DocumentCode :
1312759
Title :
On the measure of the set of factorizable polynomial bispectra
Author :
Erdem, A. Tanju ; Tekalp, A. Murat
Author_Institution :
Dept. of Electr. Eng., Rochester Univ., NY, USA
Volume :
38
Issue :
9
fYear :
1990
fDate :
9/1/1990 12:00:00 AM
Firstpage :
1637
Lastpage :
1639
Abstract :
In a recent work (1989), the authors have shown that factorization of bispectrum is not always possible. In the present work, they show that the subset of factorizable bispectra has Lebesgue measure zero in the set of polynomial bispectra, i.e. those that are obtained from finite-support bicumulants. Hence, a polynomial bispectrum cannot almost always be exactly realized as that of the output of a linear model driven by a third-order white input. This result can be generalized to multidimensional polynomial bispectra. Although it follows that a linear model driven by a third-order white input cannot almost always realize a given bispectrum or a bicumulant sequence, the use of a linear model as an approximation in certain applications can be justified if the computed bispectrum has an index value close to unity
Keywords :
polynomials; spectral analysis; Lebesgue measure; bispectrum; factorizable polynomial bispectra; factorization; finite-support bicumulants; linear model; multidimensional polynomial bispectra; third-order white input; Acoustic signal processing; Finite impulse response filter; Geometry; Interference; Multidimensional signal processing; Multidimensional systems; Polynomials; Signal processing; Speech; Tin;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/29.60081
Filename :
60081
Link To Document :
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