Modulation index
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The modulation index (β or m f) of a frequency modulated or phase modulated signal is defined as the ratio of the frequency deviation (Δf or σ) to the modulating signal frequency (fm), i.e.,
With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases, but the spacing between spectra stays the same.
If the frequency deviation is held constant and the modulation index increased, the bandwidth stays roughly the same, but the spacing between spectra decreases.