4.2 Digital Transmission Pulse Modulation Pulse Code Modulation Outlines Pulse Modulation Pulse Code Modulation Delta Modulation Line Codes EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Conversions Between Signal Types Review Conversions Between Signal Types Sampling Quantizing Encoding

PULSE MODULATION (PM) Sampling analog information signal Converting samples into discrete pulses Transport the pulses from source to destination over physical transmission medium. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Four (4) Methods of PM 1. PAM 2. PWM 3. PPM 4. PCM PAM–Pulse Amplitude Modulation, PWM-Pulse Width Modulation PPM-Pulse Position Modulation, PCM-Pulse Code Modulation Analog Pulse Modulation Digital Pulse Modulation EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Analog Pulse Modulation Carrier signal is pulse waveform and the modulated signal is where one of the carrier signal’s characteristic (either amplitude, width or position) is changed according to information signal. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Pulse Amplitude Modulation (PAM) The amplitude of pulses (carrier) is varied in accordance with the information signal. Width & position constant. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Pulse Width Modulation (PWM) Sometimes called Pulse Duration Modulation (PDM). The width of pulses is varied in accordance to information signal. Amplitude & position constant. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Pulse Position Modulation (PPM) Modulation in which the temporal positions of the pulses are varied in accordance with some characteristic of the information signal. Amplitude & width constant. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Advantages & Drawbacks of Pulse Modulation Requires greater BW to transmit & receive as compared to its analog counterpart. Special encoding & decoding methods must be used to increased transmission rates & more difficult to be recovered. Requires precise synchronization of clocks between Tx & Rx. Noise immunity. Relatively low cost digital circuitry. Able to be time division multiplexed with other pulse modulated signal. Storage of digital streams. Error detection & correction EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Sampling A process of taking samples of information signal at a rate of Nyquist’s sampling frequency. Nyquist’s Sampling Theorem : The original information signal can be reconstructed at the receiver with minimal distortion if the sampling rate in the pulse modulation system equal to or greater than twice the maximum information signal frequency. fs >= 2fm (max) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Example 1 A CD audio laser disk system has a frequency bandwidth of 20Hz to 20kHz. What is the minimum sample rate required to satisfy the Nyquist sample rate? Ans: fs=2fm(max)=40kHz. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Two basic techniques used to perform the sampling function: Natural sampling Flat-top sampling EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Natural Sampling Tops of the sample pulses retain their natural shape during the sample interval. Frequency spectrum of the sampled output is different from an ideal sample. Amplitude of frequency components produced from narrow, finite-width sample pulses decreases for the higher harmonics Requiring the use of frequency equalizers EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Natural Sampling EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Flat-top Sampling Most commonly used in PCM systems. Accomplish in a sample-and-hold circuit To periodically sample the continually changing analog input voltage & convert to a series of constant-amplitude PAM voltage levels. The input voltage is sampled with a narrow pulse and then held relatively constant until the next sample is taken. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d… Sampling process alters the frequency spectrum & introduces aperture error. The amplitude of the sampled signal changes during the sample pulse time. Advantages: Introduces less aperture distortion Can operate with a slower ADC EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Flat-top Sampling EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

PULSE CODE MODULATION (PCM) Basic scheme of PCM system Quantization Quantization Error Companding Block diagram & function of TDM-PCM communication system EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Basic scheme of PCM system The most common technique for using digital signals to encode analog data is PCM. Example: To transfer analog voice signals off a local loop to digital end office within the phone system, one uses a codec. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

codec Coder-decoder EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Because voice data limited to frequencies below 4000 Hz, a codec makes 8000 samples/sec. (i.e., 125 microsecond/sample). (Nyquist) If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

PCM Block Diagram Four step process Most common form of analog to digital modulation (better noise and interference immunity) 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) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

4 Steps Process EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Quantization Quantization-the process of converting an infinite number of possibilities to a finite number of conditions. The process of rounding off the amplitudes of flat top sample to a manageable number of levels. The process of segmenting a sampled signal in a PCM system into different voltage levels, each level corresponding to different binary number. The quantization levels determine the resolution of the digitizing system. Analog signals are quantized to the closest binary value. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d… Analog signal is sampled. Converted to discrete-time continuous-amplitude signal (Pulse Amplitude Modulation) Pulses are quantized and assigned a digital value. A 7-bit sample allows 128 quantizing levels. PCM uses non-linear encoding, i.e., amplitude spacing of levels is non-linear There is a greater number of quantizing steps for low amplitude This reduces overall signal distortion. This introduces quantizing error (or noise). PCM pulses are then encoded into a digital bit stream. 8000 samples/sec x 7 bits/sample = 56 Kbps for a single voice channel. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Quantized waveform Coded waveform 3 bit PCM pulse train Sampling pulses Quantization level (V) Quantized waveform Coded waveform 3 bit PCM pulse train EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

PCM Example EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

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). EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d… The quantization interval or quantum = the magnitude difference between adjacent steps. The resolution = the magnitude of a quantum = the voltage of the minimum step size. The quantization error (Qe) = the quantization noise (Qn) = ½ quantum = (orig. sample voltage – quantized level) Folded PCM code = (sample voltage/resolution) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Analog input signal Qe Exactly 2V No Qe Approximately +2.6 V Sample pulse PAM signal PCM code Exactly -1V No Qe Qe EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Example 2 From the information given in the previous slide, determine the following; (i) Resolution (ii) Sample voltage at t3 (iii) Qe at t3 (iv) Explain the quality of the generated PCM Ans: 1V,2.6V,0.4V, EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

