How do I create a user defined function using the fourier series?

I am supposed to create a user defined function using the Fourier series function that will do the following: (1) accept input variables c, L, N, and vecx (2) approximate the step function f(x), according to the Fourier series, over the set range of x values and (3) return an output for f(x) evaluated at each value of x. What I am thinking is that I need to use nested loops but I have no idea how to start. This is what I have so far:

function myoutput = mystep( c, L, N, vecx)
lengthx = length(vecx)
fxvec = zeros(1, lengthx)
while vecx >= 0 && vecx <= 2L
  f(x) = (c/L) + ((2/pi).*(((-1^N)/N)*sin((N*pi*c)/L)*cos((N*pi*vecx)/L)))
end

Am I correct so far or do I need to use for loops or while loops to make the Fourier series work?

[Walter Roberson]

Udf? User defined function?

[macabe banchero]

yes

Answer 1

[Abraham Boayue]

I would recommend a for loop to solve this problem. Try something like this :

function fx = fseries(c,N,x0,x1)
% All the inputs are
% constants 
% x0 and x1 are the start and values of
% x, N is the length of x;it should be
% large eniugh; say N= 100 for example.
L = x1-x0; % period of f(x)
deltax = (x1-x0)/(N-1);
x = x0:deltax:x1;% better to create  
% the vector this way than to input it.
F = zeros(1,N);
 a0 = c/L; % since a0 is a constant, 
 % no need to have in in the for loop.
for n = 1:N
    an = 2/pi*(-1)^n*sin(n*pi*c/L)
    F = an*cos(n*pi*x/L);
end
F = a0+F;
% your function is an odd function
% since bn = 0.

plot(x,F,'linewidth',2)
a = title('f(x)');

set(a,'fontsize',12);
a = xlabel('x');
set(a,'fontsize',12);
a = ylabel('y');
set(a,'fontsize',12);
end

[macabe banchero]

so basically you're taking the first part of the fourier series and setting it to "an" then multiplying it by the second part for every n.

Answer 2

[Abraham Boayue]

I made a little error, here is the correction. Replace the expression for F with the following line.

F = F + an*cos(n*pi*x/L);

I am simply performing the summation in the equation of the Fourier series. Check this link to a solution that I made for someone, you can improve your function by following the code. https://www.mathworks.com/matlabcentral/answers/388949-how-can-i-perform-a-fourier-series-on-this-function

[macabe banchero]

great thanks!

[macabe banchero]

So if I was to create a script that would ask for inputs of c,L, and N then call my function and approximate it for x values between 0 and 2L and then graph it. Would I need a for loop in here as well or no? This is what I have so far:

clear;clc;close all
input('variable c = ')
input('variable L = ')
input('variable N = ')
for x>=0 && x<=2L

Answer 3

[Abraham Boayue]

Your function wasn't designed to ask the user for inputs as you are attempting to do, although we can alter it to do that. To run the function, simply create an mfile like this. Let me know if you want the input feature. (You will get an error when you run this code, just change function fx to function F.

c = 6;
N = 100;
x0 = 0;
x1 = 10;
F = fseries(c,N,x0,x1);

[macabe banchero]

So this is what I am supposed to do, i've done parts a and b but when I try to do part c it doesn't work. Anyway you can help?

[Walter Roberson]

c = input('c');
and so on
x = linspace(0, 2*L);
f = YOUR_UDF(Appropriate Parameters Go Here);
plot(x, f);

[macabe banchero]

when you say appropriate parameters do you mean c,L,N, and x?

[Walter Roberson]

Sounds about right.

[macabe banchero]

Awesome thanks!