Name
Abstract | ||
|---|---|---|
Abstract—An important characteristic of a complex random variable is the so-called circularity property or lack of it. We study the properties of the degree of circularity based on second-order moments, called circularity quotient, that is shown to possess an intuitive geometrical interpretation: the modulus and phase of its principal square-root are equal to the eccentricity and angle of orientation of the ellipse defined by the covariance matrix of the real and imaginary part of . Hence, when the eccentricity approaches the minimum zero (ellipse is a circle), the circularity quotient vanishes; when the eccentricity approaches the maximum one, the circularity quotient lies on the unit complex circle. Con- nection with the correlation coefficient is established and bounds on,given the circularity quotient (and vice versa) are derived. A generalized likelihood ratio test (GLRT) of circularity assuming complex normal sample is shown to be a function of the modulus of the circularity quotient with asymptotic distribution. Index Terms—Circularity coefficient, complex random variable, correlation coefficient, eccentricity, EVD, noncircular random variable. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/LSP.2008.2005050 | IEEE Signal Process. Lett. |
Keywords | Field | DocType |
correlation methods,covariance matrices,geometry,random processes,asymptotic chi2 2 distribution,circularity property,circularity quotient,complex random variable,correlation coefficient,covariance matrix,eccentricity approach,generalized likelihood ratio test,intuitive geometrical interpretation,principal square-root,second-order moment,Circularity coefficient,EVD,complex random variable,correlation coefficient,eccentricity,noncircular random variable | Correlation coefficient,Random variable,Likelihood-ratio test,Eccentricity (behavior),Mathematical analysis,Quotient,Stochastic process,Covariance matrix,Ellipse,Mathematics | Journal |
Volume | ISSN | Citations |
15 | 1070-9908 | 28 |
PageRank | References | Authors |
1.38 | 9 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Esa Ollila | 1 | 351 | 33.51 |