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*To*: AUDITORY@xxxxxxxxxxxxxxx*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*Approved-by*: H.Holmes@xxxxxxxx*Comments*: To: ita katz <itakatz@xxxxxxxxx>, Hafiz Malik <hafiz.malik@xxxxxxxxx>*Delivery-date*: Tue Jun 12 11:36:01 2012*In-reply-to*: <12797_1339492403_4FD70833_12797_69_1_CANdd18XO1Az5M-3rW3iT yi9Pe96SNLZoUuS-JswAhkt2q9sARg@xxxxxxxxxxxxxx>*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*References*: <8393_1339446633_4FD65569_8393_161_1_CAHonqORSxNYbFLkEtrxS6-_MkLd=Adj+Bt-Ji2uXsyMDfZiySA@xxxxxxxxxxxxxx> <12797_1339492403_4FD70833_12797_69_1_CANdd18XO1Az5M-3rW3iTyi9Pe96SNLZoUuS-JswAhkt2q9sARg@xxxxxxxxxxxxxx>*Reply-to*: Harvey Holmes <H.Holmes@xxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

The standard way to analyze instantaneous nonlinearities is to do a distortion product analysis.

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,

m*w_1+n*w_2 or m*w_1-n*w_2, where m and n are integers). The results can give a lot of information about the nature of the nonlinearity.

A basic reference (old) is http://www.hpmemory.org/an/pdf/an_150-11.pdf.

At 16:43 12-06-12, 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?

- 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

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