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Bug 1739 - ft_specest_mtmfft: rework description and implementation of angletransform
| Status |
ASSIGNED |
| Reported |
2012-09-25 13:58:00 +0200 |
| Modified |
2013-01-18 10:43:49 +0100 |
| Product: |
FieldTrip |
| Component: |
specest |
| Version: |
unspecified |
| Hardware: |
PC |
| Operating System: |
Windows |
| Importance: |
P3 enhancement |
| Assigned to: |
Roemer van der Meij |
| URL: |
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| Tags: |
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| Depends on: |
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| Blocks: |
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| See also: |
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Roemer van der Meij - 2012-09-25 13:58:43 +0200
Rework the description and implementation, and change the respective FAQ question. The current description is not correct, the implementation is a bit unintuitive, although the result reflects the original purpose.
Being:
In an FFT, the phase of any fourier coefficient can be described as the initial phase (i.e. the phase at the first sample) of the best-fit cosine of that particular frequency with the data.
In our data, the time-point of the first sample can be different over trials. To make the absolute phases of our fft interpretable, each trial/freq needs to be phase-shifted, such that the phase of a particular frequency reflects the phase at t=0 of the best fit cosine to the data (our chosen convention).
In a simple example: if a perfect 2Hz oscillation is at it's peak at t=250ms, without a phase-shift, the phase of the 2Hz coefficient would be:
- trial starts at 0ms ---> +/- pi
- trial starts at 125ms ---> -pi/2
- trial starts at -125ms ---> pi/2
- trial starts at 250ms ---> 0
- trial starts at 500ms ---> +/- pi
After phase-shift it will be:
- trial starts at 0ms ---> +/- pi
- trial starts at 125ms ---> +/- pi
- trial starts at -125ms ---> +/- pi
- trial starts at 250ms ---> +/- pi
- trial starts at 500ms ---> +/- pi