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This study discusses the second-order improperness in the
frequency-domain colored signal model. After the realvalued
and colored signal in the time-domain is transformed
into the frequency domain, the convolutive blind source
separation (BSS) methods may generate a window indexed
vector, and minimum variance distortionless response
(MVDR) beamforming may produce an array sensor
indexed vector, and the trial structured EEG data set may
provide a trial-indexed vector. These three complex-valued
vectors have such similarities: 1) despite of resulting from
the Fourier transformation, they are not indexed by the
frequency bins; 2) its real part and image part are proved to
be correlated. Hence, such a complex-valued vector is
improper, and the pseudo-autocorrelation matrix of this
improper vector exists. Moreover, if components of an
improper complex-valued vector are uncorrelated, except
the autocorrelation matrix, the pseudo-autocorrelation
matrix 首ld also be diagonal. This one more statistics
could be useful to design better the complex-valued BSS
algorithm and MVDR beamforming algorithm. 燃料电池测试仪

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