Experimental Log: Roger Bland, January 1-3, 2002
Finishing up RAFOS detection
( logbook | ifremer on RAFOS |Garfield at NPS )

17:40 Tuesday January 1, 2002. I am just finishing up the job of making all the plots necessary to see RAFOS signals, and imagining how they will show up on these plots. I am trying to get completely tuned up on a file with no RAFOS signal, to enhance my objectivity. All I have left to do is to display the result of the quadrature cross-correlation detection, and to decide how much noise and how much signal I expect to see. Based on some pretty primitive reasoning, I expect the rms value of the product of a random signal of bandwidth f1 with another random signal of bandwidth f2 (f1 is greater than f2), as shown in the figure, to be equal to

rmsprod = rms1 * rms2 * (T1/T2) * (T2/T)1/2 * (1/2)
(6:11 Thursday January 3, 2001) Here T1 and T2 are the periods corresponding to f1 and f2, and T is the length of the time series. For the test signal r0124506.27w the rms is 17.56, and for the RAFOS quadrature replicas the rms is 0.707 . Also T = 80 sec, and (roughly) f1 = 8 Hz, f2 = 1.5 Hz. This gives
rmsprod (predicted) = 0.419
The detection scheme which I am using consists of (a) multiplying the RAFOS-band signal by a replica and averaging the values in the resulting vector; (b) doing the same for the 90-degree-out-of-phase replica; (c) and adding these two numbers in quadrature (program rafdet.pro). This should give a number averaging to the value calculated above, and peaking for a RAFOS signal at roughly (give or take a couple of factor of two) the amplitude (in original digitization units) of the RAFOS signal.

Here is the resulting signal, for r0124506.27m. The rms of the signal is equal to 0.687, in fine agreement with the 0.419 predicted above.

SHOW TIME!
It is time to look at this signal for a day's data (plotting program p20101a.pro):

r0124502.21

r0124504.24

r0124506.27

r0124508.30

r0124510.33

r0124512.36

r0124514.39

r0124516.42

r0124518.45

r0124520.48

r0124522.51
9:35 It is encouraging to see large signals showing up where we expect them. I have to go and do other things for a while.

But, here is a list of things to do next.