Lomb Scargle Periodogram
An astronomical time series data is a series of discrete events with either an even or uneven sampling rate. This can be expressed mathematically as a pointwise product between a continuous signal with a rectangular function and a dirac comb. The Discrete Fourier transform of this results in the convolution of the three functions in the omega space. The square of the Fourier transform is proportional to the power of each periodic signal in the time series or more accurately: Scargle showed that this is equivalent to fitting the time series data with the model using a least square fitting. The resulting Chi square for each frequency is indicative of the power that the signal contributed to the time series. Essentially the difference between the absolute difference between the chi square assuming non variability and the chi square assuming a sinusoidal variation in the time series is equivalent to the Power, or the classical periodogram given by Lomb. Scargle’s Method of Calcu...
