# The Sliding Window Discrete Fourier Transform

arXiv: https://arxiv.org/abs/1807.07797 · HTML: https://mlsanity.com/paper/1807.07797/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2018.

## Built on by (most cited first, 1 of 1)

- [Joint Estimation of Sea State and Vessel Parameters Using a Mass-Spring-Damper Equivalence Model](https://mlsanity.com/paper/2511.21997/) (2025)

## Abstract (arXiv)

This paper introduces a new tool for time-series analysis: the Sliding Window Discrete Fourier Transform (SWDFT). The SWDFT is especially useful for time-series with local- in-time periodic components. We define a 5-parameter model for noiseless local periodic signals, then study the SWDFT of this model. Our study illustrates several key concepts crucial to analyzing time-series with the SWDFT, in particular Aliasing, Leakage, and Ringing. We also show how these ideas extend to R > 1 local periodic components, using the linearity property of the Fourier transform. Next, we propose a simple procedure for estimating the 5 parameters of our local periodic signal model using the SWDFT. Our estimation procedure speeds up computation by using a trigonometric identity that linearizes estimation of 2 of the 5 parameters. We conclude with a very small Monte Carlo simulation study of our estimation procedure under different levels of noise.