The 2D Tree Sliding Window Discrete Fourier Transform

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.

arXiv comment15 pages, 4 figures, submitted to ACM TOMS