ECE 4371, Fall, 2013 Introduction to Telecommunication Engineering/Telecommunication Laboratory

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ECE 4371, Fall, 2013 Introduction to Telecommunication Engineering/Telecommunication Laboratory. Zhu Han Department of Electrical and Computer Engineering Class 8 Sep. 23 th , 2013. Outline. PAM/PWM/PPM/PCM TDM Quantization SNR vs. quantization level Two optimal rules VQ quantization

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### ECE 4371, Fall, 2013Introduction to Telecommunication Engineering/Telecommunication Laboratory

Zhu Han

Department of Electrical and Computer Engineering

Class 8

Sep. 23th, 2013

Outline
• PAM/PWM/PPM/PCM
• TDM
• Quantization
• SNR vs. quantization level
• Two optimal rules
• VQ quantization
• A law/u law

k1

k2

k3

k4

k5

k6

Frequency

c

f

Time

t

Time Division Multiplexing

• 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
• 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).
Time Division Multiplexing
• 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
Quantization
• Scalar Quantizer Block Diagram
• Mid-rise
Quantization SNR

, 6dB per bit

Example
• SNR for varying number of representation levels for sinusoidal modulation 1.8+6 X dB
Conditions for Optimality of Scalar Quantizers

Let m(t) be a message signal drawn from a stationary process M(t)

-A m  A

m1= -A

mL+1=A

mk mk+1 for k=1,2,…., L

The kth partition cell is defined as

Jk: mk< m  mk+1 for k=1,2,…., L

d(m,vk): distortion measure for using vk to represent values inside Jk.

Vector Quantization

image and voice compression,

voice recognition

statistical pattern recognition

volume rendering

Distortion

SQ

VQ

Rate (bps)

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(L1), mean square error (L2)
• Vector Quantizer often performs better than Scalar Quantizer with the cost of complexity
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
• More sensitive at small-amplitude range (e.g., 0 might sound different from 0.1)
• Less sensitive at large-amplitude range (e.g., 0.7 might not sound different much from 0.8)

histogram of typical

speech signals

^

^

x

y

Non-uniform Quantizer

F: nonlinear compressing function

F-1: nonlinear expanding function

F and F-1: nonlinear compander

y

Q

F

F-1

x

Example

F: y=log(x) F-1: x=exp(x)

We will study nonuniform quantization by PCM example next

A law and  law

EE 541/451 Fall 2006

 Law/A Law
• The -law algorithm (μ-law) is a companding algorithm, primarily used in the digitaltelecommunication 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).
• A-law algorithm used in the rest of worlds.
• 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.
 Law/A Law

Example 6.2 and 6.3

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
• Sigma Delta
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 ms
• Typical resolution
• 8 to 12 bits
• Cost
• 15 to 600 CHF

Vin

-

+

Counting time

StartConversion

StartConversion

Enable

S

Q

R

N-bit Output

Counter

C

Clk

Oscillator

IN

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