# Re: How one can demonstrate that microphone is a nonlinear device?

Title: Re: How one can demonstrate that microphone is a nonlinear
It is much easier and more sensitive to analyze for distortion tones than to look for a nonlinear level response.

For example, put in a sinusoid of frequency f and look for a 2f component.  However, since the speaker that you use to make the sound might be nonlinear, that won't prove that the mic is nonlinear.

It's better to make sinusoids from two speakers, and let the sounds combine in air, and look for combination tones in the microphone signal.  Use frequencies f1 and f2, and look for frequencies f1-f2 and f1+f2.  If you find them (using Fourier analysis on the received signal), they can only be from the microphone, if the speakers aren't so close together as to cause distortion in each other.

This still won't prove that the quadratic equation is a great model of the microphone, just that its nonlinearity has a quadratic component.  Next, run the experiment across a wide range of levels and quantify the combination tones, and see over what range of levels the equation provides a good fit without changing the "b" coefficient.

Dick

At 9:43 AM +0300 6/12/12, ita katz wrote:
Generally for a linear system, if you apply a gain to the input you expect to get the output amplified with the same gain. In other words if for input x the output is y, then in a linear system for input g*x the output is g*y, for every choice of g. So one option is to play the same sound at various levels, record it with the mic, and analyze the recorded signal to see if the above rule holds. Of course you have to make sure, as much as possible, that every other part of the recording chain (including the source of the input signal) is a linear system by itself.
On Mon, Jun 11, 2012 at 9:13 PM, Hafiz Malik <hafiz.malik@xxxxxxxxx> wrote:
Hi Every 1,

Microphone is generally modeled using a second-order nonlinear function, that is, y(n) = ax(n) + b x(n)^{2} where x(n) is the microphone input.

How can one demonstrate this non-linearity?

Thanks,
--
Hafiz Malik
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University of Michigan - Dearborn
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