ifourier - Inverse Fourier integral transform

Syntax

Description

f = ifourier(F) is the inverse Fourier transform of the scalar symbolic object F with default independent variable w. The default return is a function of x. The inverse Fourier transform is applied to a function of w and returns a function of x.

If F = F(x), ifourier returns a function of t:

f = f(t)

By definition

f = ifourier(F,u) makes f a function of u instead of the default x.

Here u is a scalar symbolic object.

f = ifourier(F,v,u) takes F to be a function of v and f to be a function of u instead of the default w and x, respectively.

Examples

syms a w real
f = exp(-w^2/(4*a^2));
F = ifourier(f);
F = simple(F)

F =
(exp(-a^2*x^2)*abs(a))/pi^(1/2)

syms x real
g = exp(-abs(x));
ifourier(g)

ans =
1/(pi*(t^2 + 1))

syms w t real
f = 2*exp(-abs(w)) - 1;
simplify(ifourier(f,t))

ans =
2/(pi*(t^2 + 1)) - dirac(t)

See Also

fourier | ilaplace | iztrans

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