How to plot correctly a Fourier series?

Hi,

I would like to solve this problem related with Fourier series:

I have successfully determined a0, an, and bn. Now I would like to compute first 5,10,15 terms with MATLAB.

My (semi-finished) code:

clear;

max = 5;  % first 5 terms

syms t
y = piecewise(-3<t<0,-6,0<t<3,-2);
I = [-3,3];

fplot(y, I)  % plot original func.
hold on;

syms x n;

fun1 = -6;
fun2 = -2;

fun3 = fun1 * cos((n * pi) / 3 * x);
fun4 = fun2 * cos((n * pi) / 3 * x);

fun5 = fun1 * sin((n * pi) / 3 * x);
fun6 = fun2 * sin((n * pi) / 3 * x);

a0 = (1/3) * int(fun1,x,[-3 0]) + (1/3) * int(fun2,x,[0 3]);
an = (1/3) * int(fun3,x,[-3 0]) + (1/3) * int(fun4,x,[0 3]);
bn = (1/3) * int(fun5,x,[-3 0]) + (1/3) * int(fun6,x,[0 3]);

c = 0;
AN = [];

for i = 1:max
    c= c+1;
    AN = [AN subs(an,n,c)];
    i = i+1;
end


c = 0;
BN = [];

for i = 1:max
    c= c+1;
    BN = [BN subs(bn,n,c)];
    i = i+1;
end

an and bn values are stored in AN and BN vectors. It seems that this code compute terms correctly, but I don't know how to plot this function.

Answer 1

[Aghamarsh Varanasi]

Hi,

You can create a 'fourier series' with the coefficients a0, AN and BN arrays and use fplot to plot this symbolic function.

For example, the last part of your code can be modified as follows

AN = [];
BN = [];

fourier_series = 0;

for i = 1:max
    AN = [AN subs(an,n,i)];
    BN = [BN subs(bn,n,i)];
    
    fourier_series = fourier_series + (AN(i) *  cos(i*t) + BN(i) * sin(i*t));
end

fplot(t, (a0/2 + fourier_series), [-3,3])

Hope this helps