1. ECE 4371, Fall, 2014 Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu Han Department of Electrical and Computer Engineering Class 8 Sep. 22 nd, 2014

2. Outline PAM/PWM/PPM/PCM TDM Quantization –SNR vs. quantization level –Two optimal rules –VQ quantization –A law/u law Practical ADC/DAC

3. PAM, PWM, PPM, PCM

4. Entire spectrum is allocated for a channel (user) for a limited time. The user must not transmit until its next turn. Used in 2nd generation Advantages: –Only one carrier in the medium at any given time –High throughput even for many users –Common TX component design, only one power amplifier –Flexible allocation of resources (multiple time slots). f t c k2k2 k3k3 k4k4 k5k5 k6k6 k1k1 Frequency Time Time Division Multiplexing

5. Time Division Multiplexing Disadvantages –Synchronization –Requires terminal to support a much higher data rate than the user information rate therefore possible problems with intersymbol-interference. Application: GSM  GSM handsets transmit data at a rate of 270 kbit/s in a 200 kHz channel using GMSK modulation.  Each frequency channel is assigned 8 users, each having a basic data rate of around 13 kbit/s

6. Quantization Scalar Quantizer Block Diagram Mid-tread Mid-rise

7. Equations

8. Quantization Noise

9. Quantization Noise Level

10. Quantization SNR, 6dB per bit

11. Example SNR for varying number of representation levels for sinusoidal modulation 1.8+6 X dB Number of representation level L Number of Bits per Sample, R SNR (dB) 32531.8 64637.8 128743.8 256849.8

12. Conditions for Optimality of Scalar Quantizers Let m(t) be a message signal drawn from a stationary process M(t) -A  m  A m 1 = -A m L+1 =A m k  m k+1 for k=1,2,…., L The kth partition cell is defined as J k : m k < m  m k+1 for k=1,2,…., L d(m, v k ): distortion measure for using v k to represent values inside J k.

13. Condition for Optimal Quantizer

14. Condition One

15. Condition Two

16. Vector Quantization image and voice compression, voice recognition statistical pattern recognition volume rendering

17. Rate Distortion Curve Rate: How many codewords (bits) are used? –Example: 16-bit audio vs. 8- bit PCM speech Distortion: How much distortion is introduced? –Example: mean absolute difference(L 1 ), mean square error (L 2 ) Vector Quantizer often performs better than Scalar Quantizer with the cost of complexity Rate (bps) Distortion SQ VQ

18. Non-uniform Quantization Motivation –Speech signals have the characteristic that small- amplitude samples occur more frequently than large-amplitude ones –Human auditory system exhibits a logarithmic sensitivity u More sensitive at small- amplitude range (e.g., 0 might sound different from 0.1) u Less sensitive at large- amplitude range (e.g., 0.7 might not sound different much from 0.8) histogram of typical speech signals

19. EE 541/451 Fall 2006 Non-uniform Quantizer x Q x ^ FF -1 Example F: y=log(x)F -1 : x=exp(x) y y ^ F: nonlinear compressing function F -1 : nonlinear expanding function F and F -1 : nonlinear compander We will study nonuniform quantization by PCM example next A law and  law

20.  Law/A Law The  -law algorithm (μ-law) is a companding algorithm, primarily used in the digital telecommunication systems of North America and Japan. Its purpose is to reduce the dynamic range of an audio signal. In the analog domain, this can increase the signal to noise ratio achieved during transmission, and in the digital domain, it can reduce the quantization error (hence increasing signal to quantization noise ratio).compandingdigitaltelecommunication North AmericaJapandynamic rangesignal A-law algorithm used in the rest of worlds. A-law algorithm A-law algorithm provides a slightly larger dynamic range than the mu-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it.

21.  Law

22. A Law

23.  Law/A Law Example 6.2 and 6.3

24. Analog to Digital Converter Main characteristics –Resolution and Dynamic range : how many bits –Conversion time and Bandwidth: sampling rate Linearity –Integral –Differential Different types –Successive approximation –Slope integration –Flash ADC –Sigma Delta

25. Successive approximation Compare the signal with an n-bit DAC output Change the code until –DAC output = ADC input An n-bit conversion requires n steps Requires a Start and an End signals Typical conversion time –1 to 50  s Typical resolution –8 to 12 bits Cost –15 to 600 CHF

26. Single slope integration Start to charge a capacitor at constant current Count clock ticks during this time Stop when the capacitor voltage reaches the input Cannot reach high resolution –capacitor –comparator - + IN C R S Enable N-bit Output Q Oscillator Clk Counter Start Conversion Vin Counting time

27. Flash ADC Direct measurement with 2n-1 comparators Typical performance: –4 to 10-12 bits –15 to 300 MHz –High power Half-Flash ADC –2-step technique u 1st flash conversion with 1/2 the precision u Subtracted with a DAC u New flash conversion Waveform digitizing applications

28. Sigma-Delta ADC

29. Over-sampling ADC Hence it is possible to increase the resolution by increasing the sampling frequency and filtering Reason is the noise level reduce by over sampling. Example : –an 8-bit ADC becomes a 9-bit ADC with an over-sampling factor of 4 –But the 8-bit ADC must meet the linearity requirement of a 9-bit

30. Resolution/Throughput Rate

31. Digital to Analog Converter Pulse Width Modulator DAC Pulse Width Modulator Delta-Sigma DAC Binary Weighted DAC R-2R Ladder DAC R-2R Ladder Thermometer coded DAC Segmented DAC Hybrid DAC