The FM modulation index I = d/m is the ratio of peak frequency deviation to modulating frequency

In FM synthesis, three parameters define a frequency-modulated signal: c (carrier frequency), m (modulating frequency), and d (peak frequency deviation). The modulation index I is defined as I = d/m. When I = 0, there is no modulation and only the carrier frequency is present. As I increases above 0, sideband frequencies appear above and below the carrier at intervals of the modulating frequency, and energy is progressively ‘stolen’ from the carrier and redistributed to sidebands. This single parameter is the primary control for spectral brightness and bandwidth in FM synthesis. A common point of confusion is between deviation (d, in Hz) and index (I, dimensionless): synthesizers often expose one or the other, but it is the ratio I = d/m that determines spectral content, not d alone.

Examples

For a carrier at 440 Hz and modulator at 440 Hz: I=1 gives a modest spread; I=5 gives a rich, bright spectrum with many audible sidebands. Halving the modulator to 220 Hz while keeping d the same doubles I and doubles the spectral richness.

Assessment

Given c = 500 Hz, m = 200 Hz, d = 600 Hz, calculate I. Then predict whether doubling m while keeping d constant will increase or decrease spectral bandwidth.