Analog to Digital ConversionA digital signal is superior to an analog signal because it is more robust to noise and can be easily recovered, corrected and amplified. For this reason, the tendency today is to change an analog signal to digital data. In this section we describe pulse code modulation.

Topic discussed in this section: Pulse code modulation (PCM)

PCMPCM consists of three steps to digitize an analog signal:1.Sampling 2.Quantization3.Binary encodingBefore we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate.Filtering should ensure that we do not distort the signal, remove high frequency components that effect the signal shape.

Components of PCM encoder samplingquantizingencoding11.1100Analog signalPCM encoder Quantized signal PAM signal Digital data

Sampling Analog signal is sampled every Ts seconds.Ts is referred to as the sampling interval.fs= 1/Ts is called the sampling rate or sampling frequency.There are 3 sampling methods:Ideal an impulse at each sampling instantNatural A pulse of short width with varying amplitude Flat top Sample and hold, like natural but with single amplitude value.The process is referred to as pulse amplitude modulation PAM and the outcome is a single with analog (non interger) values.

Analog versus Digital transmissionA continuously varying signal having infinite number of values is called an analog signal.

In analog communications the information transmitted is analog in nature.

Analog communication uses AM FM PAM PWM types of modulation in which pulse or sinusoidal carrier has some characteristics which is varied proportional to the modulating voltage.

4. Analog communication system uses simple circuitry and small band width.

5. Analog communication has high noise level.

Digital data signals are those which can be represented by a finite set of discrete values.

In digital communication the information of any form is converted into digital signal and then transmitted. The digital signals are coded using 1s and 0s.

Digital communication uses PCM where in the information is converted into a series of digits and each digit is represented by a binary code which will represent the approximate amplitude of the signal to be transmitted, at that instance.

Digital transmission has high transmission speed, very low noise and is very efficient.

With the invention of computers which have the ability to serve many input and output devices has made data communications essential.

Introduction to digital communications DIGITAL TRANSMISSION The transmission of digital signals between two or more points in a communication system.Can be binary or any other form of discrete level digital pulses.The original source information may be in digital form or it could be analog signals that have been converted to digital pulses prior to transmission and converted back to analog signals in the receiver.Physical facility : a pair of wires, coaxial cable or optical fiber cables required to interconnect the various points within the system.Digital pulses cannot be propagated through a wireless transmission system such as earths atmosphere or free space (vacuum)Today digital transmission systems are used to carry not only digitally encoded voice and video signals, but also digital source information directly between computers and computer networks.Digital transmission systems use both metallic and optic fiber cables for their transmission medium.

Digital communication introductionThe essence of electronic communications is the transmission, reception and producing of information with the use of electronic circuits.

Information is defined as knowledge of intelligence that is communicated (transmitted or received ) between two or more points .

Digital modulation is the transmission of digitally modulated analog signals (carriers) between two or more points in a communication systems.

The conventional AM, FM, PM are rapidly being replaced with digital modulation systems, such as ease of processing, ease of multiplexing and noise immunity.

The property that distinguishes digital system from analog modulation is the nature of modulating signal. Both use analog carriers to transport the information.

In analog system the information system is analog. Whereas in digital modulation the information is digital which could be computer generated data, or digitally encode analog signals.

Advantages of digital transmissionNoise immunity Inherently less susceptible to interference because it is not necessary to evaluate the precise amplitude, frequency or phase to ascertain its logic condition.Better suited for processing and combining using a technique called multiplexing.Digital signal processing (DSP) is the processing of analog signals using digital methods and includes band limiting the signals with filters, amplitude equalization and phase shifting.Much simpler to store and the transmission rate can be easily changed to adapt different environments and to interface with different types of equipment.More resistant to additive noise.They use signal regeneration rather than signal amplification.Can be transported longer distances than analog signalsSimpler to measure and evaluateEasier to compare the error performance of one digital system to another digital system.Transmission errors can be detected and corrected more easily and more accurate.

Disadvantages of digital signalsThe transmission of digitally encoded analog signals requires significantly more bandwidth than simply transmitting the original analog signal Bandwidth is one of the most important aspects of any communication system because it is costly and limited.Analog signals must be converted to digital pulses transmission and converted back.Requires precise time synchronization between the clocks in the transmission and receivers.Incompatible with older analog transmission system.

Introduction continuedv(t)=V sin(2ft + ) ..(1)

Referring to (1) if the information signal is digital and amplitude of the carrier is varied proportional to the information signal, a digitally modulated signal called amplitude shift keying(ASK) is produced.If frequency is varied proportional to the information signal frequency shift keying (FSK) is produced.If phase of the carrier is varied proportional to the information signal phase shift keying (PSK) is produced.If both the amplitude and phase are varied proportional to the information signal quadrature amplitude modulation is produced(QAM)ASK, FSK, PSK, QAM are forms of digital modulation techniques.

