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Re: swept sine accuracy-- Further question

Dear Dr. Beauchamp and Dear All,

Thank you very much for the valuable information. Although I am a layperson in the field of signal processing, I need some guidelines for my auditory experiments. Vanderkooy's guideline happened to be the same as my personal guideline -- it can be derived easily from a simple dimensional analysis. Poletti's guideline seems basically the same.

Now my problem comes. I may be wrong -- I am a layperson -- but we need both the frequency resolution and the temporal resolution, and we can never avoid the uncertainty between time and frequency. If the frequency resolution is at sqrt(sweep rate) Hz, then the temporal resolution should be at 1/sqrt(sweep rate) s. Thus, longer swept tones should not be always better even when we had an extremely fast computer. It seems like that we have to find an optimum sweep rate depending on our purpose. Considering the frequency resolution and the temporal resolution of the auditory system, I often utilize a sweep rate around 10,000 Hz/s. (We would be in a trouble if we used a rate of 1,000,000 Hz/s or 100 Hz/s.)

I would be glad if someone -- either in the list or in the literature -- could formulate, or correct, what I am thinking.

Best regards,
Yoshitaka Nakajima

----- Original Message ----- From: "James W. Beauchamp" <jwbeauch@xxxxxxxxxxxxxxxxxxxxxx>
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
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,