QUANTIZATION ERROR A difference between the exact value of the analog signal & the nearest quantization level. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Types of Quantization Midtread Midrise EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Example 3 Using the same information, for the PCM code for analog sample voltage of +1.07V, determine; (i) Quantized voltage (ii) Qe (iii) PCM code Ans : 1,0.07,101 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

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

Dynamic Range (DR) Ratio of the 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 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Example 4 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 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Coding Efficiency = Minimum number of bits x 100 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

Example 5 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 : Minimum sample rate. (ans: 8kHz) Minimum number of bits used (ans :n=7.65≈8) Resolution (ans : 0.01V ) Quantization error (ans: 0.01V/2=0.005V) Coding efficiency (ans: (8.63/9)x100%=95.89%) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

DIGITAL TRANSMISSION PART II

Signal to Quantization Noise Ratio (SQR) The worst-case voltage SQR SQR for a maximum input signal The signal power-to-quantizing noise power ratio R =resistance (ohm) v = rms signal voltage q = quantization interval EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

Example 2 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

Effect of Non-Linear Coding EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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

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

Companding Functions EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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 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. 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 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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

Cont’d... A-law μ-law EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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. 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

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. ANS: (6000)(7)=42,000 bps. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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

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

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

Block diagram of TDM-PCM communication system EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

DELTA MODULATION (DM) 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. Only encodes and transmits one bit per sample time 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

Cont’d… EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

Operation of Delta Modulation EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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

The transmitter of a DM System Cont’d... The transmitter of a DM System EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

The receiver of a DM system EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

Delta Modulation - Example EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

DM circuit’s problem Step size EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL MODULATION

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

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

DM Performance Good voice reproduction PCM - 128 levels (7 bit) Voice bandwidth 4kHz (line speed) 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

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

LINE CODES The line codes properties: Line code is an encoding scheme. Many possible ways to encode 0s and 1s. Converting standard logic level to a form more suitable to telephone line transmission. Different types of encoding schemes or line codes can be used to improve signal’s noise immunity and to achieve higher data rates. The line codes properties: Transmission BW should be small as possible Efficiency should be as high as possible Error detection & correction capability Transparency (Encoded signal is received faithfully) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Cont’d... Six factors must be considered when selecting a line encoding format; Transmission voltage & DC component Duty cycle Bandwidth consideration Clock and framing bit recovery Error detection Ease of detection and decoding EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Why Digital Signaling? Low cost digital circuits The flexibility of the digital approach (because digital data from digital sources may be merged with digitized data derived from analog sources to provide general purpose communication system) EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Digital Encoding Using Digital Signals to Transmit Digital Data Bits must be changed to digital signal for transmission Unipolar encoding Positive or negative pulse used for zero or one Polar encoding Uses two voltage levels (+ and - ) for zero or one Bipolar encoding +, -, and zero voltage levels are used EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Non-Return to Zero-Level (NRZ-L) Two different voltages for 0 and 1 bits. Voltage constant during bit interval. no transition, no return to zero voltage More often, negative voltage for one value and positive for the other. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Non-Return to Zero Inverted (NRZ-I) Nonreturn to zero inverted on ones Constant voltage pulse for duration of bit Data encoded as presence or absence of signal transition at beginning of bit time Transition (low to high or high to low) denotes a binary 1 No transition denotes binary 0 An example of differential encoding EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Multilevel Binary (Bipolar-AMI) zero represented by no line signal. one represented by positive or negative pulse alternately. No loss of sync if a long string of ones (zeros still a problem) No net dc component Lower bandwidth Easy error detection 0 1 0 0 1 1 0 0 0 1 1 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Pseudoternary One represented by absence of line signal Zero represented by alternating positive and negative No advantage or disadvantage over bipolar-AMI 0 1 0 0 1 1 0 0 0 1 1 EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Manchester There is always a mid-bit transition {which is used as a clocking mechanism}. The direction of the mid-bit transition represents the digital data. 1  low-to-high transition 0  high-to-low transition Consequently, there may be a second transition at the beginning of the bit interval. Used in 802.3 baseband coaxial cable and CSMA/CD twisted pair. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Differential Manchester mid-bit transition is ONLY for clocking. 1  absence of transition at the beginning of the bit interval 0  presence of transition at the beginning of the bit interval Differential Manchester is both differential and bi-phase. [Note – the coding is the opposite convention from NRZI.] Used in 802.5 (token ring) with twisted pair. Modulation rate for Manchester and Differential Manchester is twice the data rate  inefficient encoding for long-distance applications. EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

There is always a mid-bit transition, 1  low-to-high transition 0  high-to-low transition EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION mid-bit transition is ONLY for clocking , 1  absence of transition 0  presence of transition

Example 5 Sketch the data wave form for a bit stream 11010 using NRZL Bipolar AMI Pseudoternary EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION

Solution

END DIGITAL TRANSMISSION EKT 231 : COMMUNICATION SYSTEM CHAPTER 4 : DIGITAL TRANSMISSION