Papers › Fast Compressed-Domain N-Point Discrete Fourier Transform: The "Twiddless" FFT Algorithm
Fast Compressed-Domain N-Point Discrete Fourier Transform: The "Twiddless" FFT Algorithm
Saulo Queiroz
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In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the N-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an N-point signal (by a factor of p) into an N/p-point compressed signal whose DFT readily yields N/p coefficients of the original signal. However, existing compression-domain DFT analyses have been limited to computing only the even-indexed DFT coefficients. With TFFT, we overcome this limitation by efficiently computing both \emph{even- and odd-indexed} DFT coefficients in the compressed domain with O(N logN) complexity. TFFT introduces a new recursive decomposition of the DFT problem, wherein N/2ⁱ coefficients of the original input are computed at recursion level i, with no need for twiddle factor multiplications or butterfly structures. Additionally, TFFT generalizes the input length to N = c ·2ᵏ (for k ≥0 and non-power-of-two c > 0), reducing the need for zero-padding and potentially improving efficiency and stability over classical FFTs. We believe TFFT represents a \emph{novel paradigm} for DFT computation, opening new directions for research in optimized implementations, hardware design, parallel computation, and sparse transforms.
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