Inverse Fourier transform in MATLAB
Last Updated :
30 May, 2021
Inverse Fourier Transform helps to return from Frequency domain function X(ω) to Time Domain x(t). In this article, we will see how to find Inverse Fourier Transform in MATLAB.
The mathematical expression for Inverse Fourier transform is:
In MATLAB, ifourier command returns the Inverse Fourier transform of given function. Input can be provided to ifourier function using 3 different syntax.
- ifourier(X): In this method, X is the frequency domain function whereas by default independent variable is w (If X does not contain w, then ifourier uses the function symvar) and the transformation variable is x.
- ifourier(X,transvar): Here, X is the frequency domain function whereas transvar is the transformation variable instead of x.
- ifourier(X,indepvar,transvar): In this syntax, X is the frequency domain function whereas indepvar is the independent variable and transvar is the transformation variable instead of w and x respectively.
Example:
Find the Inverse Fourier Transform of
Matlab
syms w t
X=exp(-w^2/4);
x1 = ifourier(X);
x2 = ifourier(X,t);
x3 = ifourier(X,w,t);
disp( '1. Inverse Fourier Transform of exp(-w^2/4) using ifourier(X) :' )
disp(x1);
disp( '2. Inverse Fourier Transform of exp(-w^2/4) using ifourier(X,t) :' )
disp(x2);
disp( '3. Inverse Fourier Transform of exp(-w^2/4) using ifourier(X,w,t) :' )
disp(x3);
|
Output:
Example:
Find the Inverse Fourier Transform of
Matlab
syms a w t
X=exp(-w^2-a^2);
x1=ifourier(X);
x2=ifourier(X,t);
x3=ifourier(X,w,t);
disp( '1. Inverse Fourier Transform of exp(-w^2-a^2) using ifourier(X) :' )
disp(x1);
disp( '2. Inverse Fourier Transform of exp(-w^2-a^2) using ifourier(X,t) :' )
disp(x2);
disp( '3. Inverse Fourier Transform of exp(-w^2-a^2) using ifourier(X,w,t) :' )
disp(x3);
|
Output:
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