Frequency Shift Key Modulation: how are the carrier frequencies chosen

[Master1022]

TL;DR Summary

How are the two carrier frequencies for FSK modulation chosen?

Question:
For frequency shift key modulation in the binary case, how are the two carrier frequencies chosen?

From online reading, I have seen that the carriers are chosen to be different but also with the goal of minimising bandwidth and without any overlaps of the spectra, etc.

However, I have been told by a tutor that we ought to choose one carrier frequency and then multiply that value by one of the amplitudes of the wave to get the other carrier. However, I have looked on the internet (where I cannot find much clear information about this) and cannot find any source to support this statement. This suggestion runs into issues when there is a 0 amplitude (perhaps an offset would fix that) and a -1 amplitude, the latter of which leads to a case where the two carriers aren't distinct and the frequency spectra would overlap?
For example, if we had a pulse signal that was +1, -1, +1, -1, +1, -1, ... and we wanted to modulate it onto a cosine wave then, according to this suggestion, the points where the pulse changed levels would not lead to any difference in the cosine wave as $cos(\omega_c t) = cos(-\omega_c t)$. Choosing two distinct carrier frequencies seems to make more sense to me in such a scenario.

I would appreciate any guidance and/or clarification regarding this topic.

For context, I have only been exposed to these concepts at an introductory level (i.e. undergraduate)

Thanks.

 

[berkeman]

Summary:: How are the two carrier frequencies for FSK modulation chosen?

For example, if we had a pulse signal that was +1, -1, +1, -1, +1, -1, ... and we wanted to modulate it onto a cosine wave then, according to this suggestion, the points where the pulse changed levels would not lead to any difference in the cosine wave.

The carrier frequency is generally much higher than the modulation bandwidth. You will have a number of cycles of each frequency to indicate the 0/1 BFSK encoding. Does that help?

 

[Master1022]

The carrier frequency is generally much higher than the modulation bandwidth.

Understood

You will have a number of cycles of each frequency to indicate the 0/1 BFSK encoding. Does that help?

Are the carrier frequencies usually chosen irrespective of the different levels. So if we had levels 0, 1, 2, 3 (I realize this is no longer binary) then is it correct to say that the carrier frequencies won't necessarily be chosen in such a way as to make them all multiples of one another in that same ratio?

 

[berkeman]

UnderstoodAre the carrier frequencies usually chosen irrespective of the different levels. So if we had levels 0, 1, 2, 3 (I realize this is no longer binary) then is it correct to say that the carrier frequencies won't necessarily be chosen in such a way as to make them all multiples of one another in that same ratio?

I don't think you'd ever want the FSK frequencies to be multiples of each other, for orthogonality reasons. But modulation theory is an amazingly broad subject, so who knows.

I think you will enjoy reading through this link and its reference links. This is a more advanced version of modulation that should hopefully address some of the good questions you are asking yourself:

https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

 

[Averagesupernova]

Any FSK I've had any experience with simply shifts back and forth between two frequencies. This width of this signal (amount shifted) will increase as the bit rate increases. Great care is taken to shape the data signal so as to not make other frequencies than intended. Study up on AM and FM and you will understand.

 

[Baluncore]

Strictly speaking there is only one carrier, that shifts between two frequencies.

Where FSK is passed over a voice channel, which is usually the case, the frequency difference is limited by the bandwidth of the equipment used.