Why AM wave is multiplication of carrier and message signal?

[Dark_Capacitor]

Let A= (sin(x) * sin(100x)) + sin(100x).; modulation index is 1;
Let B= (sin(x) + sin (100x));
Both of these waves have same frequency and both are amplitude modulated.
When passed through an envelope detector, both will give message signal.
And B have an advantage of not having any sideband frequency. Thus allowing bandwidth to be very short.
Then why we use wave A type modulation not B. All the ssb and suppressed carrier wave also use technique A, why not B?

 

[matteo137]

B is not an up-conversion of the signal you want to transmit. In other words, let's say you want to transmit a 100 kHz signal, you do not want to amplify it an send into the antenna... what you want to do is to up-convert it in frequency, and then send an electromagnetic wave of frequency e.g. > 100 MHz. If your high frequency carrier does not have sidebands, you are not transmitting informations with it.

 

[Dark_Capacitor]

Thank you matteo137 for replying. I'm new to communication systems. Can you tell how exactly side bands carry information? All I know is that the envelope of the carrier wave has the message signal.

 

[matteo137]

The sidebands carry information because they ARE the information.

Think about the Fourier decomposition of the signal (hoping you are familiar with it).
Let's say your "information" is a 1 KHz signal, so the spectrum of this signal is a dirac-delta at that frequency. When you modulate a carrier (e.g. 100 MHz) with this signal, the spectrum of the modulated carrier is a dirac-delta at 100 MHz with two symmetric sidebands at +- 1 KHz (see picture). This shows you that when you use a carrier to transmit information, what you actually care are ONLY the sidebands, and this is true also for FM modulations.

There are even example of transmission techniques which suppress the carrier and one of the two sidebands before transmitting the signal through air, in such a way that you only send one useful sideband. (of course the receiver has to know the frequency of the carrier, and have a stable oscillator)

Picture AM spectrum:
http://en.wikipedia.org/wiki/Amplitude_modulation#mediaviewer/File:AM_spectrum.svg

 

[Dark_Capacitor]

Thanks man. You cleared up many things. And I familiar with Fourier analysis