Unit i-pcm-vsh

Digital Baseband Modulation & Waveform coding TechniquesOrSource Coding TechniquesV. S. Hendre Department of E&TC, TCOER, Pune1UNIT-I

UNIT-I: Digital Baseband Modulation Techniques and Waveform Coding TechniquesBase band system, Formatting textual data, messages, characters & symbols, Formatting analog information, Sources of corruption, PCM, Uniform and Non uniform quantization, Baseband modulation, Noise consideration in PCM systems, DPCM, DM,ADM, LPC.V. S. Hendre Department of E&TC, TCOER, Pune2

INTRODUCTIONFormatting: is to insure that the message is compatible with Digital Signal ProcessingTransmit Formatting: is a transformation from source information to digital symbols.Source coding: data compression + formattingFormattingCharacter CodingSamplingQuantizationPulse Code Modulation (PCM)V. S. Hendre Department of E&TC, TCOER, Pune3

INTRODUCTIONV. S. Hendre Department of E&TC, TCOER, Pune4FormattingCharacter CodingSamplingQuantizationPulse Code Modulation (PCM)Source CodingPredictive Coding, Block CodingVariable Length CodingSynthesis CodingLossless CompressionLossy compressionBaseband SignalingLine Codes/Data FormatsRZ,NRZ, Phase encoded, Multilevel binary, PAM, PPM ,PWM

Baseband Systems5Signal Source / information sourceSignal Sampling circuitSource quantiser encoderChannel encodermodulatorCommunication channelAWGNV. S. Hendre Department of E&TC, TCOER, Pune

6Digital info.FormatTextual info.sourcePulsemodulateTransmitEncodeSampleQuantizeAnalog info.ChannelPulsewaveformsBit streamFormatAnalog info.Low-passfilterDecodeDemodulate/DetectReceiveTextual info.sinkDigital info.Baseband SystemsV. S. Hendre Department of E&TC, TCOER, Pune

Formatting Textual Data (Character Coding)Original or baseband data is either textual or analog.If data is alphanumeric text, it will be character encoded with some standard formats.These formats are:ASCII (American Standard Code for Information Interchange)EBCDIC: Extended Binary Coded Decimal Interchange Code.V. S. Hendre Department of E&TC, TCOER, Pune7

ASCII Format (7 bit)V. S. Hendre Department of E&TC, TCOER, Pune8

EBCDIC Format V. S. Hendre Department of E&TC, TCOER, Pune9

Messages, Characters & Symbols Textual message is first encoded in digital form by using ASCII or EBCDIC format.This digital sequence of bits is called as bit stream or baseband signal.Groups of ‘K’ bits can be combined to form new digits or Symbols.Total no of symbols =M=2K .A system using a symbol size of M is called as M-ary System.M= 2- Binary System, M=3-Trinary SystemM=4 –Quaternary System, M=5- 5ary systemV. S. Hendre Department of E&TC, TCOER, Pune10

Ex: Messages, Characters & Symbols V. S. Hendre Department of E&TC, TCOER, Pune11

Formatting Analog Information If information is in Analog form then we can not be character encoded it as in textual form.Here we need to convert it in Digital form by using the processes of Sampling & QuantizationV. S. Hendre Department of E&TC, TCOER, Pune12

Sampling for Low Pass SignalsSampling is the process of taking a periodic sample of the waveform to be transmitted.Sampling of signal is the fundamental operation in digital comm. It is the process of conversing an analog signal (continuous time) into discrete time signal. Statement for Low pass Sampling Theorem: A continuous time band limited signal can be completely represented in it sample form and recovered back if the sampling freq fs ≥ 2 w. when fs- sampling freq and w- is the max freq present in the signal.V. S. Hendre Department of E&TC, TCOER, Pune13Where fs = sampling frequencyfm(max) = maximum frequency of the modulating signal

Sampling for Low Pass SignalsV. S. Hendre Department of E&TC, TCOER, Pune14

Proof for Sampling TheoremV. S. Hendre Department of E&TC, TCOER, Pune15

V. S. Hendre Department of E&TC, TCOER, Pune16V (volt)f (Hz)fs2fs3fsfm(max)fs+fm(max)fs-fm(max)SamplingThree basic condition of sampling process:Sampling at fs=2fm(max)

V. S. Hendre Department of E&TC, TCOER, Pune17V (volt)Guardbandf (Hz)fs2fsfm(max)fs-fm(max)fs+fm(max)SamplingSampling at fs>2fm(max)This sampling rate creates a guard band between fm(max) and the lowest frequency component fs-fm(max) of the sampling harmonics.

