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Analytic signal in many dimensions. (arXiv:1712.09350v1 [eess.SP])
来源于:arXiv
In this paper we extend analytic signal method to the functions in many
dimensions. First it is shown how to obtain separate phase-shifted components
and how combine them to obtain signal's envelope, instantaneous frequencies and
phases in many dimensions. Second, we show that phase-shifted components may be
obtained by positive frequency restriction of the Fourier transform defined in
the algebra of commutative elliptic hypercomplex numbers. Finally we prove that
for $d>2$ there is no corresponding Clifford-Fourier transform that allows to
recover phase-shifted components correctly. 查看全文>>