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Many systems have milder nonlinearities than abrupt clipping, and are typically described by the order of the equation that relates the instantaneous output to input. A perfectly linear system with input X and gain A would produce output Y as:
Y = AX
A system with nonlinearities would have the form:
Y = AX + BX^2 + CX^3 + DX^4 + ...
In a two-tone intermodulation test, the 2nd order term B will cause intermodulation components to appear as an f2 - f1 difference tone. This is often referred to as the "quadratic" difference tone, as in the old "quadratic formula" for solving equations with squared terms. The 3rd order term C will result in a "cubic" difference tone at 2f1 - f2. By studying the locations and strengths of the distortion products, it is possible to gain insight about the nature of the system.
Intermodulation distortion is typically a problem when you are generating two tones from the same speaker or other source at high sound levels. Since any source is nonlinear at high levels, the sound output will include not only the two tones you desire (plus harmonic distortion products from each), but also intermodulation distortion products at inharmonic sum and difference frequencies.
It is particularly important to reduce intermodulation in loudspeaker and audio amplifier designs, since inharmonic distortion is subjectively much more objectionable to the ear than harmonic distortion. It is easily detected because it adds new tone frequencies that were not present in the original signal, and are thus not masked by harmonics of voices or instruments in the program material.
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