Method on @sym: ifourier (G, w, x) ¶

Method on @sym: ifourier (G) ¶

Method on @sym: ifourier (G, x) ¶

Symbolic inverse Fourier transform.

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

syms G(w) x
f(x) = rewrite(ifourier(G), 'Integral')
  ⇒ f(x) = (symfun)
      ∞
      ⌠
      ⎮        ⅈ⋅w⋅x
      ⎮  G(w)⋅ℯ      dw
      ⌡
      -∞
      ─────────────────
             2⋅π

Example:

syms k
F = sqrt(sym(pi))*exp(-k^2/4);
ifourier(F)
  ⇒ (sym)
         2
       -x
      ℯ

F = 2*sym(pi)*dirac(k);
ifourier(F)
  ⇒ ans = (sym) 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/fourier.

Package: symbolic