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On the positive definiteness of polarity coincidence correlation coefficient matrix
Haddadi, F ; Sharif University of Technology | 2008
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- Type of Document: Article
- DOI: 10.1109/LSP.2007.911193
- Publisher: 2008
- Abstract:
- Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. (Devlin, 1975) claimed that element-wise PCC is not guaranteed to be PSD in dimensions p > 3 for real signals. However, no justification or proof was available on this issue. In this letter, it is proved that for real signals with p ≤ 3 and for complex signals with p ≤ 2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates. © 2007 IEEE
- Keywords:
- Complex signal ; Correlation coefficient ; Element by elements ; Element-wise covariance estimate ; Higher dimensions ; Polarity coincidence ; Polarity coincidence correlator ; Positive definiteness ; Positive semi-definite ; Real signals ; Power spectral density ; Pulse shaping circuits ; Covariance matrix
- Source: IEEE Signal Processing Letters ; Volume 15 , January , 2008 , Pages 73-76 ; 10709908 (ISSN)
- URL: https://ieeexplore.ieee.org/abstract/document/4418393