MATLAB: Matlab output is not matching with the mathematics…

MATLAB

S1=cos(2*pi*f1*t);
S2=cos(2*pi*f2*t);
arg1=acos(S1)=2*pi*f1*t;
arg2=acos(S2)=2*pi*f2*t;
cos(arg1-arg2)=cos(2*pi*(f1-f2)*t);
But output is not coming as expected.if you observe the frequency spectrum of both they are not same.
Why it is happening ?

Best Answer

Hi Hari,
the problem is that 2*pi*f*t is a nice linear function of t for all t, but the output of acos is restricted to the range
0<= acos <pi. With 
t = 0:.001:5;
f1 =1;
S1 = cos(2*pi*f1*t);
arg1 = acos(S1)
figure(1)
plot(t,2*pi*f1*t,t,arg1) 
grid on
you will see that the two quanities agree at the beginning, but acos gets chopped up as t increases.
If you compare the cosines of (2*pi*f1*t) and arg1, then those agree as they must. But with cos(arg1-arg2) you are taking the cosine of the difference of two chopped up quantities with different periods, and it doesn't work.
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