V. S. Hendre Department of E&TC, TCOER, Pune18V (volt)Aliasing distortionf (Hz)2fsfs3fsfs-fm(max)fm(max)fs+fm(max)SamplingSampling at fs<2fm(max) Aliasing: the distortion produced by the overlapping components from adjacent bands Aliasing occurs when a signal is sampled below its Nyquist rate

SamplingV. S. Hendre Department of E&TC, TCOER, Pune19Aliasing effect in Time Domain

SamplingV. S. Hendre Department of E&TC, TCOER, Pune20Sampling Rate: Practical ConsiderationVoice Signals: Fmmax: 3.4 KHz Nyquist Criteria: 2 x 3.4K =6.8KHz Practical Sampling Rate: 8KHz.2. High quality Music System: Max. Bandwidth : 20KHz Nyquist Criteria; 2 x 20K = 40 KHz Practical Sampling Rate:44.1 Ksamples/sec3. Studio Quality Audio : Sampling Rate: 48.0 Ksamples/secThus by an engineer’s version, Nyquist sampling Rate is

SamplingV. S. Hendre Department of E&TC, TCOER, Pune21Sampling Rate: Practical ConsiderationVoice Signals: Fmmax: 3.4 KHz Nyquist Criteria: 2 x 3.4K =6.8KHz Practical Sampling Rate: 8KHz.2. High quality Music System: Max. Bandwidth : 20KHz Nyquist Criteria; 2 x 20K = 40 KHz Practical Sampling Rate:44.1 Ksamples/sec3. Studio Quality Audio : Sampling Rate: 48.0 Ksamples/secThus by an engineer’s version, Nyquist sampling Rate is

Why Over Sample?V. S. Hendre Department of E&TC, TCOER, Pune22 Oversampling is the most economic solution for the task of transforming an analog signal to a digital signal.

This is so because signal processing performed with high performance analog equipment is typically much more costly than using digital signal processingequipment to perform the same task.Without Oversampling1. The signal passes through a high performance analog lowpass filter to limit its bandwidth.2. The filtered signal is sampled at the Nyquist rate for the (approximated) bandlimited signal. 3. The samples are processed by an analog-to-digital converter that maps the continuous-valued samples to a finite list of discrete output levels.

Why Over Sample?V. S. Hendre Department of E&TC, TCOER, Pune23With Oversampling1. The signal is passed through a low performance (less costly) analog low-pass filter (prefilter) to limit its bandwidth.2. The pre-filtered signal is sampled at the (now higher) Nyquist rate for the (approximated) bandlimited signal.3. The samples are processed by an analog-to-digital converter that maps the continuous-valued samples to a finite list of discrete output levels.4. The digital samples are then processed by a high performance digital filter toreduce the bandwidth of the digital samples.5. The sample rate at the output of the digital filter is reduced in proportion tothe bandwidth reduction obtained by this digital filter.

V. S. Hendre Department of E&TC, TCOER, Pune24CommunicationSystemContinuous WaveDigital WaveAnalogue Pulse ModulationDigital Pulse ModulationPAMPWMPPMAnalogue Pulse Modulation Chart

Analog Pulse Modulation (APM)V. S. Hendre Department of E&TC, TCOER, Pune25In APM, the carrier signal is in the form of pulse form, and the modulated signal is where one of the characteristics either (amplitude, width, or position) is changed according to the modulating/audio signal.Three common techniques of APM:Pulse amplitude modulation (PAM)Pulse Width Modulation (PWM)Pulse Position Modulation (PPM)

