Method on @sym: fourier (f, x, w) ¶

Method on @sym: fourier (f) ¶

Method on @sym: fourier (f, w) ¶

Symbolic Fourier transform.

The Fourier transform of a function f of x is a function FF of w defined by the integral below.

syms f(x) w
FF(w) = rewrite(fourier(f), 'Integral')
  ⇒ FF(w) = (symfun)
      ∞
      ⌠
      ⎮        -ⅈ⋅w⋅x
      ⎮  f(x)⋅ℯ       dx
      ⌡
      -∞

Example:

syms x
f = exp(-abs(x));
fourier(f)
  ⇒ (sym)
        2
      ──────
       2
      w  + 1

Note fourier and ifourier implement the non-unitary, angular frequency convention for L^2 functions and distributions.

*WARNING*: As of SymPy 0.7.6 (June 2015), there are many problems with (inverse) Fourier transforms of non-smooth functions, even very simple ones. Use at your own risk, or even better: help us fix SymPy.

See also: @sym/ifourier.

Package: symbolic