Fourier transform in MATLAB Last Updated : 30 May, 2021 Comments Improve Suggest changes Like Article Like Report 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 Using the above function one can generate a Fourier Transform of any expression. In MATLAB, the Fourier command returns the Fourier transform of a given function. Input can be provided to the Fourier function using 3 different syntaxes. Fourier(x): In this method, x is the time domain function whereas the independent variable is determined by symvar and the transformation variable is w by default.Fourier(x,transvar): Here, x is the time domain function whereas transvar is the transformation variable instead of w.Fourier(x,indepvar,transvar): In this syntax, x is the time domain function whereas indepvar is the independent variable and transvar is the transformation variable instead of symvar and w respectively.Now we find the Fourier Transform of e^{-t^2}. Example 1: Matlab % MATLAB code to specify the variable t % and u as symbolic ones The syms function % creates a variable dynamically and % automatically assigns to a MATLAB variable % with the same name syms t u % define time domain function x(t) x = exp(-t^2-u^2); % fourier command to transform into % frequency domain function X(w) % using 1st syntax, where independent variable % is determined by symvar (u in this case) % and transformation variable is w by default. X = fourier(x); % using 2nd syntax, where transformation % variable = y X1=fourier(x,y); % using 3rd syntax, where independent % variable = t & transformation variable = y X2=fourier(x,t,y); % Display the output value disp('1. Fourier Transform of exp(-t^2-u^2) using fourier(x) :') disp(X); disp('2. Fourier Transform of exp(-t^2-u^2) using fourier(x,y) :') disp(X1); disp('3. Fourier Transform of exp(-t^2-u^2) using fourier(x,t,y) :') disp(X2); Output: Let's take another example to find the Fourier Transform of a*abs(t). Example 2: Matlab % MATLAB code for specify the variable % a and t as symbolic ones syms a t % define time domain function x(t) % where t=independent variable & a=constant x = a*abs(t); % fourier command to transform into frequency % domain function X(w) % using 1st syntax X = fourier(x); % using 2nd syntax, where transformation % variable = y X1 = fourier(x,y); % using 3rd syntax, where transformation variable % = y & independent % variable = t (as t is the only other variable) X2 = fourier(x,t,y); % Display the output value disp('1. Fourier Transform of a*abs(t) using fourier(x):') disp(X); disp('2. Fourier Transform of a*abs(t) using fourier(x,y):') disp(X1); disp('3. Fourier Transform of a*abs(t) using fourier(x,t,y):') disp(X2); Output: Comment More infoAdvertise with us Next Article Fourier transform in MATLAB J jatan_18 Follow Improve Article Tags : Engineering Mathematics MATLAB-Maths Similar Reads 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 Inverse Fourier transform in MATLAB Inverse Fourier Transform helps to return from Frequency domain function X(Ï) 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(Ï)\} = 1/2Ï â«_{-â}^âX(Ï).e^{jÏt} dÏ In MATL 3 min read Fourier Transform Fourier transform is a mathematical model that decomposes a function or signal into its constituent frequencies. It helps to transform the signals between two different domains like transforming the frequency domain to the time domain. It is a powerful tool used in many fields, such as signal proces 5 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 Convolution Theorem for Fourier Transform MATLAB A Convolution Theorem states that convolution in the spatial domain is equal to the inverse Fourier transformation of the pointwise multiplication of both Fourier transformed signal and Fourier transformed padded filter (to the same size as that of the signal). In other words, the convolution theore 3 min read Like