I am utterly confused. When I was reading my textbook , I found something unacceptable.
While deriving an expression for a modulated wave,
It's been given that
"A sinusoidal carrier wave can be represented as c (t) = Ac sin
(ωt + Φ)
where c (t) is the signal strength of the carrier wave.
Let m (t) = Am sinωmt represent the message or the modulating signal.
The modulated signal cm (t) can be written as
cm= (Ac+Amsin ωmt) sin ωct
I wonder how's it possible! Shouldn't it be cm (t) = Acsin ωct + Am sinωmt ?
But then I made an adhoc assumption - which was not satisfactory - but I thought it could be justified from a more rigorous application of mathematics. So, I continued reading
On the next page, I found something in contrast to my "assumption".
In the topic "Production of amplitude modulated wave" -
According to my textbook "Here the modulating signal Am
sinωmt is added to the carrier signal Acsinωt to produce the signal x (t). This signal x (t) = Am sinωmt + Ac sin ωct is passed through a square law device."
Now this equation for x (t) is different from the one which was used (in the textbook) earlier.
What even is happening?