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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?

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  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?

Not at all. What the transmitter does says nothing about how the receiver is constructed!

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  • $\begingroup$ Thanks. So, according to my understanding, if we want the same phase for all signals at the transmitter, the oscillator would be more complex. It is fine but I cannot remember we have such a discussion when we use ASK. In ASK, we assume all signals have the same phase. And regarding the second question, I could not quite get what you meant. I would appreciate if you could refer me to a material (book or webpage) that discusses coherent and non-coherent receivers. $\endgroup$
    – RusselJ
    Commented Feb 9, 2021 at 11:38
  • $\begingroup$ well, it really depends. You will not often these days find an actual oscillator generating the tones for FSK; it's all software, typically, or dedicated digital hardware. Neither in ASK nor in FSK you make any assumptions on the phase! $\endgroup$
    – Marcus Müller
    Commented Feb 9, 2021 at 12:17
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Depending on the length of each symbol, a different starting phase for a symbol might be required to match the ending phase of the previous symbol in order not to create discontinuities.

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