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PULSE MODULATION

PULSE MODULATION. CHAPTER 4 Part 2. Digital Pulse Modulation. Pulse Code Modulation (PCM) Sample Quantize: Types of quantization : Uniform, non-uniform Uniform quantization: midtread , midrise Quantization error and SQR Non-uniform quantization-> Companding Encode

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PULSE MODULATION

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  1. PULSE MODULATION CHAPTER 4 Part 2 EKT343-Principles of Communication Engineering

  2. Digital Pulse Modulation Pulse Code Modulation (PCM) Sample Quantize: Types of quantization : Uniform, non-uniform Uniform quantization: midtread, midrise Quantization error and SQR Non-uniform quantization-> Companding Encode PCM Transmission Line speed Bandwidth Noise in PCM Advantages & Application EKT343-Principles of Communication Engineering

  3. Pulse Modulation • Analog pulse modulation: Sampling, i.e., information is transmitted only at discrete time instants. e.g. PAM, PPM and PDM • Digital pulse modulation: Sampling and quantization, i.e., information is discretized in both time and amplitude. e.g. PCM EKT343-Principles of Communication Engineering

  4. Analog input signal Sample at discrete time instants Analog pulse modulation, PAM signal Digital pulse modulation, PCM code EKT343-Principles of Communication Engineering

  5. PCM- PULSE CODE MODULATION • DEFINITION: Pulse code modulation (PCM) is essentially analog-to-digital (A/D) conversion where the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream. EKT343-Principles of Communication Engineering

  6. PCM Block Diagram • Most common form of analog to digital modulation • Four step process • Signal is sampled using PAM (Sample) • Integer values assigned to signal (PAM) • Values converted to binary (Quantized) • Signal is digitally encoded for transmission (Encoded) EKT343-Principles of Communication Engineering

  7. 4 Steps Process EKT343-Principles of Communication Engineering

  8. PCM-Sampling, Quantizing, and Encoding • The PCM signal is generated by carrying out three basic operations: • Sampling • Quantizing • Encoding • Sampling operation generates a flat-top PAM signal. • Quantizing operation approximates the analog values by using a finite number of levels, L. • PCM signal is obtained from the quantized PAM signal by encoding each quantized sample value into a digital word. EKT343-Principles of Communication Engineering

  9. 111 110 101 100 011 010 001 000 Digital Output Signal 111 111 001 010 011 111 011 PCM as ADC • Sampling • Makes the signal discrete in time. • If the analog input has a bandwidth of B Hz, then the minimum sample frequency such that the signal can be reconstructed without distortion, fs >= 2B • Quantization • Makes the signal discrete in amplitude. • Round off to one of q discrete levels. • Encode • Maps the quantized values to digital words that are nbits long. Analog Input Signal Sample ADC Quantize Encode EKT343-Principles of Communication Engineering Eeng 360 9

  10. Definition of Quantization • A process of converting an infinite number of possibilities to a finite number of conditions (rounding off the amplitudes of flat-top samples to a manageable number of levels). • In other words, quantization is a process of assigning the analog signal samples to a pre-determined discrete levels. The number of quantization levels, L determine the number of bits per sample, n. EKT343-Principles of Communication Engineering

  11. Quantization • The output of a sampler is still continuous in amplitude. • Each sample can take on any amplitude value e.g. 3.752 V, 0.001 V, etc. • The number of possible values is infinite. • To transmit as a digital signal we must restrict the number of possible values. • Quantization is the process of “rounding off” a sample according to some rule. • E.g. suppose we must round to the nearest discrete value, then: • 3.752 --> 3.8 0.001 --> 0 EKT343-Principles of Communication Engineering

  12. Quantization Example Analogue signal Sampling TIMING Quantization levels. Quantized to 5-levels Quantization levels Quantized 10-levels EKT343-Principles of Communication Engineering

  13. Types of Quantization 1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.

  14. Types of Uniform Quantization Midrise: Origin lies in the middle of a rising part of the staircase like graph (b), utilized for even levels Midtread: Origin lies in the middle of a tread of the staircase like graph in (a), utilized for odd levels

  15. Dynamic Range: (-8, 8) Output sample XQ 7 5 3 1 -8 -6 8 -4 -2 2 4 6 -1 -3 -5 -7 Quantization Characteristic Uniform Quantization • Most ADC’s use uniform quantizers. • The quantization levels of a uniform quantizer are equally spaced apart. • Uniform quantizers are optimal when the input distribution is uniform. When all values within the Dynamic Range of the quantizer are equally likely. Input sample X Example: Uniform n =3 bit quantizer L=8 and XQ = {1,3,5,7} EKT343-Principles of Communication Engineering Eeng 360 15

  16. Dynamic Range (DR) • Largest possible magnitude/smallest possible magnitude. • Where • DR = absolute value of dynamic range • Vmax = the maximum voltage magnitude • Vmin = the quantum value (resolution) • n = number of bits in the PCM code for n > 4 EKT343-Principles of Communication Engineering

