# Why in FSK the phase shift is allowed?

FSK modulation encodes information into the frequency of the signals. But when I checked the reference books, the formal expression for a frequency modulated signal is:

$$x_i(t) = \alpha cos(2\pi f_it + \theta_i)$$

Which means, for a binary FSK, we can consider $$x_1(t)$$ and $$x_2(t)$$ with different frequencies $$f_1$$ and $$f_2$$ (which make sense) and different phase $$\theta_1$$ and $$\theta_2$$ (which is odd to me), respectively.

(1) My first question is, why should we allow the signals have different phases? I cant see a reason for this and as far as I know, different phases result in phase discontinuity of the transmit signal.

(2) And the second question is, how this difference in phase is related to coherent and non-coherent receiver?

1. My first question is, why should we allow the signals have different phases?

Counterquestion: Why should they not be allowed? Enforcing continuous phase can make systems more complex, without any benefit.

I cant see a reason for this and as far as I know, different phases result in phase discontinuity of the transmit signal.

Depending on how you do that transition, that's not necessarily the case: you can pulse-shape $$\theta_i$$, or you can filter $$x$$.

It's less often a problem than old textbook make it out to be, to be honest.

(2) And the second question is, how this difference in phase is related to coherent and non-coherent receiver?