Assuming I have a set of frequencies $\mathbf F$, and I pick 2 frequencies $f_1$ and $f_2$ randomly from the set, generate sine waves for them, and pass the signals through a non-linear distortion process while adding them.

  • Is there any way for the harmonics or intermodulation distortion products to have a magnitude larger than the magnitude of any of the two frequencies, when calculating an FFT?
  • If yes, under what conditions, and how can I avoid that this happens?

1 Answer 1


Certainly the amplitude of a harmonic can exceed the amplitude of the fundamental, or the amplitude of an intermodulation product can exceed the amplitudes of the individual signals. But this occurs when the system is so nonlinear that it would make no sense to use it as an approximation to a linear system. Indeed, the very fact that such a nonlinear system is being used (intentionally) means that it has some properties that are useful in the application at hand.

Example: If the system is a squarer that produces output $x^2(t)$, then with $x(t) = \cos(2\pi f_c t)$, the output is entirely the second harmonic (and a DC term). Since the fundamental is entirely absent from the output, the harmonic amplitude is infinitely larger than the fundamental. If two sinusoidal inputs of frequencies $f_1$ and $f_2$ are added together before the squaring operation, then the output has second harmonics at frequencies $2f_1$ and $2f_2$, intermodulation distortion products at frequencies $f_1+f_2$ and $|f_1-f_2|$ and no fundamentals at frequencies $f_1$ and $f_2$.

Moral: Don't use a squarer and pretend it is a linear addition circuit or linear amplfier. If you are knowingly using a squarer, it is for some other useful properties (e.g. frequency doubler) of the circuit that are important to you right now.

  • 1
    $\begingroup$ thanks for your answer, if the nonlinear function is a kind of "soft limiter", would the above occur? $\endgroup$
    – b20000
    Dec 4, 2013 at 5:16
  • $\begingroup$ @b20000 Your soft limiting function can probably be described by a polynomial expansion. This may have odd and/or even powers of the signal, but it's very likely to have the fundamental too. $\endgroup$
    – Speedy
    Dec 5, 2013 at 10:22

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