  17. Coding Efficiency • A numerical indication of how efficiently a PCM code is utilized. • The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used. Coding Efficiency = Minimum number of bits x 100 Actual number of bits EKT343-Principles of Communication Engineering

  18. Example 1 • Calculate the dynamic range for a linear PCM system using 16-bit quantizing. • Calculate the number of bits in PCM code if the DR = 192.6 dB. Determine the coding efficiency in this case. EKT343-Principles of Communication Engineering

  19. Cont’d… • The quantization interval @ quantum = the magnitude difference between adjacent steps, • The resolution = the magnitude of a quantum = the voltage of the minimum step size. • The quantization error = the quantization noise = ½ quantum = (orig. sample voltage – quantize level) • The quantization range: is the range of input voltages that will be converted to a particular code. EKT343-Principles of Communication Engineering

  20. Quantization Error • A difference between the exact value of the analog signal & the nearest quantization level. • Quantization error is a round-off error in the transmitted signal that is reproduced when the code is converted back to analog in the receiver.

  21. Quantized Signal, XQ Signal X Quantization Noise, nQ Quantization Noise • The process of quantization can be interpreted as an additive noise process. • The signal to quantization noise ratio (SNR)Q=S/N is given as: EKT343-Principles of Communication Engineering

  22. Signal to Quantization Noise Ratio (SQR) • The worst possible signal voltage-to-quantization noise voltage ratio (SQR) occurs when the input signal occurs when input signal is at its minimum amplitude. SQR is directly proportional to resolution. • The worst-case voltage SQR EKT343-Principles of Communication Engineering

  23. Cont'd R =resistance (ohm) v = rms signal voltage q = quantization interval Qe = quantization error • SQR for a maximum input signal • The signal power-to-quantizing noise power ratio EKT343-Principles of Communication Engineering

  24. Example 2 • Calculate the SQR (dB) if the input signal = 2 Vrms and the quantization noise magnitudes = 0.02 V. • Determine the voltage of the input signals if the SQR = 36.82 dB and q =0.2 V. EKT343-Principles of Communication Engineering

  25. Nonuniform Quantization • Many signals such as speech have a nonuniform distribution. • The amplitude is more likely to be close to zero than to be at higher levels. • Nonuniform quantizers have unequally spaced levels • The spacing can be chosen to optimize the SNR for a particular type of signal. Output sample XQ 6 4 Example: Nonuniform 3 bit quantizer 2 -8 -6 8 -4 -2 2 4 6 Input sample X -2 -4 -6 EKT343-Principles of Communication Engineering

  26. Companding • Nonuniform quantizers are difficult to make and expensive. • An alternative is to first pass the speech signal through a nonlinearity before quantizing with a uniform quantizer. • The nonlinearity causes the signal amplitude to be Compressed. • The input to the quantizer will have a more uniform distribution. • At the receiver, the signal is Expanded by an inverse to the nonlinearity. • The process of compressing and expanding is called Companding. EKT343-Principles of Communication Engineering

  27. Cont'd • The process of compressing and then expanding. • The higher amplitude analog signals are compressed prior to transmission and then expanded in receiver. • Improving the DR of a communication system. EKT343-Principles of Communication Engineering

  28. Companding Functions EKT343-Principles of Communication Engineering

  29. Method of Companding • For the compression, two laws are adopted: the -law in US and Japan and the A-law in Europe. • -law • A-law • The typical values used in practice are: =255 andA=87.6. • After quantization the different quantized levels have to be represented in a form suitable for transmission. This is done via an encoding process. Vmax= Max uncompressed analog input voltage Vin= amplitude of the input signal at a particular of instant time Vout= compressed output amplitude A, = parameter define the amount of compression EKT343-Principles of Communication Engineering

  30. Cont’d... μ-law A-law EKT343-Principles of Communication Engineering

  31. Example 3 • A companding system with µ = 255 used to compand from 0V to 15 V sinusoid signal. Draw the characteristic of the typical system. EKT343-Principles of Communication Engineering

  32. Example 4 • A companding system with µ = 200 is used to compand -4V to 4V signal. Calculate the system output voltage for Vin = -4, -2, 0, 2 and 4V. Equation: EKT343-Principles of Communication Engineering

  33. Plot the compression characteristic that will handle input voltage in the given range and draw an 8 level non-uniform quantizer characteristic that corresponds to the given µ. EKT343-Principles of Communication Engineering

  34. SNR Performance of Compander • The output SNR is a function of input signal level for uniform quantizing. • But it is relatively insensitive for input level for a compander. • α = 4.77 - 20 Log( V/xrms) for Uniform Quantizer V is the peak signal level and xrms is the rms value • α = 4.77 - 20log[Ln(1 + μ)]for μ-law companding • α = 4.77 - 20 log[1 + Ln A]for A-law companding EKT343-Principles of Communication Engineering

