power_upper_limit

hendrics.power_upper_limit(pmeas, n=1, c=0.95)[source] [edit on github]

Upper limit on signal power, given a measured power in the PDS/Z search.

Adapted from Vaughan et al. 1994, noting that, after appropriate normalization of the spectral stats, the distribution of powers in the PDS and the Z^2_n searches is always described by a noncentral chi squared distribution.

Note that Vaughan+94 gives p(pmeas | preal), while we are interested in p(real | pmeas), which is not described by the NCX2 stat. Rather than integrating the CDF of this probability distribution, we start from a reasonable approximation and fit to find the preal that gives pmeas as a (e.g.95%) confidence limit.

As Vaughan+94 shows, this power is always larger than the observed one. This is because we are looking for the maximum signal power that, combined with noise powers, would give the observed power. This involves the possibility that noise powers partially cancel out some signal power.

Parameters
pmeas: float

The measured value of power

Other Parameters
n: int

The number of summed powers to obtain pmeas. It can be multiple harmonics of the PDS, adjacent bins in a PDS summed to collect all the power in a QPO, or the n in Z^2_n

c: float

The confidence value for the probability (e.g. 0.95 = 95%)

Examples

>>> pup = power_upper_limit(40, 1, 0.99)
>>> np.isclose(pup, 75, atol=2)
True