AES Journal Forum

Synchronized Swept-Sine: Theory, Application, and Implementation

(Subscribe to this discussion)

Document Thumbnail

Exponential swept-sine signals are very often used to analyze nonlinear audio systems. A reexamination of this methodology shows that a synchronization procedure is necessary for the proper analysis of higher harmonics. An analytical expression of spectra of the swept-sine signal is derived and used in the deconvolution of the impulse response. Matlab code for generation of the synchronized swept-sine, deconvolution, and separation of the impulse responses is given. This report provides a discussion of some application issues and an illustrative example of harmonic analysis of current distortion of a woofer. An analysis of the higher harmonics of the current distortion of a woofer is compared using both the synchronized and the non-synchronized swept-sine signals.

JAES Volume 63 Issue 10 pp. 786-798; October 2015
Publication Date:

Click to purchase paper as a non-member or you can login as an AES member to see more options.

(Comment on this paper)

Comments on this paper

Default Avatar
Raimonds Skuruls

Comment posted November 17, 2015 @ 17:42:16 UTC (Comment permalink)

Authors are too much briefly describing the concept of the start and the final frequency of the sweep. It means that the spectrum of such sweep will have components very close to zero in bands before the start frequency and after the final frequency that will be causing division by zero in the „deconvolution” process or in another words – the deconvolution filter will have enormous high gain in mentioned bands and will bring up all noses and errors of the real measurement in that bands.

Default Avatar
Author Response
Antonin Novak

Comment posted November 19, 2015 @ 21:28:34 UTC (Comment permalink)

The spectrum of the synchronized swept-sine signal have components very close to zero in bands before the start frequency and after the final frequency. This is normal (and intuitive) for all the chirp-like signals.

The division by zero problem in the „deconvolution” process appears in the classical methods (Eq.4). In our method, the deconvolution process consists in designing the "inverse filter" directly in frequency domain in an analytical way (Eq.43, derived in Appendix A.1). The deconvolution is then made using (Eq.50) in which no division appears. Since the inverse filter X_tilde(f) is designed analytically, there are no enormous high gains in you mentioned.

You can check this out using the Matlab code from Appendix A.2.4 in which the inverse filter is defined as:
X_ = 2*sqrt(f_ax/L).*exp(-j*2*pi*f_ax*L.*(1-log(f_ax/f1)) + j*pi/4);

Note, that the vector f_ax goes from 0 to fs, so that the filter X_ is defined also outside the region <f1,f2>

Subscribe to this discussion

RSS Feed To be notified of new comments on this paper you can subscribe to this RSS feed. Forum users should login to see additional options.

Join this discussion!

If you would like to contribute to the discussion about this paper and are an AES member then you can login here:

If you are not yet an AES member and have something important to say about this paper then we urge you to join the AES today and make your voice heard. You can join online today by clicking here.

AES - Audio Engineering Society