Invariance of the Null Distribution of the Multiple Coherence
In this paper we investigate the invariance of the null distribution of the multiple coherence (MC) to the statistics of the examined signals. We show that when the MC is computed between a group of signals x_i[n], i=1,...,K and a signal y[n], the null distribution of the MC is independent of the di...
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| Format: | Article |
| Language: | English |
| Published: |
Spolecnost pro radioelektronicke inzenyrstvi
2014-12-01
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| Series: | Radioengineering |
| Subjects: | |
| Online Access: | http://www.radioeng.cz/fulltexts/2014/14_04_1241_1247.pdf |
| _version_ | 1819141001703325696 |
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| author | R. Bortel P. Sovka |
| author_facet | R. Bortel P. Sovka |
| author_sort | R. Bortel |
| collection | DOAJ |
| description | In this paper we investigate the invariance of the null distribution of the multiple coherence (MC) to the statistics of the examined signals. We show that when the MC is computed between a group of signals x_i[n], i=1,...,K and a signal y[n], the null distribution of the MC is independent of the distribution of x_i[n] and y[n] if at a given frequency the joint distribution of the spectra of the segments of x_i[n] and y[n] is rotationally symmetric with respect to the rotation of the spectra of the segments of x_i[n] or y[n]. The significance of this result lies in the improvement of the multiple coherence analysis. Hitherto, the null distribution of the MC was known only for signals with the multivariate Gaussian distribution; therefore, an MC estimate could be evaluated for its statistical significance only in this limited case. With the results presented in this paper, it will be possible to evaluate the statistical significance of MC estimates for much wider class of signals. |
| first_indexed | 2024-12-22T11:47:31Z |
| format | Article |
| id | doaj.art-8052ada2b0bb4982a7a2dccc9366316e |
| institution | Directory Open Access Journal |
| issn | 1210-2512 |
| language | English |
| last_indexed | 2024-12-22T11:47:31Z |
| publishDate | 2014-12-01 |
| publisher | Spolecnost pro radioelektronicke inzenyrstvi |
| record_format | Article |
| series | Radioengineering |
| spelling | doaj.art-8052ada2b0bb4982a7a2dccc9366316e2022-12-21T18:27:06ZengSpolecnost pro radioelektronicke inzenyrstviRadioengineering1210-25122014-12-0123412411247Invariance of the Null Distribution of the Multiple CoherenceR. BortelP. SovkaIn this paper we investigate the invariance of the null distribution of the multiple coherence (MC) to the statistics of the examined signals. We show that when the MC is computed between a group of signals x_i[n], i=1,...,K and a signal y[n], the null distribution of the MC is independent of the distribution of x_i[n] and y[n] if at a given frequency the joint distribution of the spectra of the segments of x_i[n] and y[n] is rotationally symmetric with respect to the rotation of the spectra of the segments of x_i[n] or y[n]. The significance of this result lies in the improvement of the multiple coherence analysis. Hitherto, the null distribution of the MC was known only for signals with the multivariate Gaussian distribution; therefore, an MC estimate could be evaluated for its statistical significance only in this limited case. With the results presented in this paper, it will be possible to evaluate the statistical significance of MC estimates for much wider class of signals.www.radioeng.cz/fulltexts/2014/14_04_1241_1247.pdfMultiple coherencenull distributioninvariance |
| spellingShingle | R. Bortel P. Sovka Invariance of the Null Distribution of the Multiple Coherence Radioengineering Multiple coherence null distribution invariance |
| title | Invariance of the Null Distribution of the Multiple Coherence |
| title_full | Invariance of the Null Distribution of the Multiple Coherence |
| title_fullStr | Invariance of the Null Distribution of the Multiple Coherence |
| title_full_unstemmed | Invariance of the Null Distribution of the Multiple Coherence |
| title_short | Invariance of the Null Distribution of the Multiple Coherence |
| title_sort | invariance of the null distribution of the multiple coherence |
| topic | Multiple coherence null distribution invariance |
| url | http://www.radioeng.cz/fulltexts/2014/14_04_1241_1247.pdf |
| work_keys_str_mv | AT rbortel invarianceofthenulldistributionofthemultiplecoherence AT psovka invarianceofthenulldistributionofthemultiplecoherence |