Signal Encoding Techniques - Lecture 18

Signal Encoding TechniquesLecture 18OverviewWhere we Stand on LayersData Representation and Signaling UsedData EncodingReasons for Choosing Encoding SchemesFactors InvolvedDigital Data to Analog Signal (ASK, FSK, PSK)Analog Data to Digital Signal2Where We Stand @ Present3Physical LayerTransmission MediumData LinkTransmission MediaSignals and their transmission over media, ImpairmentsEncoding: From data to signalsData Link: Flow and Error controlData Communication: Synchronization, Error detection and correctionImproved utilization: MultiplexingAntenna and PropagationData Signal Combination4Data, Signaling and its Treatment5What's Going Up6Digital DataDigital SignalAnalog SignalAnalog DataLess complex, less expensive than digital-analog modulation equipmentUse of modern digital transmission And switching equipmentSome transmission media will onlypropagate analog signalsEfficient use of transmission channel : FDMData Encoding TechniquesDigital Data, Analog Signals [Modem]Digital Data, Digital Signals [Wired LAN]Analog Data, Digital Signals [Codec]Frequency Division Multiplexing (FDM)Wave Division Multiplexing (WDM) [Fiber]Time Division Multiplexing (TDM)Pulse Code Modulation (PCM) [T1]Delta Modulation7Encoding Techniques8Digital data as digital signalDigital data as analog signal: Converter (Modem)Analog data as digital signal: Converter (Codec)Analog data as analog signalIn general:When the outcome is a digital signal we use an Encoding processWhen the outcome is an analog signal we use a Modulation process But we call the modulation of analog signal by digital data shift-keyingReasons for Choosing Encoding TechniquesDigital data, digital signalEquipment less complex and expensive than digital-to-analog modulation equipmentAnalog data, digital signalPermits use of modern digital transmission and switching equipment9Reasons for Choosing Encoding TechniquesDigital data, analog signalSome transmission media will only propagate analog signals E.g., optical fiber and unguided mediaAnalog data, analog signalAnalog data in electrical form can be transmitted easily and cheaplyDone with voice transmission over voice-grade lines10Signal Encoding CriteriaWhat determines how successful a receiver will be in interpreting an incoming signal?Signal-to-noise ratioData rateBandwidthAn increase in data rate increases bit error rateAn increase in SNR decreases bit error rateAn increase in bandwidth allows an increase in data rate11Factors Used to CompareEncoding SchemesSignal spectrumWith lack of high-frequency components, less bandwidth requiredWith no dc component, ac coupling via transformer possibleTransfer function of a channel is worse near band edgesClockingEase of determining beginning and end of each bit position12Factors Used to CompareEncoding SchemesSignal interference and noise immunityPerformance in the presence of noiseCost and complexityThe higher the signal rate to achieve a given data rate, the greater the cost13Basic Encoding TechniquesDigital data to analog signalAmplitude-shift keying (ASK)Amplitude difference of carrier frequencyFrequency-shift keying (FSK)Frequency difference near carrier frequencyPhase-shift keying (PSK)Phase of carrier signal shifted14Basic Encoding Techniques15Amplitude-Shift KeyingOne binary digit represented by presence of carrier, at constant amplitudeOther binary digit represented by absence of carrierwhere the carrier signal is Acos(2πfct) 16Amplitude-Shift KeyingSusceptible to sudden gain changesInefficient modulation techniqueOn voice-grade lines, used up to 1200 bpsUsed to transmit digital data over optical fiber17Binary Frequency-Shift Keying (BFSK)Two binary digits represented by two different frequencies near the carrier frequencywhere f1 and f2 are offset from carrier frequency fc by equal but opposite amounts18Binary Frequency-Shift Keying (BFSK)Less susceptible to error than ASKOn voice-grade lines, used up to 1200bpsUsed for high-frequency (3 to 30 MHz) radio transmissionCan be used at higher frequencies on LANs that use coaxial cable19Multiple Frequency-Shift Keying (MFSK)More than two frequencies are usedMore bandwidth efficient but more susceptible to errorf i = f c + (2i – 1 – M)f df c = the carrier frequencyf d = the difference frequencyM = number of different signal elements = 2 