Statistical Analysis of the Sliding Window Fourier Transform

• Activity Number: 481 - Modeling, Analysis, and Assessment
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Lee Richardson*
• Companies: Carnegie Mellon University
• Keywords: Fourier Transform ; Sliding Windows ; Frequency ; Orthogonal Transforms ; Time Series

Abstract

The Sliding Window Fourier Transform (SWFT) computes the temporal and frequency components of a signal simultaneously. This paper explores the SWFT as a data analysis tool. First, we describe a linear time algorithm to compute the SWFT, using repeated Fast Fourier Transform calculations in overlapping windows. Next, we describe the statistical properties and common situations when analyzing data with the SWFT, such as leakage. Finally, we show how the SWFT corresponds with R local periodic signals in the time domain.