Abstract:
:The experimental identification of a non-linear biologic transducer is often approached via consideration of its response to a stochastic test ensemble, such as Gaussian white noise (Marmarelis and Marmarelis 1978). In this approach, the input-output relationship a deterministic transducer is described by an orthogonal series of functionals. Laboratory implementation of such procedures requires the use of a particular test signal drawn from the idealized stochastic ensemble; the statistics of the particular test signal necessarily deviate from the statistics of the ensemble. The notion of a fractal dimension (specifically the capacity dimension) is a means to characterize a complex time series. It characterizes one aspect of the difference between a specific example of a test signal and the test ensemble from which it is drawn: the fractal dimension of ideal Gaussian white noise is infinite, while the fractal dimension of a particular test signal is finite. This paper shows that the fractal dimension of a test signal is a key descriptor of its departure from ideality: the fractal dimension of the test signal bounds the number of terms that can reliably be identified in the orthogonal functional series of an unknown transducer.
journal_name
Biol Cybernjournal_title
Biological cyberneticsauthors
Victor JDdoi
10.1007/BF00354987subject
Has Abstractpub_date
1987-01-01 00:00:00pages
421-6issue
6eissn
0340-1200issn
1432-0770journal_volume
57pub_type
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journal_title:Biological cybernetics
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journal_title:Biological cybernetics
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journal_title:Biological cybernetics
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pub_type: 杂志文章,评审
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journal_title:Biological cybernetics
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journal_title:Biological cybernetics
pub_type: 杂志文章
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journal_title:Biological cybernetics
pub_type: 杂志文章
doi:10.1007/BF00203232
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journal_title:Biological cybernetics
pub_type: 杂志文章
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pub_type: 杂志文章,评审
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journal_title:Biological cybernetics
pub_type: 杂志文章
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更新日期:2012-07-01 00:00:00
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journal_title:Biological cybernetics
pub_type: 杂志文章
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更新日期:2013-12-01 00:00:00
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journal_title:Biological cybernetics
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pub_type: 杂志文章
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更新日期:2010-09-01 00:00:00
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journal_title:Biological cybernetics
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doi:10.1007/s00422-011-0465-3
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journal_title:Biological cybernetics
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journal_title:Biological cybernetics
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journal_title:Biological cybernetics
pub_type: 杂志文章
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journal_title:Biological cybernetics
pub_type: 杂志文章
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更新日期:2014-04-01 00:00:00
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journal_title:Biological cybernetics
pub_type: 杂志文章
doi:10.1007/BF00202449
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journal_title:Biological cybernetics
pub_type: 杂志文章
doi:10.1007/s00422-009-0338-1
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journal_title:Biological cybernetics
pub_type: 杂志文章
doi:10.1007/s004220000169
更新日期:2000-09-01 00:00:00
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journal_title:Biological cybernetics
pub_type: 杂志文章
doi:10.1007/BF00361040
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