How can I calculate the occupied bandwidth of a digital frequency modulated signal (2FSK, 2GFSK, 4FSK, 4GFSK)?
Carson’s Rule to determine the BW for an FSK signal:
where OBW is the occupied bandwidth.
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:
4FSK / 4GFSK modulation has inner and outer deviation parameters, the connection between them can be described as the following:
This way, the OBW for 4FSK / 4GFSK:
GFSK modulation uses a Gaussian filter on the transmitter side which smoothens the shape of the frequency pulse. This results that the changes between symbols are flatter than in case of general FSK modulation which causes that higher frequency components are supressed, i.e. the bandwidth decreases. This means that a GFSK modulated signal has always got a little narrower occupied bandwidth than an FSK modulated signal.
Example: data rate = 20 kbps, deviation = 10 kHz, modulation type: 2FSK / 2GFSK.
The occupied bandwidth can be calculated based on the formula above:
For FSK modulation this formula approximately gives the real occupied bandwidth of the signal, for GFSK modulation the bandwidth also depends on the value of the B*T factor of the Gaussian filter. Using B*T = 0.5 for 2GFSK modulation, the occupied bandwidth will be always smaller than for general 2FSK modulation. In the above example the OBW for 2FSK is ~40 kHz, while for 2GFSK (B*T = 0.5) it is ~35 kHz.
Note that it is not recommended to decrease the value of the B*T factor below 0.3 as it increases inter symbol interference.