# Frequency Shift Key Modulation: how are the carrier frequencies chosen

• Master1022
In summary: If the two frequencies are too far apart, then signals at the wrong frequency will cause undesired interference.
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
Master1022 said:
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
berkeman said:
The carrier frequency is generally much higher than the modulation bandwidth.
Understood

berkeman said:
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?

Master1022 said:
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

Master1022
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.

berkeman
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.

## 1. How are the carrier frequencies chosen in Frequency Shift Key Modulation?

In Frequency Shift Key Modulation, the carrier frequencies are chosen based on the desired bandwidth and the frequency range of the signal being transmitted. The carrier frequencies are typically chosen to be within the bandwidth of the transmitted signal to ensure efficient transmission and minimal interference.

## 2. What factors influence the selection of carrier frequencies in Frequency Shift Key Modulation?

The selection of carrier frequencies in Frequency Shift Key Modulation is influenced by factors such as the available frequency spectrum, the modulation scheme being used, and the desired signal-to-noise ratio. Other factors such as regulatory restrictions and interference from other signals may also impact the choice of carrier frequencies.

## 3. Can the carrier frequencies be changed during transmission in Frequency Shift Key Modulation?

Yes, the carrier frequencies can be changed during transmission in Frequency Shift Key Modulation. This technique, known as frequency hopping, is often used to improve the security and reliability of the transmission by constantly changing the carrier frequencies.

## 4. How do the carrier frequencies affect the performance of Frequency Shift Key Modulation?

The carrier frequencies play a crucial role in the performance of Frequency Shift Key Modulation. The choice of carrier frequencies can impact the signal-to-noise ratio, the bandwidth efficiency, and the ability to detect and correct errors. Therefore, careful selection of carrier frequencies is essential for optimal performance.

## 5. Are there any limitations to the selection of carrier frequencies in Frequency Shift Key Modulation?

Yes, there are some limitations to the selection of carrier frequencies in Frequency Shift Key Modulation. These include regulatory restrictions on the use of certain frequency bands, interference from other signals, and the need to maintain a certain signal-to-noise ratio for reliable transmission. Additionally, the available frequency spectrum may also limit the choice of carrier frequencies.

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