Hello, I dont know wether I've posted this in the right section but im really stuck on this question. Its from a signal processing exam paper:
Show that the signal is x(t) + y(t) is a sinusoid and determine its amplitude, frequency and phase.
The answer on the answer paper is:
x(t) + y(t) = cos (pi/2) t + sin (pi/2) t
= √2 cos ((pi/2) t - pi/4)
I have no idea how this is the answer. Am I missing something? can anyone show me the FULL working out?
Now, if we want this last term to be equal to
we must have that and , which leads to . Thus, it follows
as desired. More generally, if you want to convert to the form , you first factor out like this
and then determine from the two conditions . - In other words: from , which is to say .
Well, of course, that isn't possible because we must have and . But we could always write this as and ask for a such that and . That's possible!