FSK and IQ modulation I am having trouble understanding the FSK modulation process. There are many ways of demodulating the FSK signal. 


What is the advantage of performing the FSK using IQ modulation? 
How to demodulate the FSK signal? 
Does the FSK signal look triangular wave or sinewave?
What is the advantage of performing the FSK using IQ modulation?



You only need one RF oscillator operating at a single frequency, instead of having 2 (or more in the case of M-ary FSK) oscillators operating at separate frequencies for each bit/symbol.
Since you only have one oscillator, you don't have to worry about discontinuities in the phase of the transmitted RF signal, like this:




Sharp discontinuities contain high frequency which widens the bandwidth of the signal. With I/Q modulation you'll have a much easier time producing a continuous-phase FSK signal (CPFSK).


  How to demodulate the FSK signal?


First lets assume we are trying to demodulate a simple FSK signal where the center frequency is $f_c$, a '1' is represented by the frequency $f_c+\Delta f$, and a '0' is represented by the frequency $f_c-\Delta f$.

Before IQ sampling, you tune your RF front end receiver to $f_c$. Then when you sample you have a baseband I/Q representation of the signal, centered around 0 Hz. The only thing to do is figure out if you have a positive frequency (+$\Delta f$) or negative frequency (-$\Delta f$). The easiest way to do that is to monitor the change in phase of the baseband IQ signal. A positive phase change corresponds to a positive frequency, and a negative phase change corresponds to a negative frequency.

So monitor the phase (the angle of $I + jQ$) and watch how it changes over one symbol period. Positive change = '1', negative change = '0'.


  Does the FSK signal look triangular wave or sinewave?


If you're talking about the RF signal, it looks like a sinewave of varying frequency.

If you're talking about baseband IQ signal, it also looks sinusoidal, but with a bunch of phase shifts, like this (blue = I, orange = Q):



In this particular example, a '1' corresponds to a phase change of $+\pi/2$, and a '0' corresponds to a phase change of $-\pi/2$.