The best replacement for laplace is fourier.

The best alternatives to laplace are rated as following:
★★★★★  fourier
★★  fourier transform
★  z transform
★  mle
★  sobel
  fourier transforms
  z transforms

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Speaking about laplace, one probably shouldn't forget about step functions.

Other search terms related to laplace and their ratings are:
★★★★★ step functions
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