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

```Subject: Re: How one can demonstrate that microphone is a nonlinear device?
From:    ita katz  <itakatz@xxxxxxxx>
Date:    Tue, 12 Jun 2012 09:43:14 +0300
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--20cf307f33eeee38fe04c240c79e
Content-Type: text/plain; charset=ISO-8859-1

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@xxxxxxxx> 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?
>
> Any suggestions/comments/literature in this regard.
>
> Thanks,
> --
> Hafiz Malik
> Assistant Professor
> Electrical and Computer Engineering Department,
> University of Michigan - Dearborn
> Dearborn, MI 48128
> RN: 220 ELB
> Tel: (313)5935677
> Fax: (313)5836336
> http://www-personal.engin.umd.umich.edu/~hafiz
>

--20cf307f33eeee38fe04c240c79e
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">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 w=
ords 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 t=
he source of the input signal) is a linear system by itself.<br>
<br><div class=3D"gmail_quote">On Mon, Jun 11, 2012 at 9:13 PM, Hafiz Malik=
<span dir=3D"ltr">&lt;<a href=3D"mailto:hafiz.malik@xxxxxxxx" target=3D"_=
blank">hafiz.malik@xxxxxxxx</a>&gt;</span> wrote:<br><blockquote class=3D"=
gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-=
left:1ex">
Hi Every 1, <br><br>Microphone is generally modeled using a second-order no=
nlinear function, that is, y(n) =3D ax(n) + b x(n)^{2} where x(n) is the mi=
crophone input. <br><br>How can one demonstrate this non-linearity?<br><br>

Any suggestions/comments/literature in this regard. <br clear=3D"all"><br>T=
hanks,<span class=3D"HOEnZb"><font color=3D"#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: <a href=3D"tel:%28313%295935677" value=3D"+13135935677"=
target=3D"_blank">(313)5935677</a><br>Fax: <a href=3D"tel:%28313%295836336=
" value=3D"+13135836336" target=3D"_blank">(313)5836336</a><br><a href=3D"h=
ttp://www-personal.engin.umd.umich.edu/%7Ehafiz" target=3D"_blank">http://w=
ww-personal.engin.umd.umich.edu/~hafiz</a><br>

</font></span></blockquote></div><br></div>

--20cf307f33eeee38fe04c240c79e--
```

This message came from the mail archive
/var/www/postings/2012/
maintained by:
DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University