Two Modulators cont.

Modulation indeces are defined for each component: $I_1$ is the index that charaterizes the spectrum produced by the first modulating oscillator, and $I_2$ is that of the second.

The amplitude of the $i^{th}$, $k^{th}$ sideband ($A_{i,k}$) is given by the product of the Bessel functions

$$A_{i,k} = J_i(I_1)J_k(I_2).$$

Like in the previous case of a single modulator, when $i$, $k$ is odd, the Bessel functions assume the opposite sign. For example, if $i=2$ and $k=3^{-}$ (where the negative superscript means that $k$ is subtracted), the amplitude is $A_{2, 3} = -J_2(I_1)J_3(I_2)$.

In a harmonic spectrum, the net amplitude of a component at any frequency is the combination of many sidebands, where negative frequencies ``foldover'' the 0 Hz bin (Computer Music).