Hey guys so im stuck with determining if the following system is time-invariant.The system looks as following
y(t) = Re{sin(t)x(t)}+ Im{jcos(t)x∗(t)}
I did all of the steps with the sin(t-t0) and jcos(t-t0) and also the y2 = x1 (t-t0). But i cant seem to be able to finish the analysis. Could anyone help?
By inspection, the y(t) is full of nontrivial func(t)
expressions so how can it be time invariant?
I think the equation probably has some typos but:
sin(t) is not time invariant
x(t) might or might not be.
jcos(t) is not time invariant
x (as a constant) is undefined
(t) is obviously not time invariant.
Only if x(t) and x both equal zero, could the larger
equation be time invariant.
Perhaps you should decompose x(t) and its complex conjugate x*(t) into their arbitrary Real and Imaginary parts a±jb and make the necessary algebraic manipulation to see what comes out.
Ohhhh i see i was susposed to consider the entire system within the formula of a+jb.Okay so now a and b should be x1 right? and in the part y= a(t)*sin(t) that indicates that the number a(t) is conjugated? Not multiplication. So now if i would to insert numbers for t and t0 i should be getting diffrent end results?
Actually, and this is probably on me, im susposed to determine which one of these is it. It doenst say PROVE that its a time-variant or time-invariant function, but it just say check which one it is.