1. ECEN4503 Random Signals Lecture #39 15 April 2013 Dr. George Scheets n Read: 10.3, 11.1 n Problems: 11.1, 11.4, 11.15, 11.21 (1 st Edition) n Problems: (2 nd Edition) n Quiz #10 Autocorrelations → Power Spectrum

2. ECEN4503 Random Signals Lecture #41 19 April 2013 Dr. George Scheets n Read: 11.3 & 11.4 n Problems: 2010 Final Exam n Final Exam, Friday, 3 May, 1000-1150 hours n Exam #2 Results Hi = 84, Low = 17, Average = 50.67, σ = 18.67 A > 82, B > 67, C > 51, D > 37

3. 2 watt, 1 Vdc, GWN Sample Function & Autocorrelation

4. Output After Hard Limiting

5. Band-Limiting the White Noise n Start with 4 watts A.C. Power...

6. Band Limiting the White Noise n... take the FFT...

7. Band Limiting the White Noise n... zero out 3/4 of it...

8. Band Limiting the White Noise n... take IFFT...

9. Band Limited White Noise...that's been hard limited

10. Power Spectrum Estimate FFT of R YY (τ) Averaging a bunch of Power Spectrum Estimates yields smoothed plots.

11. Ergodic Process X(t) volts n E[X] = A[x(t)] volts u Mean, Average, Average Value n V dc on multi-meter n E[X] 2 = A[x(t)] 2 volts 2 = constant term in Rxx(τ) n = Area of δ(f), using S XX (f) u (Normalized) D.C. power watts

12. Ergodic Process n E[X 2 ] = A[x(t) 2 ] volts 2 = Rxx(0) = Area under S XX (f) u 2nd Moment u (Normalized) Average Power watts u (Normalized) Total Power watts u (Normalized) Average Total Power watts u (Normalized) Total Average Power watts

13. Ergodic Process n E[(X -E[X]) 2 ] = A[(x(t) -A[x(t)]) 2 ] u Variance σ 2 X u (Normalized) AC Power watts n E[X 2 ] - E[X] 2 volts 2 n A[x(t) 2 ] - A[x(t)] 2 n Rxx(0) - Constant term n Area under S XX (f), excluding f = 0. n Standard Deviation σ X AC V rms on multi-meter volts