1. ECEN5533. Modern Communications Theory Lecture #12. 8 February 2016 Dr
ECEN Modern Communications Theory Lecture #12 8 February 2016 Dr. George Scheets
Exam #1, 10 February
Chapters 1 & 5
Design #1 due 19 February
Quiz 1 Results
Hi = 19.4, Low = 12.4, Ave. = 16.58, σ = 2.97

2. ECEN5533 Modern Communications Theory Lecture #14 12 February 2016 Dr. George Scheets
Read: 2.1 – 2.4
Problems: 2.1, 7, 9, & 11
Reworked Exams due 19 February
Design #1 due 26 February

3. OSU IEEE February General Meeting 5:30-6:30 pm, Wednesday, 17 February
ES201b
Reps from Zeeco will
present
Dinner will be served + 3 points extra credit
All are invited

4. Testable Material
Lecture
Textbook
Homework
Communication Theory

5. To Maximize your score…
Budget your time
Tackle all the problems
Partial Credit is awarded
Show intermediate results
Obtain correct answer
Tests are full period, 4 pages, 100 points
Open book & notes
HW rework for < 1/2 of lost points

6. Analog to Digital Conversion) Part 1...
Sampler
analog
input
x(t)
discrete time
output
xs(t)
transmitter side

7. Delta Functions from Sinusoids
4 cosines
16 cosines
32 cosines

8. Sampling Ideal Sampler Realizable Sampler
Minimum Sampling Frequency > 2 * Wabs
Practically, it's about 2.2*Wabs
Output is discrete time
Contains info to precisely reconstruct original
Voltage is still Continuous
Infinite Precision → Infinite # of bits/sample

9. Video Undersampling Typical TV Video has 30 frames/second
Frame = Still Picture
Car Commercial Wheel spokes moving the wrong way Wheel spokes stationary, car moving → fs not high enough

10. The # of Round-off Levels Matters Too 24 bit color 224 = 16
The # of Round-off Levels Matters Too 24 bit color 224 = M colors

11. 256 Colors

12. 16 Colors

13. Example) Coding a Microphone Output
m(t) volts (air pressure)
time (sec)
Energy from about ,500 Hz.

14. A/D Converter m(t) volts (air pressure) 1/8000 second time (sec)
Step #1)
Sample the waveform at rate > 2*Max Frequency.
Convert samples to a bit stream.
Note: Wired telephone voice is sampled at 8,000 samples/second.

15. A/D Converter Simplest technique is PCM
Wired Telephone System
Audio Compact Disks
Pulse Code Modulation Round off to N possible voltages Equal length Code word is assigned to each voltage N Typically a Power of 2 Log2N bits per code word

16. A/D Converter. 1 bit/sample.
Example) N = 2. Assign 0 or 1 to voltage.
3.62 v, output a 1 t1
time (sec)
0 < Voltage < +5v, Assign Logic 1
-5v < Voltage < 0, Assign Logic 0
Bit Stream Out =

17. A/D Converter. 1 bit/sample.
Example) N = 2. Assign 0 or 1 to voltage.
Far side gets (13 samples)
Need to output 13 voltages.
What does a 1 represent? A 0?
Receive a 1? Output +2.5 v (mid-range)
Receive a 0? Output -2.5 v (mid-range)
Hold the voltage until next sample
0 < Voltage < +5v, Assign Logic 1
-5v < Voltage < 0, Assign Logic 0

18. A/D Converter. 1 bit/sample.
Input to the transmitter.
Output at the receiver.
+2.5 v
-2.5 v
Considerable Round-Off error exists.

19. A/D Converter. 2 bits/sample
Example) N = 4. Assign 00, 01, 10 or 11.
3.62 v, Assign 11
+2.5 v
time (sec) t1
-2.5 v
2.5 < Voltage < 5 , Assign 11
0 < Voltage < 2.5, Assign 10
-2.5 < Voltage < 0, Assign 00
-5 < Voltage < -2.5, Assign 01
Bit Stream Out =

20. A/D Converter. 2 bits/sample.
Input to the transmitter.
Output at the receiver.
+3.75 v
+1.25 v
-1.25 v
-3.75 v
Receive 11? Output 3.75v Receive 10? Output 1.25v
Receive 00? Output -1.25v
Receive 01? Output -3.75v
Reduced Round-Off error exists.

21. Wired Telephone Local Loop
WN = 3.5 KHz
Twisted
Pair Cable
Low Pass
Filter
Sampler
Fs = 8 KHz
Nonuniform
Quantize
256 levels
PCM
Coder
8 bits/sample
64 Kbps

22. Telephone Local Loop: Voice
64 Kbps
Decode
256 levels
Hold
1/8000 sec
Low Pass
Filter
Analog Out

23. Compact Disk WN = 20 KHz Audio Source Low Pass Filter Sampler
Fs = 44.1 KHz
Code
16 bits/sample
Quantize
65,536 levels
705.6 Kbps

24. Compact Disk 705.6 Kbps Decode 65,536 levels Hold 1/44,100 sec
Low Pass
Filter
Analog Out

25. Sampling & Quantizing Examples
fs = 16 KHz
4096 quantiles
256 quantiles (approximate phone quality)
32 quantiles
4 quantiles (generally 2 levels used!)
fs = 8 KHz (some interference)
fs = 2 KHz
fs = 1 KHz

26. Audio (from NPR)
"… before a joint session of Congress for his 2nd State of the Union speech, this is actually the first…"

27. 1/8th Second of Voice

28. 1/8th Second of Voice

29. 1/8th Second of Voice

30. Sampling & Quantizing Examples
fs = 16 KHz
4096 quantiles
256 quantiles (approximate phone quality)
32 quantiles
4 quantiles (generally 2 levels used!)
fs = 8 KHz (some interference)
fs = 2 KHz
fs = 1 KHz

31. Analog to Digital Conversion) Part 2...
Sampler
Quantizer
&
PCM
analog
input
x(t)
discrete
time
signal
xs(t)
bit
stream
transmitter side

32. Analog to Digital Conversion) Part 2...
Low Pass
Filter
Source
Decoder
estimate
of analog
input
discrete
time signal
estimate
bit
stream
receiver side

33. Quantization
Best Quantizer SNR occurs when round-off voltages occur with equal probability
If input is Uniformly Distributed...
Uniform Quantizer offers best SNRQuantize
If input is NOT Uniformly Distributed...
Best SNRQuantize occurs when
Step sizes are small in domain of likely voltages
Step sizes are large in domain of unlikely voltages

34. Wired Voice Telephone System
Quantizers…
Quantizer SNR Input voltage mapped to representative value Causes round-off error Uniform quantizer error tends to be
Uniformly Distributed
So long as input PDF symmetrical about 0
Wired Voice Telephone System
uses Companding