Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data Scargle, J. D.
- The power at a given frequency as computed by a periodigram (FFT is a specific case of the periodigram) of a gaussian white noise source with uniform variance is exponentially distributed:
- The corresponding CDF: or which gives the probability of a large observed power at a given freq.
- If you need to average N samples, then where
- Means of improving detection using a periodogram:
- Average in time - this means that N above will be smaller, hence a spectral peak becomes more significant.
- Cannot average too much - at some point, averaging will start to attenuate the signal!
- Decrease the number of frequencies inspected.
- Deals a good bit with non-periodic sampling, which i guess is more common in astronomical data (the experimenter may not take a photo every day, or the same time every day (clouds!).
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