The best replacement for dft is fft.

The best alternatives to dft are rated as following:
★★★★★  fft
★★★★  dtft
★★★  hf
★★★  dct
★★  hartree fock
★  ab initio
★  fft matlab
★  bist
  fcx
  lead sled plus
  mp2

Your alternative for dft is not listed? Suggest!
Speaking about dft, one probably shouldn't forget about zero padding.

Other search terms related to dft and their ratings are:
★★★★★ zero padding
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Google Trends

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