# Re: How one can demonstrate that microphone is a nonlinear device? (Harvey Holmes )

```Subject: Re: How one can demonstrate that microphone is a nonlinear device?
From:    Harvey Holmes  <H.Holmes@xxxxxxxx>
Date:    Tue, 12 Jun 2012 23:36:01 +1000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

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<body>
The standard way to analyze instantaneous nonlinearities is to do a
distortion product analysis.&nbsp; <br><br>
If the nonlinearity is only slight (e.g. well below clipping), the input
signal is usually either a sine wave A*cos(w_1*t) or a combination of two
sine waves A*cos(w_1*t) +B*cos(w_2*t+phi), and the output is analyzed for
components not at these frequencies (in particular at n*w_1, n*w_2,<br>
m*w_1+n*w_2 or m*w_1-n*w_2, where m and n are integers).&nbsp; The
results can give a lot of information about the nature of the
nonlinearity.<br><br>
A basic reference (old) is
<a href="http://www.hpmemory.org/an/pdf/an_150-11.pdf" eudora="autourl">
http://www.hpmemory.org/an/pdf/an_150-11.pdf</a>.<br><br>
<x-tab>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</x-tab>Harvey<br>
<br>
At 16:43 12-06-12, ita katz wrote:<br><br>
<blockquote type=cite class=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><br>
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>

<dl>
<dd>Hi Every 1, <br><br>

<dd>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>

<dd>How can one demonstrate this non-linearity?<br><br>

<dd>Any suggestions/comments/literature in this regard. <br><br>

<dd>Thanks,<font color="#888888"><br>

<dd>-- <br>

<dd>Hafiz Malik<br>

<dd>Assistant Professor<br>

<dd>Electrical and Computer Engineering Department,<br>

<dd>University of Michigan - Dearborn<br>

<dd>Dearborn, MI 48128<br>

<dd>RN: 220 ELB<br>

<dd>Tel: <a href="tel:%28313%295935677">(313)5935677</a><br>

<dd>Fax: <a href="tel:%28313%295836336">(313)5836336</a><br>

<dd><a href="http://www-personal.engin.umd.umich.edu/%7Ehafiz">
http://www-personal.engin.umd.umich.edu/~hafiz</a><br>
</font><br>

</dl></blockquote></body>
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