Inverse Fourier transform in MATLAB Last Updated : 30 May, 2021 Comments Improve Suggest changes Like Article Like Report 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: x(t) = F^{-1}\{X(ω)\} = 1/2π ∫_{-∞}^∞X(ω).e^{jωt} dω 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 e^{-ω^2/4} Matlab % MATLAB code specify the variable % w and t as symbolic ones syms w t % define Frequency domain function X(w) X=exp(-w^2/4); % ifourier command to transform into % time domain function x(t) % using 1st syntax, where by default % independent variable = w % and transformation variable is x . x1 = ifourier(X); % using 2nd syntax, where transformation variable = t x2 = ifourier(X,t); % using 3rd syntax, where independent variable % = w (as there is no other % variable in function) and transformation % variable = t x3 = ifourier(X,w,t); % Display the output value 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 e^{-ω^2-a^2} Matlab % MATLAB code to specify the variable % % a w and t as symbolic ones % syms a w t % define Frequency domain function X(w) X=exp(-w^2-a^2); % ifourier command to transform into % time domain function x(t) % using 1st syntax, where by default % independent variable = w % and transformation variable is x . x1=ifourier(X); % using 2nd syntax, where transformation % variable = t x2=ifourier(X,t); % using 3rd syntax, where independent % variable = w (as there is no other % variable in function) and transformation % variable = t x3=ifourier(X,w,t); % Display the output value 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: Comment More infoAdvertise with us Next Article Inverse Fourier transform in MATLAB jatan_18 Follow Improve Article Tags : Engineering Mathematics MATLAB-Maths Similar Reads Fourier transform in MATLAB Fourier Transform is a mathematical technique that helps to transform Time Domain function x(t) to Frequency Domain function X(ω). In this article, we will see how to find Fourier Transform in MATLAB. The mathematical expression for Fourier transform is:X(ω) = F\{x(t)\} = ∫_{-∞}^∞x(t).e^{(-jωt)} dt 3 min read 2-D Inverse Cosine Transform in MATLAB The 2-D inverse cosine transform is used to decode an image into the spatial domain, which is a more suitable data representation for compression (ICT). ICT-based decoding is the foundation for standards for image and video decompression. or, to put it another way, we can say that the inverse cosine 2 min read Fast Fourier Transform in MATLAB Fast Fourier Transform is an algorithm for calculating the Discrete Fourier Transformation of any signal or vector. This is done by decomposing a signal into discrete frequencies. We shall not discuss the mathematical background of the same as it is out of this article's scope. MATLAB provides a bui 3 min read Find inverse of matrix in MATLAB Inverse function in MATLAB is used to find the inverse of a matrix. Suppose A is a matrix and B is the inverse of a then A*B will be an identity matrix. This function computes the inverse of a square matrix. This is used while solving linear equations. We can compute the inverse of a matrix by passi 2 min read Inverse Laplace Transform In this Article, We will be going through the Inverse Laplace transform, We will start our Article with an introduction to the basics of the Laplace Transform, Then we will go through the Inverse Laplace Transform, will see its Basic Properties, Inverse Laplace Table for some Functions, We will also 10 min read Like