An Algorithm for the 2D Radix-2 Sliding Window Fourier Transform
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We present a new algorithm for the 2D Radix-2 Sliding Window Fourier Transform (SWFT). Our algorithm avoids repeating calculations in overlapping windows by using a tree representation of the Cooley-Tukey Fast Fourier Transform (FFT). For an N_0 × N_1 array and n_0 = 2^m_0× n_1 = 2^m_1 windows, our algorithm takes O(N_0 N_1 n_0 n_1) operations, which is faster than taking a 2D FFT in each window. We provide a C implementation of the algorithm, compare ours with existing algorithms, and show how the algorithm extends to higher dimensions.
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