Reassignment method: Difference between revisions

Revision as of 14:34, 21 February 2019

Revision as of 16:03, 6 March 2020

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introduced by several parties under various names, including

''method of reassignment'', ''remapping'', ''time-frequency reassignment'',

and ''modified moving-window method''.<ref name="hainsworth">{{Cite thesis |type=PhD |chapter=Chapter 3: Reassignment methods |title=Techniques for the Automated Analysis of Musical Audio |url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.9579 |last=Hainsworth |first=Stephen |year=2003 |publisher=University of Cambridge |accessdatedocket= |docketoclc= |oclcciteseerx=10.1.1.5.9579 }}</ref> In

the case of the [[spectrogram]] or the [[short-time Fourier transform]],

the method of reassignment sharpens blurry

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of any member of Cohen's class

<ref name = "improving">

{{cite journal |author1=F. Auger |author2=P. Flandrin |lastauthoramp=yes |date=May 1995 |title=Improving the readability of time-frequency and time-scale representations by the reassignment method |journal=IEEE Transactions on Signal Processing |volume=43 |issue=5 |pages=1068–1089 |publisher= |doi=10.1109/78.382394 |bibcode=1995ITSP...43.1068A |url= |accessdate= |citeseerx=10.1.1.646.794 }}

</ref>

.<ref>P. Flandrin, F. Auger, and E. Chassande-Mottin,

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== The method of reassignment ==

Pioneering work on the method of reassignment was published by Kodera, Gendrin, and de Villedary under the name of ''Modified Moving Window Method'' <ref>{{cite journal |author1=K. Kodera |author2=R. Gendrin |author3=C. de Villedary |last-author-amp=yes |date=Feb 1978 |title=Analysis of time-varying signals with small BT values |journal=IEEE Transactions on Acoustics, Speech, and Signal Processing |volume=26 |issue=1 |pages=64–76 | publisher= |doi=10.1109/TASSP.1978.1163047 |url= |accessdate=}}</ref> Their technique enhances the resolution in time and frequency of the classical Moving Window Method (equivalent to the spectrogram) by assigning to each data point a new time-frequency coordinate that better-reflects the distribution of energy in the analyzed signal.

In the classical moving window method, a time-___domain signal, <math>x(t)</math> is decomposed into a set of coefficients, <math>\epsilon( t, \omega )</math>, based on a set of elementary signals, <math>h_{\omega}(t)</math>, defined

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Independently of Kodera ''et al.'', Nelson arrived at a similar method for improving the time-frequency precision of short-time spectral data from partial derivatives of the short-time phase

spectrum.<ref name = "crossspectral">{{cite journal |author=D. J. Nelson |date=Nov 2001 |title=Cross-spectral methods for processing speech |journal=Journal of the Acoustical Society of America |volume=110 |issue=5 |pages=2575–2592 |publisher= |doi=10.1121/1.1402616 |pmid=11757947 |bibcode=2001ASAJ..110.2575N |url= |accessdate= }}</ref> It is easily shown that Nelson's ''cross spectral surfaces'' compute an approximation of the derivatives that is equivalent to the finite differences method.

Auger and Flandrin showed that the method of reassignment, proposed in the context of the spectrogram by Kodera et al., could be extended to any member of [[Cohen's class]] of time-frequency representations by generalizing the reassignment operations to