Waveforms for PAM, PWM and PPMV. S. Hendre Department of E&TC, TCOER, Pune26Modulating signalcarrier signalPAM(dual polarity)PWMPPM

Pulse Amplitude Modulation (PAM)V. S. Hendre Department of E&TC, TCOER, Pune27It is very similar to AMThe amplitude of a carrier signal is varied according to the amplitude of the modulating signal.Two type PAMDual- polarity PAMSingle -polarity PAM

Pulse Width Modulation (PWM)V. S. Hendre Department of E&TC, TCOER, Pune28The technique of varying the width of the constant amplitude pulse proportional to the amplitude of the modulating signal.PWM gives a better signal to noise performance than PAM

Pulse Position Modulation (PPM)V. S. Hendre Department of E&TC, TCOER, Pune29PPM is when the position of a constant width and constant amplitude pulse within prescribed time slot is varied according to the amplitude of the modulating signal.

Basic Techniquesa) Variable Length Codingb) Fixed Length CodingPCM, DM, ADM, DPCM etc.PCM-Linear Pulse code modulationNeed-Analog PAM signaldigitalV. S. Hendre Department of E&TC, TCOER, Pune30

V. S. Hendre Department of E&TC, TCOER, Pune31Advantages-1)Immunity to transmission noise

2)Regenerative repeaters-increases SNR

(occuresamplitude & phase distortion)

3)Encryption-privacy & security

4) Uniform representation of signal

Disadvantage: very large BW Basic Block diagramV. S. Hendre Department of E&TC, TCOER, Pune32

V. S. Hendre Department of E&TC, TCOER, Pune33Digital info.FormatTextual info.sourcePulsemodulateTransmitEncodeSampleQuantizeAnalog info.ChannelPulsewaveformsBit streamFormatAnalog info.Low-passfilterDecodeDemodulate/DetectReceiveTextual info.sinkDigital info.

V. S. Hendre Department of E&TC, TCOER, Pune34Quantization Process“A process of transforming the sample amplitude x(nTs) into a discrete amplitude xq(nTs)Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes.12

Operation of quantisationV. S. Hendre Department of E&TC, TCOER, Pune35X(t)Xq(t)VH7q7Quantization levelqooVL=(VH-VL)/Q, Q:no of levels-signal is divided (Q=8), Q=2N, N=bits/sample

V. S. Hendre Department of E&TC, TCOER, Pune36

V. S. Hendre Department of E&TC, TCOER, Pune37Whenever x(t) is in the range 0, xq(t) maintains the constant level qoxq(t) makes a quantum jump of step size Quantized signal-approximation of original signalapproximated signal is practically indistinguishable form original signalQuantization removes additive noise /2

Qunatization exampleV. S. Hendre Department of E&TC, TCOER, Pune38Quant. levelsboundariesx(nTs): sampled valuesxq(nTs): quantized valuesamplitudex(t) 3.1867 2.2762 1.3657 0.4552 -0.4552 -1.3657 -2.2762 -3.1867Ts: sampling timeActualSample valuet

PCM-conversionV. S. Hendre Department of E&TC, TCOER, Pune39PCM Sequence

V. S. Hendre Department of E&TC, TCOER, Pune40OutputXq(nTs)Representation levelsTransfer characteristics of quantizer/quantizer curve 7/2 5/2Maximum quantization error/2 3/2-X(nTs)InputX(nTs)/2Decision levels3402 -/2Overload levels -3/2 -5/2Peak to peak excursion of the signalQuantization error ()/2InputX(nTs) -/2

V. S. Hendre Department of E&TC, TCOER, Pune41Two types of quantization: (a) midtread and (b) midrise.13

V. S. Hendre Department of E&TC, TCOER, Pune42Model of quantizing noiseQuantization errorQuantizing error: The difference between the input and output of a quantizerMaximum quantisation error=

V. S. Hendre Department of E&TC, TCOER, Pune43Quantization NoiseIllustration of the quantization process. 14

Transmission BandwidthN-no of bits/sampleQuantization levels Q=2NSignaling rate=r=n.fsBW (PCM)=(1/2) x signaling rate (But ) V. S. Hendre Department of E&TC, TCOER, Pune44