ASKFSKPSKQAM

Digital modulation aplicationsRelatively low speed voice band data communication modems,such as those found in most personal computers.High speed data transmission systems, such as broad band digital subscriber lines (DSL)Digital microwave and satellite communication systemsCellular telephone communication systems

Block diagram of a digital communication systemencryptformatSourceencoderChannelencodermultiplexmodulateFrequencyspreadMultiple accessdecryptformatSourcedecoderChanneldecoderdemultiplexdemodulateFrequencyDespreadMultipleaccessBitstreamSyncroni-zationDigital waveformInformationsourceInformationsinkXMTRCVCHANNEL

Information theoryInformation theory is a highly theoretical study of the efficient use of bandwidth to propagate information through electronic communication systems. This theory can be used to determine the information capacityof a data communication system. Information capacity is a measure of hw much information can be propagated through a communication system and is a function of bandwidth and transmission time. Information capacity represents the number of independent symbols that can be carried through a system in a given unit of time. The basic digital symbol used to represent information is a binary digit or a bit. Therefore it is convenient to express information capacity of a system as a bit rate. Bit rate is the number of bits transmitted per second (bps).

Information theory contd.,In 1928 R.Hartley of Bell telephone labs developed a useful relationship between B.W, transmission time and information capacity,I=B x t (2) Where I : information capacity in bps B : bandwidth in Hz t : timeIn 1948 Claude Shannon showed the relation between I (information capacity) of a communication channel to BW and S/N ratio. Higher the S/N ratio, the better is the performance and higher is I.

Shannons limit for information capacity is given by I = (BW) log 2(1+S/N ) or I = 3.32(BW) log 10(1+S/N )

Encoding An important problem is communication is efficient representation of data generated by a discrete source. The process by which this representation is accomplished is called source coding.Digital and data communication system uses equipment like keyboards, video terminals, printers, etc., to receive and send data. These data are in coded form.Encoding is a process which generates a binary code corresponding to quantization level of the signal; transmitted for each sampling interval.Analog signal sampling quantization encoding digital signal.All equipments may not use the same codes there are various codes such as: ASCII, EBCDIC, baudot code, Hollerith code etc.,Basic requirements for a code are :The code words produced by the encoder are in binary formThe source coding is uniquely decodable so that the original sequence can be reconstructed perfectly from the encoded binary sequence can be reconstructed perfectly from the encoded binary sequence.They should have sufficient number of different symbols to represent all the signal levelsThey should have provision for error detection and error correction.

M-ary encodingM-ary is a term derived from the word binaryM represents a digit that corresponds to the number of conditions, levels and combinations possible for a given number of binary variables.The number of bits necessary to produce a given number of conditions is expressed mathematically as : N = log2M. Where N is the number of bits necessary. M= Number of conditions, levels or combinations possible with N bits.Simplification leads to 2N=M

Coding efficiencyIf N is the number of bits then 2N different events can be represented as N = log2M or 2N=M where N is the number of bit of information required to predict one out of M equiprobable events and by definition 2N=MCoding efficiency is defined as the ratio of the number of bits required to the number of bits used.M=bits required / bits used Eg : if binary code is to represent 26 letters then it requires N=log226=4.7 bits. But N should be an integer. Therefore the nearest integer = 5 bits is used which can represent 32 equiprobable events. The code efficiency =4.7 / 5 x 100= 94%

Baud and minimum bandwidthBaud is a term that is often misunderstood and commonly confused with bit rate (bps)Bit rate refers to the rate of change, however baud refers to the rate of change of a signal on the transmission medium after encoding and modulation have occurred.Baud=1/ts where baud=symbol rate (baud per second) and ts=time of one signaling element(seconds).Nyquist bandwidth :Binary digital signals can be propagated through an ideal noiseless transmission medium at a rate equal to two times the bandwidth of the mediumIf more than two levels are used for signaling the nyquist formulation for channel capacity is fb= 2Blog2M where fb=channel capacity(bps) B= minimum nyquist bandwidth (Hz) M= number of discrete signal or voltage levels.Therefore the minimum bandwidth necessary to pass M-ary digitally modulated carriers is B= fb/ (log2M). If N is substituted for log2M the above equation reduces to B= fb/ N where N is the number of bits encoded into each signaling element Thus Baud = fb/ N

Baud and minimum bandwidth Nyquist bandwidth: binary digital signals can be propagated through an ideal noiseless transmission medium at a rate equal to two times the bandwidth of the medium. The minimum theoretical bandwidth or sometimes the nyquist frequency.Thus fb= 2B where fb= bit rate in bps, B = ideal nyquist bandwidth.The actual bandwidth necessary to propagate a given bit rate depends on several factors :Type of encoding, modulation used, types of filter used system noise, desired error performance.

