Introduction to Computer Music: Volume One

6. Principles of Audio-rate Frequency Modulation | page 9

Here are two examples of the spectra produced for fixed values of I, computed by simply looking at the vertical example lines above. The first value of I is relatively low, so only a few sidebands are audible.

The second example shows a higher value of I, which also includes some negative strengths.

In general, as I increases, we can infer that more and more frequencies become audible. This can be a problem for digital synthesis, where the upper sidebands may reach the Nyquist frequency (see digital audio) and alias. FM is not band-limited. For this reason, most digital synthesis will have a limit on the maximum value of I.

What happens to those mysterious lower sidebands that reflect at their absolute value 180 degrees out of phase? If they are even numbered orders, take their order's Bessel function above and invert it (multiply the Bessle value by -1). If its strength would normally be in the positive domain, it will be of equal value in the negative domain. If they are odd numbered-orders, read the Besse function as, because both the reflected sideband and the odd-numbered lower partial sum two negatives to be a positive. This adds greatly to the interest of a dynamically changing harmonic spectrum where sidebands are likely to foldback on top of other sidebands because of the increased complexity of phase cancellation and summation.