I am reading modulation from this site (am a beginner). In the end, they've given this example:
I am having trouble understanding how exactly they arrived at the two modulated results for AM and FM. I have attempted to understand it, and this is my attempt (I am assuming the $x$-axis is time axis):
- Amplitude Modulation: At each time $t=t_0$, they have taken an increase factor as $k=\frac{\text{amplitude of modulating wave at } t_0}{\text{constant amplitude of carrier wave}}$. Hence, to obtain the modulated result at each instant, they've done $\text{Final displacement}=\text{Original displacement of carrier wave}\times(1+k)$. Negative amplitude of modulating wave implies decrease of carrier wave's displacement, and positive amplitude of modulating wave implies increase.
- Frequency modulation: I'd say a similar increase factor is at work here, but instead, that factor is now affecting the frequency of the carrier wave instead of its amplitude.
I am sorry if these are beginner knowledge but I don't have any good book to study from. I checked Wikipedia for these two as well. My guess for amplitude modulation's working seems reasonably close to their mathematics, especially the $y(t)=[1+m(t)]\cdot c(t)$. But, I could not understand why an integral is employed in frequency modulation. What is it supposed to do?
I hope I have a reasonably detailed and specific question here. I am looking for simple language explanations. Thank you!