost.(Refer Slide Time: 21:35)
Another means another source of impairment is that distortion, signal changes its form orshape right. Distortion can occur in composite signal made of different frequencies. So,each what happened each signal component has its own propagation speed through amedium and therefore, its own delay arriving at the destination.So, differences in the delay is create a difference in the phase which in turns not exactlythe same as the periodic periodicity of the periodic duration. So, let us see, I send acomposite signal which has number of frequency component incidentally, because of thischannel characteristics that is the channel properties the different frequencies getdifferent type of say delayed of reaching the things. So, there are no attenuation per say
(Refer Time: 22:34) but there are different delay and while it reaches the thing then whathappened it is now it is at different time duration or period duration.So, when you reconstruct you cannot reconstruct the same composite signal or in othersense you do not get back the same data. So, it if it is a here you see it was in phase datalike this is same time in phase data when we made a composite signal due to impairmentit receive there you decompose the signal it goes for a impairment like there is a shifthere with respect to this. So, there is a phase shifting phase shifting we will go for aproblem of the overall data.(Refer Slide Time: 23:19)
And finally, we have this noise as the impairment right. Several type of noise such asthermal noise, induced noise, crosstalk impulse noise may corrupt the signal right, sothere can be different noise. So, thermal noise is a random motion of electrons in wirewhich creates an extra signal not originally sent by the transmitter. So, that it is thethermal noise. Induced noise comes from source, such as motor or appliances fromdifferent source has induced noise so that is induced in the thing.Crosstalk is the effect of 1 wire on the other, 1 wire acts as a sending antenna other as thereceiving antenna. So it is a crosstalk when two things are moving, a two things are innearby location and there can be impulse noise is a spike signal with very high frequencywith very short time that comes from the power lines lightning etcetera. So, there is aimpulse and the impulse noise.
So, these are the different category of noise which distorts or creates problem in thesignal right. So, in other sense there are impairment and there is there will be a challengein reconstructing the things. So, what we see, this noise also plays a important role infaithful delivery of the signal at the other end. Now these are the things which are thereright, we need to with respective this we need to send data and type of things.So, there is one side there are lot of development or things are going on that, how moreimproved channels can be created like, you get a more faithful transmission when you doyou work with something called in fiber type of channels and type of and then otherthings that whether, I can better way encode or modulate the data. So, that the, so it canbe sent through even to some extent not so good channels and type of things.(Refer Slide Time: 25:30)
Another metric come into play or we listen now and then is a signal to noise ratio. Tofind the theoretical bit rate, we need to know the ratio of the signal power to the noisepower. So, average signal power by average noise power that is important, so get theSNR type of thing. So, average signal and average noise power are considered as thesemay change with time right. A high SNR means the signal is less corrupted by the noiseor a low SNR means the signal is more corrupted by noise. So, this is the considerationmeans that that plays a important role right. Since SNR is the ratio of 2 powers, it isoften described in decibel and SNR dB defined as SNR equal to 10. So, there is a typo at
10 log 10 SNR, so it should have been in the same line. So, similarly I can calculate aSNR and SNR dB using this right.(Refer Slide Time: 26:42)
Data rate limits. So, data rate depends on primarily on 3 factors; one is the bandwidthavailable how much bandwidth you are available. Level of signals, what are the levels ofsignals it is a 2 level, 4 level what are the levels of signals. And quality of the channellevel of noise right. So, what is the quality of the channel right like, the fiber some fibercable there will be a different quality aspect then if you have a wired cable and type ofthings. So, quality of the channel or the level of noise plays a important role.Increasing the level of the signal may reduce the availability reliability of the system. So,if I go on increasing the level of the signal because, we say that if I go on increasing thething it is more compact and I can (Refer Time: 27:32) but it hurts the reliability of thethings, more granular things more finer things there will be more likely chance ofdisruption or distortion and type of things.So, there are 2 theoretical formulas which help us in estimating that what should be mybit rate and type of things. So, one is Nyquist for noiseless channel, another is Shannonproposed by Shannon for noisy channel. So, we just see quickly that what they say theNyquist bit rate formula defines the theoretical maximum bit rate is the 2 into bandwidthinto log 2 base 2 L is the number of levels right. So, there is that is the theoretical thingin a noiseless channel.
(Refer Slide Time: 28:17)
So, consider the noiseless channel with bandwidth three 100 hertz transmitting a signalwith 2 signal level. The maximum bit level can be calculated as 2 into 3000 into log 2base 2 equal to 6000 right.Consider the same channel transmitting a signal with four signal level. So, instead of oneit has a four signal levels. So, what it goes on, it basically say 2 into this it should be12000 bps. So, changing the signal level, I can go up in the bandwidth right.(Refer Slide Time: 28:55)
So, for noisy channel that we have that Shannon’s capacity, in reality we cannot havenoiseless channel right, so there will be some form of noise or not the channel is alwaysnoisy. In long back in 1944, the Shannon introduced a formula for Shannon capacity todetermine the theoretical highest data rate for the noisy channel. So, what is the highestdata rate it can support, so bandwidth into log base 2 1 plus SNR that is the highest.(Refer Time: 29:24).Like consider an extremely noisy channel in which the value of the noise to signal tonoise ratio is almost 0 right. So, that is all you made number of levels etcetera, but thenoise is so high, the SNR value is nearing 0 right, so very low signal. Say, channelcapacity C equal to B log 2 1 by SNR and then what we can find out that irrespective ofwhat whatever you do finally, it end ups with the 0 only a 0 there is no transmission ispossible, so much noise is there.This means the capacity of the channel is 0 regardless of the bandwidth in other wordswe cannot retrieve any data through this channel right. So, this is the way it gives somelimitation of the means boundary of the things that what is the highest level you canreach with this type of channel and type of things.(Refer Slide Time: 30:28)
So, if you see for practical purpose when SNR is very high, there is we assume that theSNR plus 1 is also almost the same like if you have a huge SNR. So, practically 1 plusSNR is same or in other sense, the theoretical channel capacity can be expressed as C
equal to B into SNR dB by 3 right, so based on the things. We have a channel with 1megahertz bandwidth, the SNR of this channel is 63, what are the appropriate bit rate andsignal levels? Correct so, this is the thing we want to find out.Like first we use Shannon’s formula to find out the upper limit right. So, it is B log 2 1plus SNR and something 6 Mbps, so that is the upper limit. Now the upper limit thebetter performance we choose something lower that is 4 Mbps for example, and use theNyquist formula to find out the level. So, putting the Nyquist formula we found out thelevel equal to 4.So, somehow means if we try to look at the summarize the thing, so what we use theShannon capacity gives us the upper limit, the Nyquist formula give us the signalchannel. Now see our this basic consideration helps us in finding the what could be mychannel capacity, what amount of rate we can get, this may allow me to plan somethingthat what should be the data transmission time etcetera and type of things right that,which is very much needed for different consideration.So, let us with this thing that basic fundamental way calculation that and this digitalsignal digital data and signal and analog data and signals considerations, how we canhave some sort of estimate of approximate bit rate and the signal levels that will we haveseen and this will help us in estimating separate thing. So, with this let us conclude today,we will be continuing our discussion in our next lecture next lecture on this physicallayer.Thank you.
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