Detection and Removal of Periodic Noise in Kepler/K2 Photometry with Principal Component Analysis

We present a novel method for detrending systematic noise from time series data using Principal Component Analysis (PCA) in Fast Fourier Transforms. This method is demonstrated on time series data obtained from the inaugural campaign of the Kepler K2 mission, as well as three objects of interest from Campaign 4. Unlike previous detrending techniques that utilize PCA, this method performs the detrending in Fourier space rather than temporal space. The advantage of performing the analysis in frequency space is that the technique is sensitive purely to the periodicity of the unwanted signal and not to its morphological characteristics. This method could improve measurements of low signal-to-noise photometric features by reducing systematics. We also discuss challenges and limitations associated with this technique.