fourier (Symbolic Math Toolbox)

Fourier integral transform.

Syntax

F = fourier(f)
F = fourier(f,v)
F = fourier(f,u,v)

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.

By definition

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

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

Fourier Transform
MATLAB Command

f = exp(-x^2)

fourier(f)
returns
pi^(1/2)*exp(-1/4*w^2)

g = exp(-abs(w))
fourier(g)
returns
2/(1+t^2)

f = x*exp(-abs(x))

fourier(f,u)
returns
-4*i/(1+u^2)^2*u

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

fourier(f,v,u)
returns
-atan((u-1)/x^2)+atan((u+1)/x^2)

Fourier Transform	MATLAB Command
	`f = exp(-x^2)` `fourier(f)` returns `pi^(1/2)exp(-1/4w^2)`
	`g = exp(-abs(w))` `fourier(g)` returns `2/(1+t^2)`
	`f = xexp(-abs(x))` `fourier(f,u)` returns `-4i/(1+u^2)^2*u`
	`syms x real` `f = exp(-x^2abs(v))sin(v)/v` `fourier(f,v,u)` returns `-atan((u-1)/x^2)+atan((u+1)/x^2)`