LL = number of bits per signal element20Multiple Frequency-Shift Keying (MFSK)To match data rate of input bit stream, each output signal element is held for:Ts=LT secondswhere T is the bit period (data rate = 1/T)So, one signal element encodes L bits21Multiple Frequency-Shift Keying (MFSK)Total bandwidth required 2MfdMinimum frequency separation required 2fd=1/TsTherefore, modulator requires a bandwidth ofWd=2L/LT=M/Ts22Multiple Frequency-Shift Keying (MFSK)23Phase-Shift Keying (PSK)Two-level PSK (BPSK)Uses two phases to represent binary digits24Phase-Shift Keying (PSK)Differential PSK (DPSK)Phase shift with reference to previous bitBinary 0 – signal burst of same phase as previous signal burstBinary 1 – signal burst of opposite phase to previous signal burst25Phase-Shift Keying (PSK)Four-level PSK (QPSK)Each element represents more than one bit26Phase-Shift Keying (PSK)Multilevel PSKUsing multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achievedD = modulation rate, baudR = data rate, bpsM = number of different signal elements = 2LL = number of bits per signal element27PerformanceBandwidth of modulated signal (BT)ASK, PSK BT=(1+r)RFSK BT=2DF+(1+r)R R = bit rate0 < r < 1; related to how signal is filtered DF = f2-fc=fc-f128PerformanceBandwidth of modulated signal (BT)MPSKMFSKL = number of bits encoded per signal elementM = number of different signal elements29Quadrature Amplitude ModulationQAM is a combination of ASK and PSKTwo different signals sent simultaneously on the same carrier frequency30Quadrature Amplitude Modulation31Reasons for Analog ModulationModulation of digital signalsWhen only analog transmission facilities are available, digital to analog conversion requiredModulation of analog signalsA higher frequency may be needed for effective transmissionModulation permits frequency division multiplexing32Basic Encoding TechniquesAnalog data to analog signalAmplitude modulation (AM)Angle modulationFrequency modulation (FM)Phase modulation (PM)33Amplitude ModulationAmplitude Modulationcos2fct = carrierx(t) = input signalna = modulation indexRatio of amplitude of input signal to carriera.k.a double sideband transmitted carrier (DSBTC)34Spectrum of AM signal35Amplitude ModulationTransmitted powerPt = total transmitted power in s(t)Pc = transmitted power in carrier36Single Sideband (SSB)Variant of AM is single sideband (SSB)Sends only one sidebandEliminates other sideband and carrierAdvantagesOnly half the bandwidth is requiredLess power is requiredDisadvantagesSuppressed carrier can’t be used for synchronization purposes37Angle ModulationAngle modulationPhase modulationPhase is proportional to modulating signalnp = phase modulation index38Angle ModulationFrequency modulationDerivative of the phase is proportional to modulating signalnf = frequency modulation index39Angle ModulationCompared to AM, FM and PM result in a signal whose bandwidth:is also centered at fcbut has a magnitude that is much differentAngle modulation includes cos( (t)) which produces a wide range of frequenciesThus, FM and PM require greater bandwidth than AM40Angle ModulationCarson’s rulewhereThe formula for FM becomes41Basic Encoding TechniquesAnalog data to digital signalPulse code modulation (PCM)Delta modulation (DM)42Analog Data to Digital SignalOnce analog data have been converted to digital signals, the digital data:can be transmitted using NRZ-Lcan be encoded as a digital signal using a code other than NRZ-Lcan be converted to an analog signal, using previously discussed techniques43Pulse Code ModulationBased on the sampling theoremEach analog sample is assigned a binary codeAnalog samples are referred to as pulse amplitude modulation (PAM) samplesThe digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse44Pulse Code Modulation45Pulse Code ModulationBy quantizing the PAM pulse, original signal is only approximatedLeads to quantizing noiseSignal-to-noise ratio for quantizing noiseThus, each additional bit increases SNR by 6 dB, or a factor of 44647PCM48The most common technique to change an analog signal to digital data (digitization) is called pulse code modulation (PCM). A PCM encoder has three processes.1. The analog signal is sampled.2. The sampled signal is quantized.3. The quantized values are encoded as streams of bits.The analog signal is sampled every Ts, where