How to get a period of cosinus function ?

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Ilan Moshe
Ilan Moshe 2020-5-25
评论： Ilan Moshe 2020-5-27
Hi,
I have to find the period of the cosinus function using only the vector time and the vector data of the function.
Cosinus function
Vector data
time data
  2 个评论
Rik
Rik 2020-5-25
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
Ilan Moshe 2020-5-25
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.

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Rik
Rik 2020-5-25
编辑：Rik 2020-5-25
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.
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Rik
Rik 2020-5-25
Frequency is the inverse of period.

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