How to do a Fourier series with two for loops for a Periodic Function ?

Hey guys i need your help:

I m new to matlab and i m trying to do a Fourier Series with two for loops for a periodic Function.

I m getting the following error and i dont rly understand why and could need some help :D

Array indices must be positive integers or logical values.

Error in mHsl (line 39)

a_mhsl(j)=0;

clear

clc

close all

% Fourierkoeffizienten von Bewegungsverlauf aus mHsl

sk = [0.0014-0.0870276855443134 0.295151170426641 0.416092219888434...

-0.0299873173682189 -0.290504199655492 -0.111557021687448 ...

0.0451411005902953 0.0283060937157195 -0.000416681595205368];

ck = [0 0.220518023785692 0.275639019529607 -0.198509704076127 ...

-0.413001715701831 -0.0889925072469301 0.143231479398419 ...

0.0726292539758752 -0.00629044571050385 -0.00521997196551305];

%Taktzeit in s

tT = 1;

%Übertragungsfaktor phi = omega * t mit Omega in rad/s

omega = tT*2*pi; %Zeitvektor für neues Signal

t_mHsl = linspace(0,tT,1000);

p = 2;

%Bestimmung des Beschleunigungsvorgabe

a_mhsl = zeros(length(1),length(t_mHsl));

for j = 0:length(t_mHsl)

a_mhsl(j)=0;

for k = 0:1:length(sk)-1

a_mhsl(j) = a_mhsl(j)-k^4*(ck(k+1)*cos((p*pi/2)+k*omega*t_mHsl(j))

+sk(k+1)*sin((p*pi/2)+k*omega*t_mHsl(j)));

end

end

%Ausgabe des Beschleunigungsverlaufes

mhsl.time = t_mHsl';

mhsl.a = a_mhsl;

figure()

plot(mhsl.time,mhsl.a)

[Torsten]

Array indices in MATLAB start at 1, not at 0.

So you get an error if you try to address a_mhsl(0).

[enrico Rothe]

thx for the help torsten,

but it still doesent work if i change it like that:

tT = 2*pi;

%Übertragungsfaktor phi = omega * t mit Omega in rad/s

omega = (1/tT)*2*pi; %Zeitvektor für neues Signal

t_mHsl = linspace(0,tT,1000);

p = 2;

%Bestimmung des Beschleunigungsvorgabe

a_mhsl = zeros(length(1),length(t_mHsl));

for j = tT/1000:length(t_mHsl)

for k = 1:length(sk)-1

a_mhsl(j) = k^2*(-ck(k+1)*k^2*cos((p*pi/2)+k*omega*t_mHsl(j+0.001))-sk(k+1)*(k+1)^2*sin((p*pi/2)+(k+1)^2*omega*t_mHsl(j+0.001)));

end

end

[Torsten]

array indices j and k must be integers > 0. Thus tT/1000 cannot be used as an array index.

Just shift the loop indices for j and k by one unit.

for j = 1:length(t_mHsl)
    a_mhsl(j)=0;
    for k = 1:length(sk)      
        a_mhsl(j) = a_mhsl(j)-(k-1)^4*(ck(k)*cos((p*pi/2)+(k-1)*omega*t_mHsl(j))+sk(k)*sin((p*pi/2)+(k-1)*omega*t_mHsl(j)));
    end
end

And insert a space between the first two elements of sk.

[enrico Rothe]

thx a lot Torsten !! It worked! you made my day !

[enrico Rothe]

what do u exactly mean by inserting a space between the first two elements ? and is it correct that if i start with k=1to length(sk)-1 that i dont need (k+1) in the equation ?

thats my final equatione now. what do u think ?

omega = (1/tT)*2*pi; %Zeitvektor für neues Signal

t_mHsl = linspace(0,tT,10000);

p = 2;

%Bestimmung des Beschleunigungsvorgabe

s_mhsl = zeros(length(1),length(t_mHsl));

a_mhsl = zeros(length(1),length(t_mHsl));

for j = 1:length(t_mHsl)

a_mhsl(j)=0;

for k = 1:length(sk)-1

a_mhsl(j) = k^2*(-ck(k)*k^2*cos((p*pi/2)+k*omega*t_mHsl(j))-sk(k)*(k)^2*sin((p*pi/2)+(k)*omega*t_mHsl(j)));

end

end

%Ausgabe des Beschleunigungsverlaufes

mhsl.time = t_mHsl';

mhsl.a = a_mhsl;

figure()

plot(mhsl.time,mhsl.a)

[Torsten]

I just see that shifting the k-loop was not necessary because the arrays ck and sk are addressed with indices running between 1 and length(sk). So you can just use your first code and only shift the j-loop by one unit:

for j = 1:length(t_mHsl)
   a_mhsl(j) = 0;
   for  k = 0:1:length(sk)-1
      a_mhsl(j) = a_mhsl(j)-k^4*(ck(k+1)*cos((p*pi/2)+k*omega*t_mHsl(j))+sk(k+1)*sin((p*pi/2)+k*omega*t_mHsl(j)));
   end
end

But if you shift the k-loop by one unit, you will have to replace all k's in your equation for a_mhsl by k-1, thus

for j = 1:length(t_mHsl)
   a_mhsl(j) = 0;
   for  k = 1:length(sk)
      a_mhsl(j) = a_mhsl(j)-(k-1)^4*(ck(k)*cos((p*pi/2)+(k-1)*omega*t_mHsl(j))+sk(k)*sin((p*pi/2)+(k-1)*omega*t_mHsl(j)));
   end
end

what do u exactly mean by inserting a space between the first two elements ?

Look at your matrix sk. There is no space between 0.0014 and -0.0870276855443134.

[enrico Rothe]

thx again. the space problem would have cost me a lot of time to find out ^^

i guess i m not the Charma-god but helping strangers on the internet can t be to bad for it. thanks again and take care :D