- #1

- 63

- 2

## Homework Statement

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) = A

(ωt + Φ)

where c (t) is the signal strength of the carrier wave.

Let m (t) = A

The modulated signal c

c

I wonder how's it possible! Shouldn't it be c

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 A

sinω

Now this equation for x (t) is different from the one which was used (in the textbook) earlier.

What even is happening?

While deriving an expression for a modulated wave,

It's been given that

"A sinusoidal carrier wave can be represented as c (t) = A

_{c}sin(ωt + Φ)

where c (t) is the signal strength of the carrier wave.

Let m (t) = A

_{m}sinω_{m}t represent the message or the modulating signal.The modulated signal c

_{m}(t) can be written asc

_{m}= (A_{c}+A_{m}sin ω_{m}t) sin ω_{c}tI wonder how's it possible! Shouldn't it be c

_{m}(t) = A_{c}sin ω_{c}t + A_{m}sinω_{m}t ?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 A

_{m}sinω

_{m}t is added to the carrier signal A_{c}sinωt to produce the signal x (t). This signal x (t) = A_{m}sinω_{m}t + A_{c}sin ω_{c}t 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?

Last edited: