About The Project
The Software was developed by Yohan Alexander as a research project, funded by the CNPq Institution, and it is a Open Source initiative. The program allows the user to calculate periodograms using the statistics a la Buccheri et al. 1983.
The is a periodogram based on the Rayleigh method, which applies the time samples in a signal to a Fourier analysis. This method has been shown to be useful in detecting periodic signals at high frequencies associated with the rotation of compact objects.
First, each event is reduced to a phase value , in the range of 0 to 1, where such that for the -th event we have the following equation, where is the time of the event under analysis minus the time of the first detected event .
The power spectrum, where is the number of harmonics included in the power, and is the number of events, is calculated from the equation which is defined as follows.
Note that this is potentially very computationally expensive, as there are two variables by which we are doing a loop, which represents the frequencies, and which are the indices of the event.
Think of the loop as being within the loop . For each new , we get the full range of , which is why the periodogram can sometimes be very slow, since the execution time of the algorithm grows at a exponential rate .
The Z2n Software was built using the
Python open source language, and optimized with the
Numba JIT (just-in-time) compiler.