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      • Calculation of the occupied bandwidth for digital frequency modulation

        dasimon | 02/48/2015 | 09:26 AM

        Question

        How can I calculate the occupied bandwidth of a digital frequency modulated signal (2FSK, 2GFSK, 4FSK, 4GFSK)?

        Answer

        The occupied bandwidth of a digital frequency modulated signal can be described with the following approximate formula:

        Untitled.png

        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:

        Untitled.png

         

        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.

         

        Let's see an example: data rate = 20 kbps, deviation = 10 kHz, modulation type: 2FSK / 2GFSK.

        The occupied bandwidth can be calculated based on the formula above:

        Untitled.png

        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.

      • Calculation of the modulation index for digital frequency modulation

        dasimon | 02/35/2015 | 10:55 AM

        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:  

        Modulation_index.png

        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:

        Modulation_index_2GFSK.png

        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:

        Outer_dev.png

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

        Modulation_index_4GFSK.png

        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.