ECEN5533 Modern Communications Theory Lecture #111 January 2016 Dr. George Scheets n Review Chapter n Ungraded Homework Problems: 1.1a-c, 4, & 5

ECEN5533 Modern Communications Theory Lecture #213 January 2016 Dr. George Scheets n Read Chapter Problems: 1.9, 13, 14 n Quiz #1 u Wednesday, 27 January, Lecture 7 u Chapter 1, Review

ECEN5533 Modern Communications Theory Lecture #315 January 2016 Dr. George Scheets n Read Chapter Problems: 1.15, 16, 20 n Quiz #1 u Wednesday, 27 January, Lecture 7 u Chapter 1, Review

OSI IEEE n January General Meeting n 5:30 - 6:30 pm, Wednesday, 20 January n ES201b n Reps from Georgia-Pacific will present n +3 pts extra credit & dinner will be served n All are invited

Grading n In Class: 2 Quizzes, 2 Tests, 1 Final Exam Open Book & Open Notes WARNING! Study for them like they’re closed book! n Graded Homework: 2 Design Problems n Ungraded Homework: Assigned most every class Not collected Solutions Provided Payoff: Tests & Quizzes

Why work the ungraded Homework problems? n An Analogy: Commo Theory vs. Soccer n Reading text = Reading a book about soccer n Looking at the problem solutions = watching a scrimmage n Working the problems = practice or playing in a scrimmage n Quiz = Exhibition Game n Test = Big Game

To succeed in this class... n Show some self-discipline!! Important!! For every hour of class put in 1-2 hours of your own effort. n PROFESSOR'S LAMENT If you put in the time You should do fine. If you don't, You likely won't.

Prerequisites n Probability & Statistics Random Processes n Fourier Transforms Linear Systems n Some knowledge of Modulation Schemes u Nice to have, but not critical

Cheating n Don’t do it! Expect to get an “F!” in the course n My idol: Judge Isaac Parker U.S. Court: Western District of Arkansas a.k.a. “Hanging Judge Parker” a.k.a. “Hanging Judge Parker”

French Optical Telegraph Source: January 1994 Scientific American nDnDnDnDigital M-Ary System uMuMuMuM = 8 x 8 x 4 = 256

French System Map Source: January 1994 Scientific American

Trend is to Digital n Phonograph → Compact Disk n Analog NTSC TV → Digital HDTV n Video Cassette Recorder → Digital Video Disk n AMPS Wireless Phone → 4G LTE n Terrestrial Commercial AM & FM Radio n Last mile Wired Phones

Review of Autocorrelation n Autocorrelations deal with predictability over time. I.E. given an arbitrary point x(t1), how predictable is x(t1+τ)? time Volts t1 tau

Review of Autocorrelation n Autocorrelations deal with predictability over time. I.E. given an arbitrary waveform x(t), how alike is a shifted version x(t+τ)? Volts τ

Review of Autocorrelation t1+T t1+T R XX (τ) = lim (1/T) x(t)x(t+τ)dt T→∞ t1 Example R XX (1) Take x(t1)*x(t1+1) Take x(t1+ε)*x(t1+1+ ε) x(t2)*x(t2+1)... Add these all together, then average

R xx (0) n The sequence x(n) x(1) x(2) x(3)... x(255) n multiply it by the unshifted sequence x(n+0) x(1) x(2) x(3)... x(255) n to get the squared sequence x(1) 2 x(2) 2 x(3) 2... x(255) 2 n Then take the time average [x(1) 2 +x(2) 2 +x(3) x(255) 2 ]/255

R xx (1) n The sequence x(n) x(1) x(2) x(3)... x(254) x(255) n multiply it by the shifted sequence x(n+1) x(2) x(3) x(4)... x(255) n to get the sequence x(1)x(2) x(2)x(3) x(3)x(4)... x(254)x(255) n Then take the time average [x(1)x(2) +x(2)x(3) x(254)x(255)]/254

Review of Autocorrelation n If the average at offset τ is positive... u Then x(t) and x(t+τ) tend to be alike Both positive or both negative n If the average at offset τ is negative u Then x(t) and x(t+τ) tend to be opposites If one is positive the other tends to be negative n If the average is zero u There is no predictability

255 point discrete time White Noise waveform (Adjacent points are independent) time Volts 0 V dc = 0 v, Normalized Power = 1 watt If true continuous time White Noise, No Predictability.

Autocorrelation Estimate of Discrete Time White Noise tau (samples) Rxx 0

255 point discrete time White Noise waveform (Adjacent points are independent) time Volts 0 V dc = 0 v, Normalized Power = 1 watt If true continuous time White Noise, No Predictability.

255 point Noise Waveform (Low Pass Filtered White Noise) Time Volts 23 points 0

Autocorrelation Estimate of Low Pass Filtered White Noise tau samples Rxx 0 23

Autocorrelation & Power Spectrum of C.T. White Noise Rx(τ)Rx(τ) tau seconds 0 A G x (f) Hertz0 A watts/Hz Rx(τ) & Gx(f) form a Fourier Transform pair. They provide the same info in 2 different formats.

Autocorrelation & Power Spectrum of Band Limited C.T. White Noise R x (tau) tau seconds 0 G x (f) Hertz0 A watts/Hz -W N Hz 2AW N 1/(2W N ) Average Power = ? D.C. Power = ? A.C. Power = ?

Cosine times a Noisy Serial Bit Stream X = Cos(2πΔf)