Mitchell, T. J. (2010) An exploration of evolutionary computation ...

Figure 1.2: FM spectrum plots with increasing modulation index, adapted from Chowning (1973)
As illustrated in figure 1.2, the bandwidth of the modulated signal varies in proportion to
the modulation index and modulator frequency. Notice, however, that there is a complex
relationship between partial amplitudes and the modulation index I (the envelope of the
spectrum is shaped by a non-linear function). The amplitudes of the partials are governed
by Bessel functions of the first kind and order , denoted , where the argument to the
Bessel function is the modulation index. The Bessel functions are described by the
following equation:
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