How to get a period of cosinus function ?

Hi,

I have to find the period of the cosinus function using only the vector time and the vector data of the function.

[Rik]

This looks like the sum of two cosines, not just one. Do you want the cosine with the largest magnitude? Are you allowed to use a Fourrier transform?

[Ilan Moshe]

Yes, it is actually a sum of cosines by using this code :

function [t,x]=getSumOfCosines(delta_t,Tlim,f)
t=0:delta_t:Tlim;
x=sum(cos(2*pi*t.*f));
end

The only restriction is to not use any loop and to use only x and t vectors.

Answer 1

[Rik]

Because this is homework, I won't provide a copy-paste ready solution.

If you follow the example from the documentation for fft, you get the code below.

%recreate data
delta_t=0.1;Tlim=5;f=[1;2];
t=0:delta_t:Tlim;
x=sum(cos(2*pi*t.*f));

%figure(1),clf(1)
%plot(t,x)

Fs=1/mean(diff(t));%sampling frequency
L=numel(x);
Y = fft(x);
P2 = abs(Y/L);
P1 = P2(1:floor(L/2)+1);
f = Fs*(0:(L/2))/L;
figure(1),clf(1)
plot(f,P1,'-*')
title('Fourrier transform'),xlabel('frequency'),ylabel('magnitude')

Now you can clearly see there are two frequencies that have a high magnitude.

[Ilan Moshe]

Thanks for ur input )

Could you just explain what is the relationship between theses frequencies and the period of the former function ?

[Rik]

Frequency is the inverse of period.

[Ilan Moshe]

Thanks :)