The base DFT calculator in R, stats::fft, uses the Mixed-Radix algorithm of Singleton (1969). In this vignette we show how this calculator compares to FFT in the fftw package (Krey et al., 2011), which uses the FFTW algorithm of Frigo and Johnson (2005). For univariate DFT computations, the methods are nearly equivalent with two exceptions which are not mutually exclusive: (A) the series to be transformed is very long, and especially (B) when the series length is not highly composite. In both exceptions the algorithm FFT outperforms fft
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