Matlab output is not matching with the mathematics...
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Hari Ijjada
le 25 Nov 2019
Commenté : Walter Roberson
le 25 Nov 2019
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 ?
2 commentaires
per isakson
le 25 Nov 2019
Modifié(e) : per isakson
le 25 Nov 2019
Which values do you use for f1, f2 and t ? What differences do you see? Are they large compared to the expected floating point error?
KALYAN ACHARJYA
le 25 Nov 2019
arg1=acos(S1)=2*pi*f1*t;
This is not a valid Matlab statement.
Réponse acceptée
David Goodmanson
le 25 Nov 2019
Modifié(e) : David Goodmanson
le 25 Nov 2019
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.
4 commentaires
Walter Roberson
le 25 Nov 2019
i followed this process........x1=acos(Signal1)....acos------>gives inverse of the Signal1.......2*pi*fc*t
That process is incorrect. acos(cos(2*pi*fc*t)) does not give 2*pi*fc*t outside of t in [0, 1/(2*fc)]
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Walter Roberson
le 25 Nov 2019
arg1=acos(S1)=2*pi*f1*t;
arg2=acos(S2)=2*pi*f2*t;
Not correct. As you increase t past one period, acos(cos(x)) becomes mod(x,period) rather than x. Those mod() of the two components interact with each other.
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