ECEN4523 Commo Theory Lecture #26 19 October 2015 Dr. George Scheets n Read 6.2 (skim quantization material) n Problems: 6.1-5, 9 & n Quiz #6, 23 October (Live) u Remote DL students < 30 October n Exam #2, 30 October (Live) u Remote DL students < 6 November n Design Problem, due 6 November (Live) u Remote DL students < 13 November

ECEN4523 Commo Theory Lecture #27 21 October 2015 Dr. George Scheets n Read 7.1 & 7.2 n Problems: 6.2-2, & 4 n Quiz #6, 23 October (Live) u Remote DL students < 30 October n Exam #2, 30 October (Live) u Remote DL students < 6 November n Design Problem, due 6 November (Live) u Remote DL students < 13 November

Design Problem n Simulate above Analog Commo System n Design Post Filter u Minimize Average e(t) 2 a.k.a. MSE

M Tap Finite Impulse Response Post Filter W0W(M-1)W1 Delay ? * ts Delay ? * ts Σ Input Output H(f) desired? Find h(t). Wn = h(nt s ). Figure of Merit MSE*M 0.63 Lower is Better.

Grading n Real World RFP: u 1 team gets full credit u Everyone else gets a zero n Partial credit u Awarded on Quizzes & Tests u NOT AWARDED ON DESIGN PROJECTS! n Real world designs don't get partial credit u Either Work or They Don't n Double check your work!!!

Digitizing an Analog Signal n Sample u Continuous Time → Discrete Time u fs > 2(Signal BW) with Ideal Sampler u Practically speaking, fs ≈ 2.2(Signal BW) n Quantize u Continuous Voltage → Discrete Voltage u Introduces Round-Off Error u We'll focus on PCM

Pulse Code Modulation n What most off-the-shelf A/D Converters do n Rounds voltage to one of L possible values n L usually a power of 2 n Each Voltage assigned equal length code word u Binary 1's and 0's u N = log 2 L bits per word u EX) L = 256 voltages? N = 8 bits

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

A/D Convertor time (sec) m(t) volts (air pressure) Step #1) Sample the waveform at rate > 2*Max Frequency. Telephone voice is sampled at 8,000 samples/second. 1/8000 second

A/D Convertor n Legacy Wired Telephone System uses PCM n Pulse Code Modulation One of N possible equal length Code Words is assigned to each Voltage N Typically a Power of 2 Log 2 N bits per code word u Wired Phone System: N = 256 & 8 bits/word u Compact Disk: N = 65,536 & 16 bits/word

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

A/D Convertor. 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

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

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

A/D Convertor. 2 bits/sample. Input to the transmitter. Output at the receiver. 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 v v v v

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

Circuit Switched Voice (POTS)  Bandwidth ≈ 3,500 Hertz  A/D Converter  samples voice 8,000 times/second  rounds off voice to one of 256 voltage levels  transmits 8 bits per sample to far side  D/A Converter  receives 8 bit code word  outputs one of 256 voltage levels for 1/8000th second  64,000 bps

Compact Disk  Bandwidth ≈ 20,000 Hertz  A/D Converter  samples voice 44,100 times/second  rounds off voice to one of 65,536 voltage levels  transmits 16 bits per sample to far side  D/A Converter  receives 16 bit code word  outputs one of 65,536 voltage levels for 1/44100th second  705,600 bps

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

1/8th Second of Voice

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

Fourier Transforms n Are 1 to 1 mappings u x(t) has one and only one X(f) volts/Hz u R X (τ) has one and only one S X (f) watts/Hz n Many different x(t) can map to same R X (τ) u Random Bit Streams u Sinusoids u Random Noise, etc. n Mapping of x(t) to S X (f) is many to one u Why S X (f) is useful for commo analysis

Basic Block Diagram source: Figure 1.2, Lathi & Ding, MODERN DIGITAL AND ANALOG COMMUNICATION SYSTEMS This is all in the telecom Physical Layer.

Basic Block Diagram (Digital) source: Figure 1.2, Lathi & Ding, MODERN DIGITAL AND ANALOG COMMUNICATION SYSTEMS This is all in the telecom Physical Layer.

Input Transducer n Analog Signal In? u Sampler u PCM… F Quantize F Assign binary code word (1's and 0's) u …or Application Specific Coder F Voice or Video F Generate binary output n Digital Signal in? u May want to clean up and retime

Basic Block Diagram (Digital) source: Figure 1.2, Lathi & Ding, MODERN DIGITAL AND ANALOG COMMUNICATION SYSTEMS This is all in the telecom Physical Layer.

Transmitter (Digital) n Binary Bit Stream In n May Not Want to Transmit Binary u Can reduce RF BW by going M-Ary u Transmitting M possible symbols F Multiple bits mapped to each symbol F EX) 90 Mbps → 10 bits/symbol (M = 2 10 =1,024) Baud rate = 9 M symbols/second

24 bit color 2 24 = M colors

256 Colors

16 Colors

Manchester Pulse X(f) Fourier Transform of 1/2 Pulse Fourier Transform of Manchester Pulse

Ethernet Uses Manchester Coding time +1 volts 0 T 00 Logic One Logic Zero All symbols have a transition in the middle.

Ethernet Uses Manchester Coding time +1 volts 0 T High Pass Filters Emphasize Change

High Pass Filter Output time +1 0

Rectify (Absolute Value) time +1 0 T Result always has pulses T seconds apart. Useful for receiver synchronization.

Serial Bit Stream: NRZ Coding time +1 volts 0 T 00 Logic One Logic Zero Called ‘Non Return to Zero’ because voltage never dwells on zero volts. T