FM sidebands that fall below 0 Hz reflect into the positive spectrum with a phase inversion

When the lower sidebands (c − nm) fall below 0 Hz, they fold back (‘reflect’) around 0 Hz into the positive frequency domain, but with an inverted phase. These reflected components then add algebraically to the existing positive-frequency sidebands: components with the same phase add constructively, components with opposite phase cancel partially. This reflection mechanism is what makes FM spectra so surprisingly complex and rich even with just two oscillators. It explains why a 1:1 carrier-to-modulator ratio (c=m) produces a full harmonic series from a single modulation pair: reflected lower sidebands fill in the harmonic slots below the carrier. Without accounting for reflection, predicted spectra differ dramatically from what is actually heard.

Examples

c=100Hz, m=100Hz, I=4: the sideband at c−2m=−100Hz reflects to +100Hz (the carrier frequency) and adds constructively to J0, boosting the carrier component. The sideband at c−3m=−200Hz reflects to +200Hz and adds with opposite sign to J1, modifying the second harmonic.

Assessment

For c=100Hz, m=100Hz, I=4, predict whether the energy at 200Hz increases or decreases relative to the unmodulated case, and explain the role of phase in that result.