Fourier Series and SCILAB

Today I wrote a code that calculates the Fourier Coefficients.

In case you don’t know what a Fourier Series is, then, basically it is a way of approximating or representing a periodic function by a series of simple harmonic(sine and cosine) functions.

You can check out the wikipedia for  more information on it:

For a waveform
f(x) with period 2L=2π/k, we have that k=2π/2L=π/L and nkx =nπx/L , Then we have
fourier series coefficients
So, here’s how my code works:
I created a function


l :half of the period, (periodicity of the function f which is to be approximated by Fourier Series)

n: no. of Fourier Coefficients you want to calculate

 f: function which is to be approximated by Fourier Series

A0: The first fourier coefficient.

A: An array/matrix whose nth element is the nth coefficient An.

B: An array/matrix whose nth element is the nth coefficient Bn.

The code is:

//Fourier Series Coefficients
//The following function returns the fourier coefficients,'a0', 'An' & 'Bn'
//User needs to provide the following arguments:
//l=periodicity of the function f which is to be approximated by Fourier Series
//n=no. of Fourier Coefficients you want to calculate
//f=function which is to be approximated by Fourier Series
//*Some necessary guidelines for defining f:
//*The program integrates the function f from -l to l so make sure you define the function f correctly in the interval -l to l.
//for more information on Fourier Series visit:
//Written by: Manas Sharma([email protected])
//For more useful toolboxes and tutorials on Scilab visit:
function [a0, A, B]=fourier(l, n, f)
    for i=1:n
        function b=f1(x, f)
        function c=f2(x, f)


fourier output


That’s it. I hope it was not too difficult to understand. If you have any questions I will be glad to answer them.


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10 thoughts on “Fourier Series and SCILAB

  1. Hi! thank you for the tutorial. I was just wondering if you need to change the function where would you have to make the change. For example if you have a square plot.

  2. Hi,Thank you for the tutorial, I was wondering how to take fourier series of some other function for that matter of fact if i wanted to plot FS of triangular wave where and how would I define f(x) in this case.

    1. Hi Lalith,
      To find out the FS of any periodic function, you first need to understand how to define a periodic function. For that please check out this post:
      Then you can also read another post on FS:
      I have also created a toolbox for FS calculatoon and plotting. Links are in the post.
      Good luck!

  3. in exam one question came find Fourier series coefficient of f(x)=3x^2 in(-pi,pi)for n=5 .Plase reply how to solve this kind of problem

  4. Hi,
    Manas i need your help regarding a scilab prog.To solve the S -wave schrodinger equation for the ground state and first excited state of hydrogen atom :(m is the reduced mass of electron.Obtain the energy eigen value and plot the corresponding value wave function. e=3.795 (eVA)1/2, h=1973(eVA) and m=0.511*106 eV/c2

  5. Hello Sir;
    I want to just ask you that the error is displaying while executing this prog in my PC at line 20 i.e.
    x=-5*l:0.1:5*l . Its showing that there is undefined variable ‘l’.
    Can you just help me out.

  6. Madam i have a trignometric fourier series with all coefficients how can i plot it . do u have code forthat ?

  7. Is this code for piecewise function too? i couldn’t use, so can you make the video for piecewise function too?

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