Amplitude modualtion and frequency component!

[sajib333]

Hello Everyone!

About Amplitude Modulation, Usually it is seen in the book or web that (e.g. **broken link removed** )
'''' The message signal can be represented by m(t) = Mb cos(2πfb + φ)
and the carrier signal can be represented by c(t) = Ac cos(2πfc + φ),
Now Modulated signal = m(t) * c(t) ''

My question is does m(t) represents only the highest frequency component in such a case? Or this is the fundamental frequency component?
Or, this represents the whole message in that all the frequency components/harmonics lying within m(t)? If, this represents the whole message, why only a single frequency component is written (i.e fb)?

If, this represents the max frequency component, why we are only considering only this one? Provided that most of the information of the message is contained in the fundamental frequency? SO, why we are not considering the other ones?

I understand these are very silly queries, I would highly appreciate your time answering me these.


Thanks in advance!

 

[barry]

That m(t) is just for example purposes. In the real world m(t) would be ALL the components of message signal, e.g.

m(t)= M1cos(2af)+M2cos(2bf)+M3cos(2cf)... but the math gets pretty messy.

 

[jiripolivka]

The best way to understand AM is to use an AM modulated signal generator and a spectrum analyzer.
You will see that the carrier stays fixed at its frequency while each modulation frequency generates a par of side "bands", rather spectrum lines under and above the carrier line, the distance between the carrier line and each side line equals to the modulation frequency.
Amplitudes of the side lines depend upon the modulation "depth" or index which is how much the carrier is modulated. When the index becomes >1, the "over-modulation" causes that harmonics of the modulating frequency appear.

A more complex case is FM, the frequency modulation, where Bessel functions govern the spectrum (due to the products of creating sinusoids). With FM, modulation index causes the carrier to be reduced and then regrown according to the Bessel-function pattern.

Mathematic analysis is not so attractive and instructive as the simple experiments

 

[chuckey]

"and the carrier signal can be represented by c(t) = Ac cos(2πfc + φ),
Now Modulated signal = m(t) * c(t) ''"
your "now modulated signal" is a Cos * Cos product. This can be substituted by fc-fb and a fc+fb product by the means of trig identities :-http://www.sosmath.com/trig/Trig5/trig5/trig5.html
These show that the highest frequency is fc+fb and the lowest fc-fb.
Must go and iron my anorak now
Frank