# Re: How one can demonstrate that microphone is a nonlinear device? ("Richard F. Lyon" )

```Subject: Re: How one can demonstrate that microphone is a nonlinear device?
From:    "Richard F. Lyon"  <DickLyon@xxxxxxxx>
Date:    Tue, 12 Jun 2012 07:51:17 -0700
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

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<div>It is much easier and more sensitive to analyze for distortion
tones than to look for a nonlinear level response.</div>
<div><br></div>
<div>For example, put in a sinusoid of frequency f and look for a 2f
component.&nbsp; However, since the speaker that you use to make the
sound might be nonlinear, that won't prove that the mic is
nonlinear.</div>
<div><br></div>
<div>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.&nbsp; Use frequencies f1 and f2, and look for
frequencies f1-f2 and f1+f2.&nbsp; 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.</div>
<div><br></div>
<div>This still won't prove that the quadratic equation is a great
model of the microphone, just that its nonlinearity has a quadratic
component.&nbsp; 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 &quot;b&quot;
coefficient.</div>
<div><br></div>
<div>Dick</div>
<div><br></div>
<div><br></div>
<div>At 9:43 AM +0300 6/12/12, ita katz wrote:</div>
<blockquote type="cite" cite>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.<br>
</blockquote>
<blockquote type="cite" cite>On Mon, Jun 11, 2012 at 9:13 PM, Hafiz
Malik &lt;<a
href="mailto:hafiz.malik@xxxxxxxx">hafiz.malik@xxxxxxxx</a>&gt;
wrote:<br>
<blockquote>Hi Every 1,<br>
<br>
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.<br>
<br>
How can one demonstrate this non-linearity?<br>
<br>
<br>
Thanks,<font color="#888888"><br>
--<br>
Hafiz Malik<br>
Assistant Professor<br>
Electrical and Computer Engineering Department,<br>
University of Michigan - Dearborn<br>
Dearborn, MI 48128<br>
RN: 220 ELB<br>
Tel:</font> <a href="tel:%28313%295935677"><font
color="#888888">(313)5935677</font></a><font color="#888888"><br>
Fax:</font> <a href="tel:%28313%295836336"><font
color="#888888">(313)5836336</font></a><font color="#888888"><br>
</font><a
href="http://www-personal.engin.umd.umich.edu/%7Ehafiz"><font
color="#888888">http://www-personal.engin.umd.umich.edu/~hafiz</font></a
></blockquote>
</blockquote>
<div><br></div>
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