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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 Müllerand Paulo Massarani, "Transfer-Function Measurement with
Sweeps", JAES 49 (6), 443-471, June, 2001.

Thanks again,