V. S. Hendre Department of E&TC, TCOER, Pune45Bandlimits fm-3.3KHzFlat TopPAMQuantized PAMPCMN bitq-levelParallel to serial converterLow passFilterSample & hold circuitQuantiser(uniform)Binary encoderGood SNR8 bit-approximation-rounding off-reduces additive noise fc=fmFs>>2fm@ 8KHzR=64 kbpsAnalog Speech signal(300Hz- 3.3 KHz)PulseGeneratorBasic Block diagramPCM TransmitterX(t)

PCM receiverV. S. Hendre Department of E&TC, TCOER, Pune46

ADC (Analog to Digital Converter)V. S. Hendre Department of E&TC, TCOER, Pune47IC :0808/ 0809 SpecificationsMax Input Voltage: 0 to 5V or -2.5V to +2.5V

No of bits per Sample: v or N = 8 bits

Quantization levels Q=2N = 256

Bandwidth= ½ x N x Fs = 32 KHzBlock diagram of regenerative repeatersV. S. Hendre Department of E&TC, TCOER, Pune48Decision making DeviceAmplitude EqualiserRegenerated PCM waveDistorted PCM waveTiming Circuit

V. S. Hendre Department of E&TC, TCOER, Pune49sAmplifieri/p x(t)outputCUnity gain

Low o/p impd.Large load impd.Sample & Hold Circuit

V. S. Hendre Department of E&TC, TCOER, Pune50OutputXq(nTs)Representation levelsSignal to Quantization noise ratio: SNRq 7/2 5/2Maximum quantization error/2 3/2-X(nTs)InputX(nTs)/2Decision levels3402 -/2Overload levels -3/2 -5/2Peak to peak excursion of the signalQuantization error ()/2InputX(nTs) -/2

Signal to Quantization noise ratio: SNRqV. S. Hendre Department of E&TC, TCOER, Pune51If the range of amplitude is from – Xmax to + XmaxThe step size

Signal to Quantization noise ratio: SNRqV. S. Hendre Department of E&TC, TCOER, Pune52

Signal to Quantization noise Ratio: SNRqFor quantizerNoise powerNoise by r.v. & its PDF Mean square valueV. S. Hendre Department of E&TC, TCOER, Pune53

V. S. Hendre Department of E&TC, TCOER, Pune54Mean square value of r.v. xPutting II) into I), mean square value of noise voltage =At R=1, noise power is normalized Normalized noise power/ quantization noise power =

Equn 1)V. S. Hendre Department of E&TC, TCOER, Pune55=max. signal to quantisation noise ratio* S/N & n relationIf input x(t)-normalised, Mmax=1

If input signal power is normalised, P≤1,

S/N ≤ 3 x 22n ……v)normalised (S/N)qV. S. Hendre Department of E&TC, TCOER, Pune56(S/N)q==>dB

V. S. Hendre Department of E&TC, TCOER, Pune57Virtues, Limitations and Modifications of PCM Advantages of PCM 1. Robustness to noise and interference 2. Efficient regeneration 3. Efficient SNR and bandwidth trade-off 4. Uniform format 5. Secure

PCM waveformsV. S. Hendre Department of E&TC, TCOER, Pune58Criteria for comparing and selecting PCM waveforms:Spectral characteristics (power spectral density and bandwidth efficiency)Bit synchronization capabilityError detection capabilityInterference and noise immunityImplementation cost and complexity

Uniform and non-uniform quantisationV. S. Hendre Department of E&TC, TCOER, Pune59Uniform (linear) quantizing: step size -uniformNo assumption about amplitude statistics and correlation properties of the input.Not using the user-related specificationsRobust to small changes in input statistic by not finely tuned to a specific set of input parametersSimply implementedOver complete range of signal max=|/2|Application of linear quantizer:Signal processing, graphic and display applications, process control applications