Amplitude shift keyingThe simplest digital modulation technique is amplitude shift keying (ASK). Where a binary information signal directly modulates the amplitude of an analog carrier.In ASK, a carrier wave is switched ON and OFF by the input data or binary signals. During a mark (binary 1) a carrier wave is transmitted and during a space (binary 0) the carrier is suppressed.Hence it is also known as ON-OFF keying (OOK).Mathematically, amplitude shift keying is Vask(t)= {1+Vm(t)} [(A/2)cosct]Where Vm(t) is modulating signal (volts)A/2 is the unmodulated carrier amplitudec is the analog carrier frequencyIn the above equation the modulating signal Vm(t) is a normalized binary waveform, where +1V=logic 1 and -1V=logic 0. therefore for a logic 1 input Vm(t)= +1V and the equation reduces toVask(t)= {1+1} [(A/2)cosct]= (A/2)cosctAnd for a logic 0 input , Vm(t)= -1V and the equation reduces to Vask(t)= {1-1} [(A/2)cosct]=0Thus the modulated wave Vask(t) is either (A/2)cosct or 0. hence the carrier is either ON or OFF Therefore amplitude shift keying is also called ON OFF keying

Frequency shift keyingFSK is a constant amplitude angle modulation similar to frequency modulation except the modulating signal varies between the two discrete voltage levels rather than a continuously changing waveform.The general expression for FSK is

Vfsk(t)=Vccos{2[fc+Vm(t)f]t}

Where Vc= peak analog carrier amplitude (volts) fc= analog carrier center frequency(Hz) f = peak change (shift) in the analog carrier frequency (Hz) Vm(t)= binary input modulating signal (volts)From the above equation it is seen that the peak shift in the carrier frequency f is proportional to the amplitude of the binary input signal Vm(t) and the direction of the shift is determined by the polarity.

FSK contd.,Logic 0 logic 1 (binary input waveform). The modulating signal is a normalized binary waveform where logic 1 = +1V and logic 0 = -1V. Thus for a logic 1 input Vm(t)=+1V. The above equation can be written as Vfsk(t)=Vccos{2[fc+f]t} and for logic 0 we have Vfsk(t)=Vccos{2[fc-f]t}. Thus the output frequency changes between two frequencies : a mark , or logic 1 and a space, or logic 0 frequency (fs). The mark and space frequencies are separated from the carrier frequency by the peak deviation f.f= (|fm-fs|)/2In FSK the time of one bit is the same as the FSK output is a mark of space frequency fs.. Thus the bit time equals the time of an FSK signaling element and the bit rate equals baud. Baud = fb / N = fb/1= fbB.W.= |((fs-fb) - (fm-fb)| = | fs - fm| + 2 fb = 2(f+fb)

Phase shift keying PSK is another form of angle modulated constant amplitude digital modulation.PSK is a M-ary digital modulation scheme with a binary input and there are limited number of phases possible.

Bandwidth requirementsBandwidth is the range of frequencies occupied by the digital signal. It is seen that as the number of bits/sec increases the bandwidth also increases.Therefore bandwidth depends on the rate at which the bits are changing.A digital signal cannot have any value of bandwidth. It will be limited depending on the transmitting channel.For example : the digital signal transmitted in a telephone channel cannot occupy any bandwidth. The standard telephone channel bandwidth allotted is 3.1KHz that is between 300Hz to 3400Hz.This range does not occupy the full audio range(20Hz to 20KHz) but speech signal is fitted in this bandwidth. Which implies that the signal should be within 3.1KHz to be transmitted through a telephone line. This restricts the bit rate.

Bandwidth requirements contd.,Information theory is a highly theoretical study of the efficient use of bandwidth to propagate information through electronic communication system. This theory can be used to determine the information capacity of a data communication system. Information capacity is a measure of how much information can be propagated through a communication system and is a function of bandwidth and transmission time. It represents the number of independent symbols that can be carried through a system in a given unit of time. The basic digital symbol used to represent information is a binary digit or a bit. Therefore it is convenient to express information capacity of a system as a bit rate.

