Question

How can I calculate the modulation index for a digital frequency modulated signal (2FSK, 2GFSK, 4FSK, 4GFSK)?

Answer

The general formula for the modulation index is the following:  

where H is the modulation index, M is the modulation alphabet size (e.g. M=2 for 2FSK / 2GFSK).

For 2FSK / 2GFSK modulation the symbol rate is equal to the data rate, and unlike 4FSK / 4GFSK modulation there is only one deviation. This way, the formula can be simplified to the following form:

For example, if one would like to have H = 1 modulation index, 40 kbps data rate, then the necessary deviation for 2FSK / 2GFSK modulation will be 20 kHz.

For 4FSK / 4GFSK modulation the modulation alphabet size is M = 4. In this case there is an inner and an outer deviation, and the connection between them can be described as the following:

The modulation index can be expressed with inner deviation for 4FSK / 4GFSK:

For example, if one would like to have H = 1 modulation index, 100 ksps symbol rate, then the necessary inner deviation for 4FSK / 4GFSK modulation will be 50 kHz. In this case the outer deviation will be 150 kHz.