Pulse Modulation Introduction Sampling Process PulseAmplitude Modulation Other

Pulse Modulation • • • • Introduction Sampling Process Pulse-Amplitude Modulation Other forms of Pulse Modulations Bandwidth-Noise Trade-off Quantization Process Pulse-Code Modulation Noise Consideration in PCM Systems Time-Division Multiplexing Digital Multiplexers Virtues, Limitations, and Modifications of PCM Linear Prediction Differential PCM Adaptive Differential PCM Delta Modulation 2

Introduction Continuous-Wave Modulation: Some parameter (amplitude, phase, or frequency) of a sinusoidal carrier wave is varied continuously in accordance with the message signal. Analog Pulse Modulation: Some parameter (amplitude, duration, or position) of each pulse (in a periodic pulse train) is varied in a continuous manner in accordance with the corresponding sample value of the message signal. (Information transmission in analog form, but transmission at discrete times. ) Digital Pulse Modulation: The message signal is represented in a form that is discrete in both time and amplitude, thereby permitting its transmission in digital form as a sequence of coded pulses. 3

Sampling Process (1) fs = 2 W Ts = 1/(2 W) 4

Sampling Process (2) Sampling theorem: A band-limited signal of finite energy, which has no frequency components higher than W Hertz, 1) is completely described by specifying the values of the signal at instants of time separated by 1/(2 W) seconds. 2) may be completely recovered from a knowledge of its samples taken at the rate of 2 W samples per second. fs < 2 W fs > 2 W 5

Pulse Amplitude Modulation (1) 6

Pulse Amplitude Modulation (2) Reconstruction filter Aperture effect: Flat-top samples Amplitude distortion and T/2 delay Equalizer 7

Other forms of Pulse Modulation Modulating signal Carrier Pulse Duration Modulation (Pulse Width Modulation) Pulse Position Modulation 8

Bandwidth-Noise Trade-off (1) PPM is the optimum form of analog pulse modulation, and has similar noise performance as FM: 1) Both systems have a figure of merit proportional to the square of the transmission bandwidth normalized with respect to the message bandwidth. 2) Both systems exhibit a threshold effect as the signal-to-noise ratio is reduced. Can we produce a trade-off better than a square law? Yes, by Digital Pulse Modulation. 9

Bandwidth-Noise Trade-off (2) A basic form of DPM is Pulse Code Modulation: • Discrete in both time and amplitude. • Transmission of the message signal as a sequence of coded binary pulses. • The effect of channel noise at the receiver output can be reduced to a negligible level simply by making the average power of the transmitted binary PCM wave large enough compared to the average power of the noise. Two fundamental processes are involved in the generation of a binary PCM wave: 1) Sampling: Discrete-time representation of the message signal 2) Quantization: Discrete –amplitude representation of the message signal Possibility to realize an exponential law for the bandwidthnoise trade-off. 10

Quantization Process (1) midtread midrise 11

Quantization Process (2) Quantization Noise 12

Quantization Process (3) Quantization Noise (SNR)O Increases exponentially with the number of bits. 13

Quantization Process (4) Example: Sinusoidal Modulating Signal L (levels) R (bits) SNR (d. B) 256 8 49. 8 1024 10 61. 8 4096 12 73. 8 16384 14 85. 8 65536 16 91. 8 14

Pulse Code Modulation (1) Basic Elements 15

Pulse Code Modulation (2) Quantization (Compression & Expansion) μ Law A Law Typical used values: μ = 225 , A = 87. 6 16

Pulse Code Modulation (3) Line Codes: Unipolar NRZ Polar NRZ Unipolar RZ Bipolar RZ (AMI) Manchester (Split Phase) 17

Pulse Code Modulation (4) Line Codes: Unipolar NRZ Polar NRZ Unipolar RZ Bipolar RZ Manchester 18

