# Modulate a digital message using FSK/PSK combination

I am beginner and I want to modulate the digital signal: 101101 based on the combination: frequency/phase (2 frequencies/2 phases). For that, I set the 4 possible combinations: f1ph1, f1ph2, f2ph1, and f2ph2 where: f1 represents 1 cycle, f2 represents two cycles, ph1 represents 180, and ph2 represents 0. Now, I wonder how to link between the four combinations and 00, 01, 10, and 11 in order to be able to graphically represent the digital signal.

• It won't work. FSK and PSK aren't only non-orthogonal, they're so entangled as to be almost the same thing in some ways. You can't decode them independently. Get your two bits per symbol by using 4FSK or QPSK. Commented Mar 11 at 22:56

FSK modulates the frequency of a signal, PSK the phase. Frequency is the derivative of phase with respect to time, so you can't freely modulate both at the same time.

So, I'm agreeing with hobbs, but you can constrain your FSK transmitter artificially for it to make sense to speak of different phases at different frequencies whenever you change the frequency. However, it would be a pure waste of spectrum and complexity:

To be able to get the phase information from the received signal, you need a coherent receiver anyways (due to your frequency shift, you couldn't do differential PSK, because that literally is an FSK in disguise).

But if you have a coherent receiver, you can just as well do QPSK, in the same bandwidth that you can do BPSK. That way, you would use way less bandwidth for the same data.

In addition, to be able to track phase across frequency changes, you need to keep your phase coherent over longer times – so you need to keep the same phase control loops as you would for QPSK!

Technically, FSK receivers are not anymore inherently easier to build than PSK receivers; the same is true for transmission. On the contrary, in software and in CMOS electronics in a microchip, there's good reasons to aim for complex baseband or other equivalent signal representations of a single digitized signal. So, FSK is just something that you find pretty rarely in modern systems – it's spectrally inefficient and hard to build.

Short answer is "No."

"Frequency modulation and phase modulation are the same thing." is an exact quote from a time that I now wish I'd spent more time knowing "Grau, teurer Freund, ist alle Theorie und grün des Lebens goldner Baum." Marcus Muller Has an explanation (in English) in his answer, and maybe, for my quotation.

Here are are two sinusoids, with slightly different frequencies, 1kHz (A, blue) and 1.2kHz (B, orange):

Even though I have not introduced any phase shift, at any time, to either, clearly the phase relationship between them changes over time. The left green marker show B slightly leading A, and the right marker shows B trailing.

Without having a reference signal, perfectly sychronised with the transmitter (which would require transmitting two signals), the receiver will be unable to distinguish between a phase shift, and a frequency change.

You can't combine PSK and FSK in the same encoding scheme. Either you keep frequency fixed, and you modulate phase, or you keep phase fixed, and modulate frequency. Not both.

• I mean, you can go the MSK route and ensure your carrier phase at the end of each symbol has a defined value; and then you can choose the "start" phase of the next symbol. But that's really just reinventing OQPSK, which, as the name suggests, is a PSK modulation (though it also happens to be a specific configuration of an MSK, therefore a specialty FSK). Commented Mar 12 at 12:45