Dis-advantages:Uniform QuantisationV. S. Hendre Department of E&TC, TCOER, Pune601) let n=4 bits Q=2n=24=16 levels =2/q=(2/16)=(1/8) v max=|/2|=(1/16) If signal range=16 V, max=1 V is acceptable But it is very Harmful for signal amplitudes 2, 3 V….Lower Acceptable-signal amplitudes 15, 16… Higher Non-Uniform quantization

V. S. Hendre Department of E&TC, TCOER, Pune611.0Probability density function0.52.01.03.0Normalized magnitude of speech signal0.02) Statistical of speech amplitudesIn speech, weak signals are more frequent than strong ones.Using equal step sizes (uniform quantizer) gives low for weak signals and high for strong signals.Adjusting the step size of the quantizer by taking into account the speech statistics improves the SNR for the input range.

2) Statistical of speech amplitudesAnother way: Crest Factor = Peak Value / RMS ValueFor speech or music signals Crest factor is very high.

V. S. Hendre Department of E&TC, TCOER, Pune63Non-Uniform Quantisation-Uses the input statistics to tune quantizerparameters-Larger SNR than uniform quantizing with same number of levels-Non-uniform intervals in the dynamic range with same quantization noise variance-Application of non-uniform quantizer:Commonly used for speech -for voice-amplitude values-concentrated near zero-variable step size-directly not applicable (generates error)-process:-signal amplification-at low level & -signal attenuation –at high level & - Uniform quantization-overall effect-Non-Uniform Quantization

Nonuniform QuantizerUsed to reduce quantization error and increase the dynamic range when input signal is not uniformly distributed over its allowed range of values.allowed valuesinputvalues for mostof timetime

“Compressing-and-expanding” is called “companding.”Nonuniform quantizerDiscretesamplesUniformQuantizerdigital signalsCompressor • • • •Channel • • • •outputDecoderExpanderreceiveddigital signals

Practical Implementation of µ-law compressor

Output SNR of 8-bit PCM systems with and without companding.

V. S. Hendre Department of E&TC, TCOER, Pune69compression+expansion compandingNon-uniform quantization….processAt the transmitter Uniformly quantizing the “compressed” signal. At the receiver, an inverse compression/expansion characteristic, called “expansion” is employed to avoid signal distortion. CompressQauntizeExpandChannelTransmitterReceiver

Companding curveV. S. Hendre Department of E&TC, TCOER, Pune70

Companding CurveV. S. Hendre Department of E&TC, TCOER, Pune71O/P. Voltage of CompanderCompressionExpansionI/P. Voltage of CompanderExpansionCompression

Effect of compandingV. S. Hendre Department of E&TC, TCOER, Pune72

Compression lawsTwo Laws-’’ Law-United states, Canada, Japan (=225)‘A’ Law- Europe & India (A=87.6)’’ Law Defn:V. S. Hendre Department of E&TC, TCOER, Pune73W1(t)-input to compressor, allowed value= 1W2(t)-output of compressorAppli: speech, music signals, PCM systems

SNR Performance of PCM with  LawV. S. Hendre Department of E&TC, TCOER, Pune74Fixed SNR-irrespective of wide variations of signal levels among individual talkers

Compression characteristic for  LawV. S. Hendre Department of E&TC, TCOER, Pune75As µ  ∞, Linear AmplificationStandard Value of µ=255

‘A’ Law characteristicsV. S. Hendre Department of E&TC, TCOER, Pune76Compression characteristicsAs A  ∞, Linear AmplificationStandard Value of A=87.6

V. S. Hendre Department of E&TC, TCOER, Pune77Figure 3.14 Compression laws. (a) m-law. (b) A-law.

Noise consideration in PCM systems (Channel noise, quantization noise)V. S. Hendre Department of E&TC, TCOER, Pune78

Examples on PCMV. S. Hendre Department of E&TC, TCOER, Pune79A low pass signal of 3 KHz B.W. & amplitude over -5 volts to +5 volts range is sampled at Nyquist rate & converted to 8 bit PCM using uniform quantization. The mean squared value of message signal is 2 volt-squared. Calculate i) normalized power for quantization noise ii) Bit transmission rate iii) (S/N)Q in dBSoln: Given : W=3KHz, VL =-5V, VH =5V, N=8i) Normalized quantization noise:

