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fourier
Fourier transform of a symbolic expression.
Category: Mathematics > Calculus
Syntax
F = fourier(f, t, w)Transforms f(t) into F(w) = int(f(t)*exp(-1i*w*t), t, -Inf, Inf).
Description
The Fourier transform breaks a signal into its frequencies. With the default parameters (see sympref('FourierParameters')), the transform of exp(-abs(t)) is 2/(w^2 + 1) and that of exp(-t^2) is pi^(1/2)*exp(-w^2/4): the Gaussian stays a Gaussian. The transform of the impulse dirac(t) is the constant 1.
Input arguments
f- Symbolic expression in
t. t- Original variable.
w- Frequency variable.
Output arguments
F- Symbolic expression in
w.
Example
Two signals
syms t w
fourier(exp(-abs(t)), t, w)
fourier(exp(-t^2), t, w)Output
ans = 2/(w^2 + 1)
ans = pi^(1/2)*exp(-w^2/4)