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In general, there is an infinite number of equally valid decompositions for a multi-component signal. The separability property must be considered in the context of the desired decomposition. For example, in the analysis of a speech signal, an analysis window that is long relative to the time between glottal pulses is sufficient to separate harmonics, but the individual glottal pulses will be smeared, because many pulses are covered by each window (that is, the individual pulses are not separable, in time, by the chosen analysis window). An analysis window that is much shorter than the time between glottal pulses may resolve the glottal pulses, because no window spans more than one pulse, but the harmonic frequencies are smeared together, because the main lobe of the analysis window spectrum is wider than the spacing between the harmonics (that is, the harmonics are not separable, in frequency, by the chosen analysis window).
== In biology ==
Gardner and Magnasco (2006) argues that the [[auditory nerve]]s may use a form of the reassignment method to process sounds. These nerves are known for preserving timing (phase) information better than they do for magnitudes. The authors come up with a variation of reassignment with complex values (i.e. both phase and magnitude) and show that it produces sparse outputs like auditory nerves do. By running this reassignment with windows of different bandwidths (see discussion in the section above), a "consensus" that captures multiple kinds of signals is found, again like the auditory system. They argue that the algorithm is simple enough for neurons to implement.<ref name=Gar06>{{cite journal |last1=Gardner |first1=Timothy J. |last2=Magnasco |first2=Marcelo O. |title=Sparse time-frequency representations |journal=Proceedings of the National Academy of Sciences |date=18 April 2006 |volume=103 |issue=16 |pages=6094–6099 |doi=10.1073/pnas.0601707103}}</ref>
== References ==
{{realist}}
== Further reading ==
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* [http://www.cerlsoundgroup.org/Loris/ Loris - Open-source software for sound modeling and morphing]
* [http://musicalgorithms.ewu.edu/algorithms/roughness.html SRA - A web-based research tool for spectral and roughness analysis of sound signals] {{Webarchive|url=https://web.archive.org/web/20191118182132/http://musicalgorithms.ewu.edu/algorithms/Roughness.html |date=2019-11-18 }} (supported by a Northwest Academic Computing Consortium grant to J. Middleton, Eastern Washington University)
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{{Compression methods}}
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