My first project is to replicate the lightcurve analysis of my Minor Planet Targets currently undertaken by MPC Canopus software.  I find it disturbing, after 5 years analysis work, that I lack an understanding of the science and math behind the analysis I take for granted.   All I knew was that the data passed through a Fourier transform that would magically produce a power spectrum immediately identifying the best period fit to the data.  I was wrong.

Power Spectrum - Analysis of Lightcurve data for Minor Planet  (689) Zita

Now to visit and read a few papers; one from Harris and Young, one from Pravec and one from Behrend (See references below).  They all gave the same Discreet Fourier Transform formula but no detail on how to use it.

Next step - trial and error, lots of research on the internet, buy a book on the analysis of time series and in the end it came down to finding a demonstration project published in the Mathematic Journal from 1997 written by Keith Briggs of the University of Western Australia (1997).  As it turns out, the analysis of data from discrete time series using observations undertaken at unequal intervals is not a simple matter of using a straight Fourier transform.

The method used by Briggs appears to replicate that outlined in Harris and Young using a Fourier integration and a Least Squares fit to determine the co-efficients.  The process then uses a non linear regression to fit the data to a periodic function.  I still have little idea what this actually means at the but I will be attempting to code up a version using the Harris and Young technique (as used in many of the current software packages such as MPO Canopus and Peranso)

For those with Mathematica, I have attached a notebook plus the sample data.  For those without the notebook then you can read the pdf file or obtain a copy of Mathematica Player (and free 80mb download last time I looked).

The work is far from finished and I would love to get feedback.  My aim will be to continue the work to also include a simple binary curve subtract and a second round of analysis on the resulting data.

Astronomy/mathematica/LightCurve Analysis.pdf

Astronomy/mathematica/Zita.TXT

Astronomy/mathematica/NEFFT-ItWorks.zip

References:
Harris and Young et al, "Photoelectric Observations of Asteroids", Icarus 77 (1989) 171-186
Pravec et al, "Photometric survey of binary near-Earth asteroids", Icarus 181 (2006) 63-93
Behrend et al, "Four new binary planets", Astronomy & Astrophysics 446 (2006) 1177-1184