in reply to Re^2: Calculating cross-correlation
in thread Calculating cross-correlation

I checked your references and they agree with me: Both clearly state that the second series (and third for wolfram) is derived from the first; the wolfram version has a total of three series but in which the two complex functions f and g are both derived from the same starting series. In both cases there is only one driving variable, everything else is derived. If you start with two series, you want ordinary correlation, not cross-correlation.

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Re^4: Calculating cross-correlation
by BrowserUk (Patriarch) on Nov 25, 2010 at 15:49 UTC

    Isn't the point of cross-correlation to determine if two datasets are, or approximate to, being described by the same series, but with different offsets?

    Therefore the OPs talk of "two series" is correct until the determination is made that they might actually be the same series.

    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority".
    In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
      The point of cross-correlation is to determine if two signals are similar or not and to which degree. If they are different, no matter the offset, the cross-correlation value will be very small (close to 0). In the case of auto-correlation, the signal is cross-correlated to itself. So, it will be always picked (1.0) at 0 lag.
[reply]
        The point of cross-correlation is to determine if two signals are similar or not

        In other words, prior to having made the determination, the OP is perfectly correct in saying "two series", because at that point in time he doesn't know if they are related. That's why he is running the cross-correlation.

        So, you are agreeing with me. Thanks.

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
      Actually, he has to provide the offset on one and then instead of cross-correlating with the original he has to (standard-) correlate that result with the other. I know enough to provide a better answer now...

      One world, one people

[reply]
        Actually, he has to provide the offset on one

        Actually, no. Cross correlation can be used to determine the required offset.

        From the Wikipedia page (my emphasis):

        Explanation

        For example, consider two real valued functions f and g that differ only by an unknown shift along the x-axis. One can use the cross-correlation to find how much g must be shifted along the x-axis to make it identical to f.

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
Re^4: Calculating cross-correlation
by Anonymous Monk on Nov 25, 2010 at 15:39 UTC
    Wikipedia states clearly: "In signal processing, cross-correlation is a measure of similarity of TWO waveforms as a function of a time-lag applied to one of them.". TWO waveforms or TWO signals, etc... (two not one). You are confusing cross-correlation with auto-correlation... The auto-correlation is the correlation of a signal with itself.
[reply]

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