Pulse Code Modulation (5) Line Codes: Unipolar NRZ DC component and thus waste of DC power Nonzero spectrum near zero frequency Lack of synchronization Polar NRZ High spectrum near zero frequency Lack of synchronization Unipolar RZ DC component and high Spectrum near zero frequency Need for more power than Polar NRZ and twice bandwidth Good for timing recovery Bipolar RZ No DC component Low spectrum near zero frequency (if equal probability for “ 1”s and “ 0”s) Good for timing recovery Manchester No DC component Low spectrum near zero frequency (regardless of signal statistics) Very good for timing recovery Twice bandwidth 19

Pulse Code Modulation (6) Differential Encoding 20

Pulse Code Modulation (6) Regeneration: 1) Channel noise and interference Wrong decisions Bit errors 2) Deviation of spacing between received pulses Jitter Distortion Decoding: Generating a pulse the amplitude of which is the weighted sum of all the pulses in the code word. Filtering: Low-pass reconstruction filter whose cutoff frequency is equal to the message bandwidth. 21

Noise Considerations in PCM Systems (1) Two major sources of Noise: Channel Noise • Is introduced anywhere between the transmitter output and the receiver input. • Always present, once the equipment is switched on. Quantization Noise • Is introduced in transmitter and is carried all the way along to the receiver output. • Is signal-dependent. It disappears when the message signal is switched off. Measure for fidelity of PCM transmission: Average probability of symbol error Bit Error Rate (BER) 22

Noise Considerations in PCM Systems (2) Error Threshold: Eb/N 0 (d. B) Pe Time between errors (Bit Rate = 105 bps) 4. 3 10 -2 10 -3 Second 8. 4 10 -1 Second 10. 6 10 -6 10 Seconds 12 10 -8 20 Minutes 13 10 -10 1 Day 14 10 -12 3 Months Eb/N 0: The ratio of the transmitted signal energy per bit, to the noise spectral density. 23

Time-Division Multiplexing Block Diagram of TDM System 24

Digital Multiplexer 1 1 2 Multiplexer High-speed Transmission Line 2 Demultiplexer N Data Sources T 1 Digital Hierarchy DS 0: 64 Kbps DS 1: 1. 544 Mbps DS 2: 6. 312 Mbps DS 3: 44. 736 Mbps DS 4: 274. 176 Mbps DS 5: 560. 160 Mbps N Destinations one voice channel (twenty four DS 0) {(1+24 x 8)x 8 KSamples/Sec} (four DS 1) (seven DS 2) (six DS 3) (two DS 4) 25

Virtues, Limitations and Modifications of PCM (1) Advantages: 1) Robustness to channel noise and interference 2) Efficient regeneration of the coded signal along the transmission path. 3) Efficient exchange of increased channel bandwidth for improved signal-to-noise ratio, obeying an exponential law. 4) A uniformat for the transmission of different kinds of baseband signals, hence their integration with other forms of digital data in a common network. 5) Comparative ease with which message sources may be dropped or reinserted in a time-division multiplex system. 6) Secure communication through the use of special modulation scheme or encryption. 26

Virtues, Limitations and Modifications of PCM (2) Limitations: 1) Increased system complexity >> Cost effective fashion using VLSI 2) Increased channel bandwidth >> Availability of wideband channels (satellite, fiber optics) >> Data compression techniques Modifications: 1) Differential PCM 2) Adaptive Differential PCM (DPCM) (ADPCM) 27

Linear Prediction (Finite-duration Impulse Response (FIR) Discrete-time Filter) Linear Adaptive Prediction 28

Differential Pulse Code Modulation Transmitter Receiver 29

Adaptive Differential Pulse Code Modulation Adaptive Quantization with: • Forward estimation (AQF) • Backward estimation (AQB) AQB Adaptive Prediction with: • Forward estimation (APF) • Backward estimation (APB) APB 30

Delta Modulation (1) • Sampling at higher rates • One bit for each sample 31

Delta Modulation (2) Transmitter Receiver 32

Delta Modulation (3) Slope Overload Required condition: (for no overload) 33

Delta Modulation (4) Delta-Sigma Modulation • Simplification of the receiver • Pre-emphasis of low-frequency content of the input signal • Increasing correlation between adjacent samples reduction the variance of the error signal 34