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DIGITAL TRANSMISSION PART B 1 Review… PCM Block Diagram • Most common form of analog to digital modulation (better noise and interference immunity) • Four step process 1. Signal is sampled using PAM (Sample) 2. Integer values assigned to signal (PAM) 3. Values converted to binary (Quantized) 4. Signal is digitally encoded for transmission (Encoded) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 2 Review… Types of Quantizer 1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 3 Review… Dynamic Range (DR) □ Ratio of the largest possible magnitude/smallest possible magnitude. Vmax Vmax DR Vmin resolution DR 2n 1 □ Where DR (dB) 20 log( DR ) □ DR = absolute value of dynamic range □ Vmax = the maximum voltage magnitude □ Vmin = the quantum value (resolution) □ n = number of bits in the PCM code EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 4 Review… Review Example.. 1. Calculate the dynamic range for a linear PCM system using 16-bit quantizing. 2. Calculate the number of bits in PCM code if the DR = 192.6 dB EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 5 Review… 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 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 6 Review… Review Example Given A PCM system with the following parameters Maximum analog input frequency = 4kHz. Maximum decoded voltage at Rx = ±2.55V. Minimum dynamic range = 46 dB Determine : (i) Minimum sample rate. (ans: 8kHz) (ii) Minimum number of bits used (ans :n=7.63≈8) (iii) Resolution (ans : 0.01V ) (iv) Quantization error (ans: 0.01V/2=0.005V) (v) Coding efficiency (ans: (8.63/9)x100%=95.89%) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION 7 Signal to Quantization Noise Ratio (SQR) □ The worst-case voltage SQR SQR(min) resolution Qe □ SQR for a maximum input signal SQR(max) Vmax Qe R =resistance (ohm) v = rms signal voltage q = quantization interval □ The signal power-to-quantizing noise power ratio average signal power SQR( dB ) 10 log average quantizati on noise power 10 log EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION v2 R 2 ( q 12) R v2 10 log q 2 12 8 Example 2 1. Calculate the SQR (dB) if the input signal = 2 Vrms and the quantization noise magnitudes = 0.02 V. 2. Determine the voltage of the input signals if the SQR = 36.82 dB and q =0.2 V. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 9 Effect of Non-Linear Coding EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 10 Nonlinear Encoding □ Quantization levels not evenly spaced □ Reduces overall signal distortion □ Can also be done by companding EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 11 Companding • 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. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 12 Companding Functions EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 13 Method of Companding □ For the compression, two laws are adopted: the -law in US and Japan and the A-law in Europe. □ -law □ Vout □ A-law Vout Vmax ln( 1 Vin Vmax ) ln( 1 ) A Vin Vmax Vmax 1 ln A Vin 1 ln( A Vmax ) 1 ln A Vin 1 0 Vmax A 1 Vin 1 A Vmax 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 □ The typical values used in practice are: =255 and A=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. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 14 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. □ Draw an 8 level non-uniform quantizer characteristic that corresponds to the mentioned µ. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 15 16 Cont’d... μ-law EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION A-law 17 PCM Line Speed □ Line speed is the data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line. line speed samples bits X second sample □ 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 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 18 Example 4 □ 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. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 19 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 baseband signals. □ Flexible TDM. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 20 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. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 21 Time-Division Multiplexing □ This technique combines time-domain samples from different message signals (sampled at the same rate) and transmits them together across the same channel. □ The multiplexing is performed using a commutator (switch). At the receiver a decommutator (switch) is used in synchronism with the commutator to demultiplex the data. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 22 Cont’d… □ TDM system is very sensitive to symbol dispersion, that is, to variation of amplitude with frequency or lack of proportionality of phase with frequency. This problem may be solved through equalization of both magnitude and phase. □ One of the methods used to synchronize the operations of multiplexing and demultiplexing is to organize the multiplexed stream of data as frames with a special pattern. The pattern is known to the receiver and can be detected very easily. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 23 Block diagram of TDM-PCM communication system EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 24 □ Conventional PCM- multiple bit codes required to represent the sample value. □ DM-Uses a single-bit PCM code to achieve digital transmission of analog signals. □ Logic ‘0’ is transmitted if current sample is smaller than the previous sample □ Logic ‘1’ is transmitted if current sample is larger than the previous sample EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 25 Cont’d… EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 26 Operation of Delta Modulation EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 27 Cont’d... □ Analog input is approximated by a staircase function □ Move up or down one level () at each sample interval (by one quantization level at each sampling time) output of DM is a single bit. □ Binary behavior □ Function moves up or down at each sample interval □ In DM the quantization levels are represented by two symbols: 0 for - and 1 for +. In fact the coding process is performed on eq. □ The main advantage of DM is its simplicity. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 28 Cont’d... The transmitter of a DM System EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 29 The receiver of a DM system EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 30 Delta Modulation - Example EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 31 DM circuit’s problem EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 32 Cont’d… •Slope overload distortion is due to the fact that the staircase approximation mq(t) can't follow closely the actual curve of the message signal m(t ). In contrast to slope-overload distortion, granular noise occurs when is too large relative to the local slope characteristics of m(t). granular noise is similar to quantization noise in PCM. •It seems that a large is needed for rapid variations of m(t) to reduce the slope-overload distortion and a small is needed for slowly varying m(t) to reduce the granular noise. The optimum can only be a compromise between the two cases. •To satisfy both cases, an adaptive DM is needed, where the step size can be adjusted in accordance with the input signal m(t). EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 33 Cont’d... □ In summary □ Slope overload □ Due to the input analog signal amplitude changes faster than the speed of the modulator □ to minimize : the product of the sampling step size and the sampling rate must be equal to or larger than the rate of change of the amplitude of the input analog signal. □ Granular noise □ Due to the difference between step size and sampled voltage. □ To minimize : increase the sampling rate, decrease the step size of modulator EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 34 DM Performance □ Good voice reproduction □ PCM - 128 levels (7 bit) □ Voice bandwidth 4kHz □ Should be 8000 x 7 = 56kbps for PCM □ Data compression can improve on this □ e.g. Interframe coding techniques for video EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 35 Cont’d... □ Adaptive Delta Modulation (ADM) □ A Delta Modulation system where the step size of the DAC is automatically varied depending on the amplitude characteristics of the analog signal. □ A well designed ADM scheme can transmit voice at about half the bit rate of a PCM system with equivalent quality. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION 36