Keywords: Fourier, Periodicity, Sliding Window
The Sliding Window Fourier Transform (SWFT) analyzes the temporal and frequency components of a signal simultaneously. We introduce the SWFT as a tool for data analysis. We discuss a linear time algorithm to compute the SWFT in one and two dimensions. Next, we discuss the statistical properties of the SWFT assuming the input signal is white noise. We conclude by showing how the SWFT can be used to detect local periodic signals, extending Fishers well known periodicity test.