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.

f(x) with period 2L=2π/k, we have that k=2π/2L=π/L and nkx =nπx/L , Then we have

So, here’s how my code works:
I created a function

[A0,A,B]=fourier(l,n,f)

Arguments:

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: https://en.wikipedia.org/wiki/Fourier_series
//
//Written by: Manas Sharma([email protected])
//For more useful toolboxes and tutorials on Scilab visit: https://www.bragitoff.com/category/compu-geek/scilab/
funcprot(0);
function [a0, A, B]=fourier(l, n, f)
a0=1/l*intg(-l,l,f,1e-2);
for i=1:n
function b=f1(x, f)
b=f(x)*cos(i*%pi*x/l);
endfunction
function c=f2(x, f)
c=f(x)*sin(i*%pi*x/l);
endfunction
A(i)=1/l*intg(-l,l,f1,1e-2);
B(i)=1/l*intg(-l,l,f2,1e-2);
end
endfunction

Output:

Tutorial:

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

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

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.

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.

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

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.

That is the letter ‘L’ in lowercase, in case you were confusing it with capital ‘i’.

In case you copied it correctly, then I don’t understand why the error is there because ‘l’ is defined in the function definition:
function [a0,A,B]=fourierplot(l,n,f)

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.

Hi Eric,

Thanks for your comment.

I have already shown that in a post: https://www.bragitoff.com/2016/03/defining-a-periodic-function-in-scilab/

Hope it helps.

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.

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: https://www.bragitoff.com/2016/03/defining-a-periodic-function-in-scilab/

Then you can also read another post on FS:

https://www.bragitoff.com/2016/03/calculating-fourier-series-and-plotting-it-scilab/

I have also created a toolbox for FS calculatoon and plotting. Links are in the post.

Good luck!

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

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

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.

I think you’re talking about the code posted here: https://www.bragitoff.com/2016/03/calculating-fourier-series-and-plotting-it-scilab/

That is the letter ‘L’ in lowercase, in case you were confusing it with capital ‘i’.

In case you copied it correctly, then I don’t understand why the error is there because ‘l’ is defined in the function definition:

function [a0,A,B]=fourierplot(l,n,f)

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

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