In this analysis we used power statistic for H1 in band 250.45-250.55 Hz (180 bins) over the entire S2 run. As can be seen from earlier plots this band is well behaved with respect to absence of visible artifacts and values of KS statistic.
For purposes of this analysis bin 1 is 250.25 Hz with successive bins in increments of 1/1800 Hz.
Instead of correlating raw power we used a logarithm of it as the expected distribution is exponential.
First we plot correlation of bins around bin 90. The correlation of 1.0 corresponds to bin 90 itself and is expected to be so. The two smaller values around it come from Hann window and are also expected. Note that other correlations are generally positive and reach values as high as 0.12.
Same plot but zoomed in Y axis
Here we adjusted the data by subtracting the median of each segment. Here is the plot of the medians:
Plot of correlations of adjusted data. Note that we see a similar structure to raw correlations but far correlations can be both positive and negative and are less than 0.07 in absolute value:
Same plot but zoomed in Y axis
Since far bin should (theoretically) be independent from one another a question arises whether we should be satisfied with correlation values as large as 0.07 in absoluted value.
To test this we generated a table of 1800x180 simulated exponentially distributed random values (with parameter of exponential distribution set to 1.0) and applied our adjustment procedure to them.
The plot of correlations below shows exactly the same structure as in the case of actual data, modulo the absence of two high correlation values due to Hann window which was not modelled in this data:
Same plot but zoomed in Y axis
