autocorrelation

Question 1

when do we have the max correlation between 2 signals

Answer 1

when they are perfectly supposed

Question 2

what is the autocorrelation function computed for a null time lag equal to

Answer 2

it’s equal to the mean square value

Question 3

when do we have a perfect match in the autocorrelation

Answer 3

when tau=0 (time lag=0)

Question 4

autocorrelation is an …… function

Answer 4

even ( Rxx(k)=Rxx(-k) )

Question 4

application of signal autocorrelation

Answer 4

find a possible periodicity of the signal (if the signal is noisy, the correlation function is useful to find the period and thus the deterministic part of the signal)

Question 4

why do we use the cross correlation

Answer 4

if we have 2 signals from 2 phenomena and we want to compare them we use this function to get rid of the phase shift between these 2 signals to get them to be superimposed

Question 5

whats the difference in the “unbiased” cross-correlation

Answer 5

in the cross correlation the normalization factor is independent from tau.In case of records with a finite time-length, this leads to get decaying values of Rxx as tau
grows (because tje integral is from 0 to t-tau).
That is why the “unbiased” version of the Rxx function is given where instead of 1/T we have 1/(T-tau)

Question 6

for which type of phenomenon we use the auto-correlation, cross-correlation and trigger

Answer 6

-auto-correlation for deterministic, periodic phenomenon
-cross-correlation and trigger for deterministic non-periodi phenomenon