The 2D Tree Sliding Window Discrete Fourier Transform

TL;DR

This paper introduces a novel 2D SWDFT algorithm that efficiently computes Fourier transforms over sliding windows by leveraging a tree structure, reducing redundant calculations and extending easily to higher dimensions.

Contribution

The paper presents a new tree-based algorithm for 2D SWDFT that improves computational efficiency and extends to higher dimensions, with a C implementation for Radix-2 cases.

Findings

Algorithm operates in $O(N_0 N_1 n_0 n_1)$ time

Provides a C implementation for Radix-2 case

Demonstrates extension to higher dimensions

Abstract

We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey Fast Fourier Transform (FFT). For an $N_0 \times N_1$ array and $n_0 \times n_1$ windows, our algorithm takes $O(N_0 N_1 n_0 n_1)$ operations. We provide a C implementation of our algorithm for the Radix-2 case, compare ours with existing algorithms, and show how our algorithm easily extends to higher dimensions.