fourier - Fourier integral transform

Syntax

Description

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

If f = f(w), fourier returns a function of t.

F = F(t)

By definition,

where x is the symbolic variable in f as determined by symvar.

F = fourier(f,v) makes F a function of the symbol v instead of the default w.

F = fourier(f,u,v) makes f a function of u and F a function of v instead of the default variables x and w, respectively.

Examples

syms x
f = exp(-x^2);
fourier(f)

ans =
pi^(1/2)*exp(-w^2/4)

syms w
g = exp(-abs(w));
fourier(g)

ans =
2/(v^2 + 1)

syms x u
f = x*exp(-abs(x));
fourier(f,u)

ans =
-(u*4*i)/(u^2 + 1)^2

syms v u
syms x real
f = exp(-x^2*abs(v))*sin(v)/v;
fourier(f,v,u)

ans =
piecewise([x ~= 0,...
atan((u + 1)/x^2) -...
atan((u - 1)/x^2)])

See Also

ifourier | laplace | ztrans

Free Symbolic Math Interactive Kit

See how symbolic computations can help you find analytical solutions to math and engineering problems.

Get free kit

Trials Available

Try the latest version of symbolic math products.

Get trial software