ECEN4503 Random Signals
Lecture #30
31 March 2014
Dr. George Scheets
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Problems 8.7a & b, 8.11, 8.12a-c (1st Edition)
Problems 8.11a&b, 8.15, 8.16 (2nd Edition)
ECEN4503 Random Signals
Lecture #31
2 April 2014
Dr. George Scheets
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Problems: 8.15, 8.18, 8.24 (1st Edition)
Problems: 8.2, 8.19, 8.22 (2nd Edition)
Quiz #8, 4 April, 2nd Order PDF's & Autocorrelation
Exam #2, 18 April
2014 OSU ECE Spring Banquet
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Hosted by Student Branch of IEEE
Wednesday, 16 April, at Meditations
Doors open at 5:30 pm, meal at 6:00 pm
Cash Bar
Sign up in ES201 to reserve your seat(s)
$20 value!
$5 if pay in advance and resume submitted
to OSUIEEEresume@gmail.com
< 5:00 pm, 14 April. Otherwise $8.
Speaker: Dr. Legand Burge, USAF (retired)
Dean of Engineering, Tuskegee University
Dress is Business Casual
Many door prizes available!
+6 points extra credit
All are invited!
Sponsored in part by:
Ergodic Process X(t) volts
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E[X] = A[x(t)] volts
 Mean
 Average
 Average
Value
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Vdc on multi-meter
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E[X]2 = A[x(t)]2 volts2
 (Normalized)
D.C. power watts
Ergodic Process
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E[X2] = A[x(t)2] volts2
 2nd
Moment
 (Normalized) Average Power watts
 (Normalized) Total Power watts
 (Normalized) Average Total Power watts
 (Normalized) Total Average Power watts
Ergodic Process
E[X2] - E[X]2 volts2
 A[x(t)2] - A[x(t)]2
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σ2X
 (Normalized) AC Power watts
 Variance
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E[(X -E[X])2] = A[(x(t) -A[x(t)])2]
Deviation σX
AC Vrms on multi-meter volts
 Standard
Histogram of Sinusoid Voltages
PDF of a 3vp Sinusoid

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3
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3
1
dx  1
Area under PDF
2
 9  x
3
2
x
dx  4.5
E[X2]
2
 9  x
3
Find PDF of voltage by treating Time as Uniform RV.
Then map time → voltage.
A[*] = E[*] when Ergodic.
Voltage PDF for Clean
Sinusoid
 If
x(t) = α cos(2πβt + θ)
then
fX(x) = 1 / [π(α2 - x2)0.5]; - α < x < α
Autocorrelation
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Statistical average E[X(t)X(t+τ)]
 using Random Processes & PDF's
Time average A[x(t)x(t+τ)]
 using a single waveform
How alike is a waveform & shifted version of itself?
Given an arbitrary point on the waveform x(t1), how
predictable is a point τ seconds away at x(t1+τ)?
RX(τ) = 0?
 Not alike. Uncorrelated.
RX(τ) > 0?
 Alike. Positively correlated.
RX(τ) < 0?
 Opposite. Negatively correlated.