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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: swept sine accuracy-- Further question*From*: Nakajima <nakajima@xxxxxxxxxxxxxxxxxxxxx>*Date*: Wed, 11 Mar 2009 00:18:15 +0900*Approved-by*: nakajima@xxxxxxxxxxxxxxxxxxxxx*Delivery-date*: Tue Mar 10 12:09:03 2009*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*: <20090309235211.76E658FE8@xxxxxxxxxxxxxxxxxxxxxxx>*Reply-to*: Nakajima <nakajima@xxxxxxxxxxxxxxxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Dear Dr. Beauchamp and Dear All,

Best regards, Yoshitaka Nakajima

To: <AUDITORY@xxxxxxxxxxxxxxx> Sent: Sunday, March 08, 2009 3:52 AM Subject: Re: swept sine accuracy

Thanks very much to everyone who responded to my question. This was actually for an undergraduate signal processing course I've been teaching where we have just encountered frequency response of linear time-invariant systems. The text discusses transfer functions and implies that you need really long duration sine waves of constant frequency to measure frequency response and doesn't consider practical methods like the swept sine method. I was explaining this method to the class and mentioned that you can't sweep too fast, but I didn't have a simple formula that captured how fast you could sweep based on required resolution. I was not considering the possibilities of noise or nonlinearity. Two people offered formulas that I think would be useful: 1) frequency resolution (Hz) = sqrt(sweep rate (Hz/s)) This is based on John Vanderkooy, "Another Approach to Time-Delay Spectrometry," JAES, 1986 July/Aug. (thanks to Dan Mapes-Riordan) 2) sweep rate << 1/(pi*t^2), where t = duration of filter impulse response. This is based on M. A. Poletti, "Linearly Swept Frequency Measurements, Time-Delay Spectrometry, and the Wigner Distribution, JAES 36(6), 457-468, 1988. (thanks to Christian Ciao) Also, this paper was frequently mentioned: Swen Mテシllerand Paulo Massarani, "Transfer-Function Measurement with Sweeps", JAES 49 (6), 443-471, June, 2001. Thanks again, Jim

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