Examples on PCMV. S. Hendre Department of E&TC, TCOER, Pune80ii) Bit Transmission Rate:iii) (S/N)Q in dB:

Examples on PCMV. S. Hendre Department of E&TC, TCOER, Pune812. A compact disc recording system samples each of the two stereo signals with 16 bit A/D converter at 44.1Kbps. Determine i) output S/N ratio for full scale sinusoid ii) The bit stream of digitized data is augmented by addition of error correcting bits, clock extraction bits etc., these additional bits represents 100% overhead. Determine output bit rate of the system. iii) The CD can record an hours worth of music. Determine no of bits recorded on CD.Soln: i) Output (S/N) = (1.76+6*N) = 97.76 dBii) Bit rate of single channel: 16*44.1=705.6KbpsFor two channels :705.6*2=1.411MbpsFor additional 100% overheadFinal Bit rate = 1.411*2=2.8224Mbpsii)This o/p bit rate represents 2.8224Mbps bits are coming per second (1 second). So, number of bits recorded in hour (3600 seconds) will be=2.8224Mbps x 3600=1.016 x 10^10 bits.

Delta ModulationV. S. Hendre Department of E&TC, TCOER, Pune83PCM-drabacks-1)Large signalling rate -2) Larger transmission BWDelta modulation:- 1bit/samplePresent sample-compared with previousResult-Increase/Decrease in amplitudeInput x(t)approximated , fixed step size Diffn:x(t) & staircase approximated 2 levels:+ or -If diffn:+ve, increased by one step  & has step with Ts=delay timeIf diffn:-ve, decreased by one step  & has step with Ts=delay time

V. S. Hendre Department of E&TC, TCOER, Pune84For reduced step – ‘0’-transmittedFor increased step- ‘1’-transmitted for each sample-one bit transmittedDelta modulator/transmitter

Waveform representationV. S. Hendre Department of E&TC, TCOER, Pune85

V. S. Hendre Department of E&TC, TCOER, Pune89“start up interval”-interval required to meet approximated signal to input signal“Hunting” of approximated signal:-condition whenever input signal is almost constant or flatError (kTs) Granular NoiseWhen input signal increases or decreases too rapidly, approximated signal lags behind “Slope Overload error”Advantages:1) transmits only 1 bit/sample signaling rate & transmission BW-reduced 2)transmitter & receiver –implementation –easyDisadvantages:-1)Granular noise,2)slope overlaod Overcome-ADM

V. S. Hendre Department of E&TC, TCOER, Pune90The modulator consists of a comparator, a quantizer, and an accumulatorTwo types of quantization errors :Slope overload distortion and granular noise

Slope Overload ConditionThe slope overload distortion will occur if

Examples on DMV. S. Hendre Department of E&TC, TCOER, Pune93A delta modulated system is designed to operate at five times the nyquist rate for a signal with 3Khz B.W. Determine the max. amplitude of a 2KHz input sinusoid for which the delta mod doesn't have slope overload. Quantizing step size is 250mVSoln: Given : W=3KHz, fm =2 KHz, fs =5 * 3 *2= 30KHz,

Examples on DMV. S. Hendre Department of E&TC, TCOER, Pune942. A 1KHz signal sampled by 8KHz, is to be encoded by using 1) 12 bit PCM 2) DM system. If 20 cycles of 1 KHz are digitized, state how many bits will be there in digital output signal in each case. State signaling rate and B.W. in each case.Soln: 1) 12 bit PCM: Signaling Rate= v * fs=96Kbps B.W. = 48KHz Tm = 1/1000, Ts =1/800, Samples in one cycle= Tm/Ts = 8In 20 cycles = 8*20 =160 samplesNo of bits transmitted = 160 * 12 =19202) DM systems Signaling Rate: 8Kbps, B.W.=4KHz No of bits transmitted= 160bits

