Nested for loop fourier series

I'm trying to use a nested for loop to do a fourier series. I have to evaluate n to 10 then use the new n for each pass to analyze t. n=10 t=10 I'm not quite sure how to do the nested for loop section. Any help is highly appreciated

This is what I have so far

y = [1.0668 1.8288 2.7432 3.5662 4:2977 4.6634 2.5908 2.3165 2.6518 3.0785 3.3223 ... 2.6213 0.3200 - 0.5791 - 1.0668 - 1.4326 - 1.4630 - 1.1887 - 0.5182 0.1524 1.0668];

n=10

T=2*pi %Period

O=2*pi/T %omega

t=linspace(0,2*pi,length(y))

a0=1/2*pi*trapz(t,y)

an(i)=(2/T)*trapz(t,y.*cos((n(i)*O.*t))) %finds an for i=n

bn(i)=(2/T)*trapz(t,y.*sin((n(i)*O.*t))) %finds bn for i=n

for i=1:n

    for j=1:length(y)

        n(i)=i

    an1(j)=(2/T)*trapz(t,y.*cos((n(i)*O.*t))) %finds an1 using each n and a different t each loop

    bn1(j)=(2/T)*trapz(t,y.*sin((n(i)*O.*t))) %finds bn1 using each n and a different t each loop

    end
end

M=a0+an1+bn1

Answer 1

[Andrei Bobrov]

To = 2*pi;
s = numel(y);
t = linspace(0,To,s).';
n = 1:10;
ang = t*n;
a0_1 = 1/To*trapz(t,y);
abn_1 = 2/To*trapz(t,[bsxfun(@times,y,[cos(ang), sin(ang)]);

an_1 = abn_1(n);
bn_1 = abn_1(n(end)+n);

or with use fft

nn = numel(y);
x = fft(y(1:end-1));
a0_1 = x(1)/(nn-1);
abn_2 = 2/(nn-1)*x(2:end);

[Carlos So]

Sorry, but it has to be done using a nested for loop.