Need to solve Fourier Series script

clear all;clc;

x = 0:0.01:1;

for i = 1: size(x,2)

y(i) = exact(x(i));

f(i) = fourier(x(i),3);

g(i) = fourier(x(i),6);

end

function func = phi(x,n)

func = cos(pi * (n - 1/2) * x);

end

function coef = c(n)

beta = pi * (2 * n - 1);

coef = 8 * (cos(beta / 4) - cos(beta / 2)) / beta^2;

end

function f = fourier(x,N)

f = 0;

for n = 1: N

f = f + c(n) * phi(x,n);

end

end

function f = exact(x)

if x < 1/2

f = 1/2;

else

f = 1 - x;

end

end

plot(x,y,'-','LineWidth',5,x,f,'--','LineWidth',5,x,g,'-','LineWidth',5);

legend('Exact','Fourier (3 terms)','Fourier (6 terms)');

Answer 1

[madhan ravi]

 plot(x,y,'-',x,f,'--',x,g,'-','LineWidth',5);
legend('Exact','Fourier (3 terms)','Fourier (6 terms)'); % use this line before function

[madhan ravi]

You could preallocate variables before the for loop

[NANDEESWARAN]

Thanks Sir.

Answer 2

[VBBV]

if you have the entire code in one script file, then you can put all the functions after the plot function call as below otherwise,if you have them in separate function files, you can just call plot function as below

clear all;clc;
x = 0:0.01:1;
for i = 1: size(x,2)
    y(i) = exact(x(i));
    f(i) = fourier(x(i),3);
    g(i) = fourier(x(i),6);
end

hold on
plot(x,y,'-','LineWidth',2)
plot(x,f,'--','LineWidth',2)
plot(x,g,'-','LineWidth',2);
legend('Exact','Fourier (3 terms)','Fourier (6 terms)');

function f = exact(x)
if x < 1/2
    f = 1/2;
else
    f = 1 - x;
end
end
function f = fourier(x,N)
f = 0;
for n = 1: N
    f = f + c(n) * phi(x,n);
end
    
end

function func = phi(x,n)
    func = cos(pi * (n - 1/2) * x);
end
function coef = c(n)
    beta = pi * (2 * n - 1);
    coef = 8 * (cos(beta / 4) - cos(beta / 2)) / beta^2;
end

[NANDEESWARAN]

Thanks Sir . I appreciate your reply, Its working now.