Ts is the sample interval or period. The inverse of the sampling interval is called the sampling rate or sampling frequency and denoted by fs, where fs = 1/Ts. PCM49There are three sampling methods: ideal, natural, and flat-top.In ideal sampling, pulses from the analog signal are sampled. This is an ideal sampling method and cannot be easily implemented. In natural sampling, a high-speed switch is turned on for only the small period of time when the sampling occurs. The result is a sequence of samples that retains the shape of the analog signal. The most common sampling method, called sample and hold, however, creates flat-top samples by using a circuit.Sampling Rate50We can sample a signal only if the signal is band-limited. In other words, a signal with an infinite bandwidth cannot be sampled. The sampling rate must be at least 2 times the highest frequency, not the bandwidth. If the analog signal is low-pass, the bandwidth and the highest frequency are the same value. If the analog signal is bandpass, the bandwidth value is lower than the value of the maximum frequencyPCM (Example)51A complex low-pass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?SolutionThe bandwidth of a low-pass signal is between 0 and f, where f is the maximum frequency in the signal. Therefore, we can sample this signal at 2 times the highest frequency (200 kHz). The sampling rate is therefore 400,000 samples per second.Example52A complex bandpass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?SolutionWe cannot find the minimum sampling rate in this case because we do not know where the bandwidth starts or ends. We do not know the maximum frequency in the signal.Example PCM (Example)PCM Quantization53Quantization and encoding of a sampled signalOriginal Signal Recovery 54The recovery of the original signal requires the PCM decoder. The decoder first uses circuitry to convert the code words into a pulse that holds the amplitude until the next pulse. After the staircase signal is completed, it is passed through a low-pass filter to smooth the staircase signal into an analog signal. The filter has the same cutoff frequency as the original signal at the sender. If the signal has been sampled at (or greater than) the Nyquist sampling rate and if there are enough quantization levels, the original signal will be recreated. Note that the maximum and minimum values of the original signal can be achieved by using amplification. QuestionA PCM encoder accepts a signal with a full-scale voltage of 10 V and generates 8-bit codes using uniform quantization. The maximum normalized quantized voltage is 1-2-8. Determine (a) normalized step size, (b) actual step size in volts, (c) actual maximum quantized level in volts, (d) normalized resolution, (e) actual resolution,and (f) percentage resolution.55PCMA total of 28 quantization levels are possible, so the normalized step size is 2–8 = 0.003906.The actual step size, in volts, is: 0.003906 x 10V = 0.03906VThe maximum normalized quantized voltage is 1 - 2 -8 = 0.9961. Thus the actual maximum quantized voltage is: 0.9961 x 10V = 9.961VThe normalized step size is 2 -8. The maximum error that can occur is one-half the step size. Therefore, the normalized resolution is:The actual resolution isThe percentage resolution is5657Delta ModulationAnalog input is approximated by staircase functionMoves up or down by one quantization level () at each sampling intervalThe bit stream approximates derivative of analog signal (rather than amplitude)1 is generated if function goes up0 otherwise58Delta Modulation59Delta ModulationTwo important parametersSize of step assigned to each binary digit ()Sampling rateAccuracy improved by increasing sampling rateHowever, this increases the data rateAdvantage of DM over PCM is the simplicity of its implementation60Reasons for Growth of Digital TechniquesGrowth in popularity of digital techniques for sending analog dataRepeaters are used instead of amplifiersNo additive noiseTDM is used instead of FDMNo intermodulation noiseConversion to digital signaling allows use of more efficient digital switching techniques61SummaryLayered PositionData and SignalingEncoding SchemesReasons for Different Encoding SchemesPerformance Factors InvolvedDigital Data to Analog Signal (ASK, FSK, PSK)Analog Data to Digital Signal (PCM, Delta)62