Astrophysics (index)

Fourier Transform

(systematic method of breaking down functions into periodic components)

The Fourier Transform breaks down a function (e.g., over time) into components that are periodic functions. The forward transformation is:

F(s) is

∫  f(x)e-2πisxdx


  • x is a real number.
  • f(x) is a function on x.
  • s is a real number with the inverse unit of x, e.g., if x is time, s is a Frequency.
  • F(s) is the transformed function.
  • i is the square root of -1.

There is also an inverse transform, from s to x.

The Fourier transform is used to determine what sine-like components make up a particular periodic function, i.e., break a signal down into its harmonics.


Referenced by:
Canada-France-Hawaii Telescope (CFHT)
Fast Fourier Transform (FFT)
Fourier Space
Imaging Fourier Transform Spectroscopy (IFTS)
Linear Theory
Spectral Density