The best replacement for fourier transform is laplace transform.

The best alternatives to fourier transform are rated as following:
★★★★★  laplace transform
★★★★★  fourier series
★★  fast fourier transform
★★  wavelet transform
★★  discrete fourier transform
★  laplace
★  z transform
★  fft
★  cosine transform
  power spectral density
  inverse fourier transform
  wavelet
  fourier transform

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fourier transform
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