DM receiverV. S. Hendre Department of E&TC, TCOER, Pune95*When received binary 1-accumulator adds + to previous o/p*When received binary 0-accumulator subtracts  from previous o/p

Adaptive Delta Modulation (ADM)V. S. Hendre Department of E&TC, TCOER, Pune96Step size -adaptive to variations of input signal x(t)Step size-reduced for slowly varying signalStep size-increased for steep segment of signal ADM transmitter

ADM-waveformV. S. Hendre Department of E&TC, TCOER, Pune97

ADM-receiverV. S. Hendre Department of E&TC, TCOER, Pune98

Why DM is not alternative for PCM for voice Signals?V. S. Hendre Department of E&TC, TCOER, Pune99Let us consider 8 bit PCM, N=8, Q=256,

V. S. Hendre Department of E&TC, TCOER, Pune100Delta-Sigma modulation (sigma-delta modulation) -Delta modulator with integrator -removes draw back of delta modulation -(Input to quantizer-approximation-derivative of input signal-demodulation-error)Beneficial effects of using integrator: 1. Pre-emphasize the low-frequency content 2. Increase correlation between adjacent samples (reduce the variance of the error signal at the quantizer input ) 3. Simplify receiver designBecause the transmitter has an integrator , the receiver consists simply of a low-pass filter. (The accumulator in the conventional DM receiver is cancelled by the differentiator )

V. S. Hendre Department of E&TC, TCOER, Pune101F>nyquist rate1Product modulatoroutput+1-ve i/p+ve i/p-1 Two equivalent versions of delta-sigma modulation system.

A single period of the trigonometric sine function, sampled 100 times and represented as a PDM bitstream, is:0101011011110111111111111111111111011111101101101010100100100000010000000000000000000001000010010101V. S. Hendre Department of E&TC, TCOER, Pune102

ApplicationsV. S. Hendre Department of E&TC, TCOER, Pune104Data conversion systemsFrequency SynthesizersSMPSmotor controls Sony’s Super Audio CD (SACD) format

V. S. Hendre Department of E&TC, TCOER, Pune105Differential Pulse-Code Modulation (DPCM)PCM has the sampling rate higher than the Nyquist rate .

encoded signal contains redundant information (audio & video – adjucent samples ~same)DPCM can efficiently remove this redundancy.

-Difference in adjucent samples (present & previous)-encoded-transmitted

Reduces overall bit rate & no. of bits required to transmitDPCM TransmitterV. S. Hendre Department of E&TC, TCOER, Pune106Q levelPrincipal of working: Prediction

V. S. Hendre Department of E&TC, TCOER, Pune107predictionUnquanitsedi/p signal Quantisation errorQuantised version of signalOriginal sample valueQuantisation error (+/-)

DPCM receiverV. S. Hendre Department of E&TC, TCOER, Pune108

ComparisionV. S. Hendre Department of E&TC, TCOER, Pune109

PCM with NoiseV. S. Hendre Department of E&TC, TCOER, Pune110The reconstructed message contains two types of noise: 1) Quantization Noise 2) Decoding NoiseDecoding Noise: Random Noise added to PCM signal at the receiver causes regeneration errors that appears as erroneous digits in the codeword is called as decoding noise.Expression for Decoding Noise power:Let us consider a binary PCM with uniform quantization.Let ‘v’ no of bits/samples & PCM is having very small bit error probability ‘Pe’.Bit error probability: probability of a particular bit in error When Pe << 1, The Prob. of one error in given word is P= v Pe --------- (i)

PCM with NoiseV. S. Hendre Department of E&TC, TCOER, Pune111If we consider that the PCM word bits are given by bv-1, bv-2,……………….. b1, b0,If there is error in mth bit , the decoded codeword is shifted by ±2mFor Ex. The transmitted codeword: 00001000& error occurred at bo bitReceived codeword is :00001001Decoded codeword is shifted by ±20 = ± i.e. by one step.Thus Error in mth bit is given by:m=±2m ……………..(ii)

PCM with NoiseThe random bit error can be obtained by mean square value

Unit i-pcm-vsh

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