We can capture frequency response, phase response and reverb in recording of impulse response. Then we can use it to simulate audio system and/or space by convolving it with dry audio signal.

Is there similar technique for measuring and simulating non-linear distortion?

I thought of measuring how the amplitude of output signal corresponds to amplitude of input signal. Then I could simulate this system by waveshaping. Will it work? Is there any better method?

  • $\begingroup$ Some non-LTI systems can be characterized by using sine sweeps as described by Farina $\endgroup$ – nispio Nov 5 '13 at 16:12

Nonlinear systems are very hard to classify and there's no unified theory like for linear systems. In general, you cannot measure/identify non-linear systems in finite time. There are some specific classes of nonlinear systems which allow for identification or at least approximation.

You already named a trivial one: The memoryless nonlinear system. In this case you can learn the nonlinear transfer function (i.e. your waveshaping function) by just looking at the map from input to output.

Any interesting real system does have memory however, and there we can start with a specific model for the system and adapt the parameters until the model output and the real output match. There are nonlinear optimization techniques that will help to find the proper set of parameters.

If you know little about the internals of the system you want to simulate, then you can use a generic model. The most popular such model is described by the Volterra series and requires that the system is expandable in a series similar to the taylor series but involving convolution terms and that this series converges quickly enough (and in the entire domain you're interested in) to be practically useful. The theory of Volterra kernels delivers the mathematical tool to find the series expansion from input/output observations without the need for non-deterministic optimization techniques.

So summing up, your best chance to really capture the behavior of a nonlinear system is to understand the system in detail and model its components. The black box approach is very difficult and only works under very specific conditions.


Modelling non-linear systems is VERY complicated since the whole concept of impulse response and transfer function doesn't apply any more. Typically it requires very detailed models of the actual non-linearity. Examples for non-linear transducer modeling are http://www.klippel.de/ and for non-linear amp/speaker modeling are http://www.line6.com


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