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 Bessel 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 Bessel function as is, 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 fold back on top of other sidebands because of the increased complexity of phase cancellation and summation.

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