Hi everyone. Considering the addition of the following two discrete signals:
x1 = sin (2pi . 1 . nts) // 1 Hz sinusoid of peak amplitude 1
x2 = sin (2pi . 3 . nts) // 3 Hz sinusoid of peak amplitude 1
I have been investigating the theoretical output from a system that adheres to the following equation:
y = x_squared
when I apply the addition of x1+x2 to it.
I have proven that the system is non-linear because the theoretical output is a bunch of components that were not present in the original signals, as follows:
0Hz @ amplitude 1
2Hz @ amplitude 0.5
4Hz @ amplitude -1
6Hz @ amplitude -0.5
I calculated these with the help of trigonometric identities (and a text book )
I understand all of this, but... what about the 0Hz component? What does this look like in practice? Would it be seen as a D.C. level?
Brian
Hi again,
Ok, when you say x1+x2 that means you add the two signals.
What you seem to want to do is to multiply the two signals, which would
be equivalent to using a modulator with the two signals, which is also
sometimes called "mixing" the two signals.
Then, it appears that you want to apply that resulting signal to the
squaring circuit and then analyze the components output from that.
This would be equivalent to:
ya=(sin(w1*t)*sin(w3*t))^2
Now when you 'mix' two signals yes you get the sum and difference
frequencies 2 and 4, but when you square THAT you should also
get double frequencies 2, 4, 6 and 8, which would mean you should see
components of 2Hz, 4Hz, 6Hz, and 8Hz. If any of these are missing
from the output equation then there is still an error.
Another little hint is that the DC component is in fact present, but
it is not equal to 1.
Also, you can easily check (and you really need to do this) at least
one random point with the original equation ya above and your
resulting equation. Since you are saying that your resulting equation
is still the same (as in my previous post) you still do not have the
right answer, so if you want to prove this for sure you have to look
at your equations again. Sorry to inform you of this, but i assume
you want to know so that in the future you can get it more accurate.
BTW, your most recent post seems to be missing exponents or something as
a^ makes no sense, and i assume you meant to write a^2.