In my former life as a neurobiologist, we analysed the relationship between
rodent investigative sniffing and the limbic theta rhythm. In short, rodents
tend to exhibit a preferred phase relationship between these two signals,
both of which run about 5-9 Hz. We analysed short (1-2 sec) epochs. For each
interval we used FFTs to determine the "dominant" frequency in the 5-9 Hz
band and the phase difference between the two signals at the dominant
frequency. Given enough observations, we were able to determine that there
was a high correlation between the dominant frequencies in the two signals
and that for each frequency (using a 1-Hz window) there was a preferred
phase difference between the two. Furthermore, the preferred phase
difference varied in a linear fashion with the dominant frequency. We
concluded that the animals were "entraining" their sniffing to the limbic
theta rhythm in such a way that there was a preferred LATENCY between any
given phase of the sniffing signal and some equivalent phase point on the
theta signal. Since the underlying constant was this latency relationship,
the result was a linearly progressive phase difference as a function of
frequency.
The analysis was conceptually simple - that is, compute dominant frequency
and phase difference using FFTs, cast the data into a bivariate distribution
(frequency and phase difference) and use simple statistics to describe the
relationship. There was actually a bit more to it than that, but not much.
I guess when you post to the usenet you never know what kinds of responses
you may get...
Bill Forbes
Austin, TX
G. Anthony Reina <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> I'm looking for a way to show how two continuous signals are correlated
> over time. In other words, if x(t) and y(t) are correlated signals (with
> some phase lag between them), does that correlation change over time?
> (and if so, then how does it vary)
>
> What I'd ideally like to get is something like the spectrogram except
> instead of frequency vs time, the axes would be correlation vs. lag vs.
> time.
>
> The most obvious solution I've thought of is to use a sliding window on
> each signal to evalute the cross-correlation (at different lags) over
> small epochs. I'm wondering if there are other more elegant solutions
> out there.
>
> I'd appreciate any advice on the subject.
>
> Thanks.
> -Tony Reina
>
>
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