Autocorrelation t1+T t1+T R x (τ) = (1/(T-τ)) x(t)x(t+τ)dt t1 Example R x (1) Take x(t1)*x(t1+1) Take x(t1+ε)*x(t1+1+ ε) x(t1+T-1)*x(t1+T)... Add these all together, then average
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ECEN3513 Signal AnalysisECEN3513 Signal AnalysisLecture #4 28 August 2006Lecture #4 28 August 2006
Example RExample Rxx(1)(1)Take x(t1)*x(t1+1)Take x(t1)*x(t1+1)Take x(t1+Take x(t1+ε)*x(t1+1+ ε)...ε)*x(t1+1+ ε).......x(t1+T-1)*x(t1+T).......x(t1+T-1)*x(t1+T)...Add these all together, then averageAdd these all together, then average
Autocorrelation
If the average (RIf the average (Rxxxx(tau)) is positive...(tau)) is positive... Then x(t) and x(t+tau) tend to be alikeThen x(t) and x(t+tau) tend to be alike
Both positive or both negativeBoth positive or both negative If the average (RIf the average (Rxxxx(tau)) is negative(tau)) is negative
Then x(t) and x(t+tau) tend to be oppositesThen x(t) and x(t+tau) tend to be oppositesIf one is positive the other tends to be negativeIf one is positive the other tends to be negative
If the average (RIf the average (Rxxxx(tau)) is zero(tau)) is zero There is no predictabilityThere is no predictability
255 point Noise waveform(Adjacent points are independent)
time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
Rxx(0) The sequence x(n)The sequence x(n)
x(1) x(2) x(3) ... x(255)x(1) x(2) x(3) ... x(255) multiply it by the unshifted sequence x(n+0)multiply it by the unshifted sequence x(n+0)
x(1) x(2) x(3) ... x(255)x(1) x(2) x(3) ... x(255) to get the squared sequenceto get the squared sequence