Bit rate is the number of bits transmitted per second (bps).In 1928 R.Hartley of Bell telephone labs developed a useful relationship between B.W. transmission time and information capacity.I = B x tWhere I= information capacity (bps) B= bandwidth (Hz) t= time (sec)In 1948 Claude Shannon showed the relation between I (information capacity) of a communication channel to B.W. and S/N ratio, the better is the performance and higher is I.Shannons limit for information capacity is given by I = (B.W) log 2(1+S/N)

Data transmission speeds Transmission speed : The data transmission speed is also called its signaling rate. Signaling rate is the number of bits transmitted in one second. It is expressed as bps. It depends on channel bandwidth and numbers of nits in one word and the sampling signal frequency used converting analog signal to digital signal. The rate of data transfer depends on several aspects of the transmission channel. The transmission speed of a communication channel is measured in channels baud rate.In a system where all pulses have equal duration, the speed in baud is equal to the maximum rate at which signal pulses transmitted.For example in system in which only one information bit/signaling pulse (such as binary system), baud rate = bit rate.In a system which encodes the data in such a way that more than one information bit is placed on signaling pulse, the information bit rate > baud rate.

Nyquist determined that one cycle of transmission can contain maximum of two bauds. Implies maximum signaling speed in bauds = 2B(twice the bandwidth). This theoretical value can be achieved in an ideal channel which has no noise or distortion.Baud is a unit of signaling speed, but information transfer can occur at a rate > baud rate.Multilevel and encoded data elements can be used to provide information transfer rate > baud rate. For example : in a four level encoding each 2 bit pair can have only one of 4 values, 00 01 10 11. each of the 2 bit pair is converted to the phase value i.e., 00-90, 01-180, 10-270, 00-90, 11-0.Each of the two bits is called a dibit. Therefore dibit encoded data can be transmitted using half the number of bauds compared to the non-encoded data. This implies multi level encoding increases information rate.

Cross talkAny transmission system which conveys more than one signal simultaneously can experience cross talk. Cross talk refers to one channel picking up some of the signal that is traveling on the other.Causes: Cross talk occurs between cable pairs conveying separate signals.It occurs in the multiplexed links in which several channels are transmitted over the same facility.It is more in FDM where each carrier signal is allotted a frequency band. If the signal in one channel is over modulated, its bandwidth may exceed and interfere with the adjacent channel producing cross talk.It occurs in the microwave links where one antenna picks up minute reflected portion of the signal from another antenna on the same tower.It occurs because of capacitive and inductive coupling.It occurs in exchanges or switching centers where large number of wires run parallel to each other because if induction.

Cross talk between two wire circuit will increase with ---increased length ---increased signal strength ---increased signal frequencyRemedy : cross talk due to e.m.induction can be overcome with large separation between adjacent pair or with periodic reversal of the wires that is using twisted pair of cables. It can be reduced by using proper electrical shield separating the wires for each direction.It can be reduced by using balanced circuit. In a balanced circuit a transformer is placed at each end of the circuit. The transformers are carefully constructed to provide a center tap which is at the exact electrical center of the winding which connects to the transmission circuit. The center taps of each are grounded.

Distortion Communication channels tend to react to signals of different speeds in different ways. Signals of different frequencies may be passed by a channel at different speeds and different magnitudes of amplitude attenuation. As a result there will be distortion.When one signal is passed through the channel at a speed different from that of the other signals there may be inter symbol interference.Systems using phase modulation may undergo phase delay distortion. Phase delay distortion occurs in a channel when signals of one frequency are passed through the circuit at a different speed than other signals.Equalizers : phase delay distortion can be reduced to acceptable levels by using equalization on the channel.

NoiseShannon Hartleys law is related to random noise. The different types of noise in digital communication systems are Random noiseCode noise or impulse noiseTransmission noiseWhite noise

Random noise : it is also called quantization noise. This occurs when the analog signal is being quantized while converting to digital signal. The maximum error that can occur is half the size of the sampling interval. As the quantization error occurs randomly, it is termed as noise.This can be reduced by increasing the number of standard levels until noise becomes acceptable.Code or impulse noise : this is the main source of errors in data. It can saturate the channel and blot out the data.During sampling process the noise pulse may be interpreted as a data bit. If the bit impulse occurs at the time of sampling and has an amplitude > or equal to the levels of coding, coding errors occurs. Therefore it is called coding noise.This noise increases with increase in the number of levels. Therefore in multilevel coding noise level is high. This is reduced if S/N is improved.Transmission noise: this occurs on the digital signal while transmission in the channel. This may be caused by circuit faults such as poor soldering and dirty relay contacts and jacks, and twisted joint of a T-line. An extra signal or an impulse in one cannel may affect the other channel while multiplexing. To reduce this noise S/N has to be improved. This depends on the channel capacity and cooling levels.

Echo suppressorsThe signal reflected from the receiver end back to the transmitted end is called as echo signal or echo.The main cause for echo is the mismatch in the T-line which is not properly terminated.The echo signal is the reflected signal which travel from receiving end to the transmitting end.This signal may superimpose on the transmitting signal thus causing distortion.Echoes can be overcome by using circuits called echo suppressors and echo cancellers.In an echo suppressor circuit reduces the return transmission by inserting a large amount of loss into the return path and zero attenuation for the forward path.