  35. Encoding • The output of the quantizer is one of L possible signal levels. • If we want to use a binary transmission system, then we need to map each quantized sample into an n bit binary word. • Encoding is the process of representing each quantized sample by n bit code word. • The mapping is one-to-one so there is no distortion introduced by encoding. EKT343-Principles of Communication Engineering Eeng 360 35

  36. PCM encoding example Levels are encoded using this table Table: Quantization levels with belonging code words L=8 Chart 2. Process of restoring a signal. PCM encoded signal in binary form: 101 111 110 001 010 100 111 100 011 010 101 Total of 33 bits were used to encode a signal Chart 1. Quantization and digitalization of a signal. Signal is quantized in 11 time points & 8 quantization segments. EKT343-Principles of Communication Engineering

  37. PCM Example EKT343-Principles of Communication Engineering

  38. Nonlinear Encoding • Quantization levels not evenly spaced • Same concept as non-uniform quantization • Reduces overall signal distortion • Can also be done by companding EKT343-Principles of Communication Engineering

  39. PCM Line Speed • The data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line. • Where • Line speed = the transmission rate in bits per second • Sample/second = sample rate, fs • Bits/sample = no of bits in the compressed PCM code • Line speed also known as bit rate EKT343-Principles of Communication Engineering

  40. Example 5 • For a single PCM system with a sample rate fs = 6000 samples per second and a 7 bits compressed PCM code, calculate the line speed. EKT343-Principles of Communication Engineering

  41. Channel Bandwidth • The channel bandwidth, B required to transmit a pulse is given by • Where • κ = a constant with a value between 1 to 2 • n = number of bits • W = signal bandwidth • Channel BW = transmission BW EKT343-Principles of Communication Engineering

  42. Bandwidth of PCM Signals • The spectrum of the PCM signal is not directly related to the spectrum of the input signal. • The bandwidth of (serial) binary PCM waveforms depends on the bit rate R and the waveform pulse shape used to represent the data. • The Bit Rate R is R=nfs Where n is the number of bits in the PCM word (M=2n) and fsis the sampling rate. EKT343-Principles of Communication Engineering

  43. For no aliasing case (fs≥ 2B), the MINIMUM Bandwidth of PCM Bpcm(Min) is: Bpcm(Min)= R/2 = nfs//2 The Minimum Bandwidth of nfs//2 is obtained only when sin(x)/x pulse is used to generate the PCM waveform. • For PCM waveform generated by rectangular pulses, the First-null Bandwidth is: Bpcm= R = nfs EKT343-Principles of Communication Engineering

  44. Example 6 A signal with a bandwidth of 4.2 MHz is transmitted using binary PCM. The number of representation levels is 512. Calculate • The code word length • The bit rate • The transmission bandwidth, assuming that, κ = 2 • Find the SQR in dB for the signal given that peak signal voltage is 5Vp EKT343-Principles of Communication Engineering

  45. Bandlimited Analog signal Flat-top PAM signal Analog signal LPF BW=B Sampler & Hold Encoder Quantizer No. of levels=M Quantized PAM signal PCM signal Channel, Telephone lines with regenerative repeater Decoder Reconstruction LPF PCM signal Quantized PAM signal Analog Signal output PCM transmitter/receiver EKT343-Principles of Communication Engineering

  46. Noise in PCM Systems • Two main effects produce the noise or distortion in the PCM output: • Quantizing noise that is caused by the M-step quantizer at the PCM transmitter. • Bit errors in the recovered PCM signal, caused by channel noise and improper filtering. • If the input analog signal is band limited and sampled fast enough so that the aliasing noise on the recovered signal is negligible, the ratio of the recovered analog peak signal power to the total average noise power is: EKT343-Principles of Communication Engineering

  47. Cont’d • The ratio of the average signal power to the average noise power is • M is the number of quantized levels used in the PCM system. • Pe is the probability of bit error in the recovered binary PCM signal at the receiver DAC before it is converted back into an analog signal. EKT343-Principles of Communication Engineering

  48. Effects of Quantizing Noise • If Pe is negligible, there are no bit errors resulting from channel noise and no ISI, the Peak SNR resulting from only quantizing error is: • The Average SNR due to quantizing errors is: • Above equations can be expresses in decibels as, Where, M = 2n α = 4.77 for peak SNR α = 0 for average SNR EKT343-Principles of Communication Engineering

  49. Virtues & Limitation of PCM The most important advantages of PCM are: • Robustness to channel noise and interference. • Efficient regeneration of the coded signal along the channel path. • Efficient exchange between BT and SNR. • Uniform format for different kind of base-band signals. • Flexible TDM. EKT343-Principles of Communication Engineering

  50. Cont’d… • Secure communication through the use of special modulation schemes of encryption. • These advantages are obtained at the cost of more complexity and increased BT. • With cost-effective implementations, the cost issue no longer a problem of concern. • With the availability of wide-band communication channels and the use of sophisticated data compression techniques, the large bandwidth is not a serious problem. EKT343-Principles of Communication Engineering

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