First just want to make sure we use the same terms
You talk about
. I assume you are talking about the flux values read from “decoded stream data” (for example from raw KF or SCP files). With DD MFM these values are generally close to 4000, 6000, or 8000 ns. For example
3620 5993 7990 3953 4037 6034 5951 ...
If things were perfect the exact same series of values would appear again in the second revolution exactly 200 ms later.
You are talking about
a(z^0), b(z^-1), … where (z^0) is timezero sample, (z^-1) is the sample before that... here: a,b,c,... are the polynomial coefficients
Not sure why you say sample "before that" when you actually use the value "after that"?
I assume that a(z^0) indicates that the first sampled value ‘a’ is equal to 3620 not 3620 multiplied by (z^0) ?
So here we have a(z^0)=3620, b(z^1)=5993, c(z^2)=7990 etc.
Now about your
Usually if we have two series of samples s1=[a b c d e] and s2=[f g h i j] the correlation is defined as
C = af + bg + ch + di + ej (as shown here https://www.youtube.com/watch?v=_r_fDlM0Dx0
And not the strange polynomial multiplication as you define?
Now back to the purpose of the ‘autocorrelation’. From what I understand correlation allows to express similarity of two time series by one number (normalized version of covariance).
The auto-correlation is defined as the correlation between two parts of one series (for example between two halves of a series) – why called auto – to find out if the series repeats itself. In our case the series of flux transitions repeats itself after one revolution. So for a “normal” track we should get a number close to 1 (not exactly 1 due to variations). For an unformatted track the second series would not be related to the first one so the correlation would be close to 0.
Nowhere I have seen indication of taking a series and correlate with the “reversed” series? This might be useful if you want to show that a series has symmetrical values which is obviously not the cases with a normal track? How can this gives information about the track structure?
But the concept of correlation is interesting with track flux data to find out about unformatted track (no correlation between two revolutions), similar track (correlation between two tracks or track and template). Not sure if this can also be used to find out about fuzzy bits?
From what I understand a similar concept is used in HxC (Jeff are you looking?). A track is sliced in several pieces and similarities of slices between revolutions is made using a sliding pattern. But I do not know if the actual comparison is done using correlation computation or pure value comparison with margin?
interesting reference http://dsp.stackexchange.com/questions/ ... re-similar