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• W2034935457 abstract "An extension of the notion of the analytical signal to multidimensional signals is presented. The real and imaginary parts of this signal are a linear combination of the original signal and of its complete and partial Hilbert transforms. Its Fourier image exists only in one orthant of the multidimensional frequency space. The orthant is a half-axis in one dimension, a quadrant in two dimensions, an octant in three dimensions, etc. A multidimensional complex signal makes it possible to introduce the definitions of instantaneous amplitude, instantaneous phase, and partial instantaneous complex frequencies (partial derivatives of the instantaneous phase) and to formulate a modulation theory of a multidimensional harmonic carrier. The 2-D equivalent of 1-D single-sideband modulation is defined and called single quadrant modulation. It is shown that the multidimensional complex signal with a signal orthant spectrum may be defined as a convolution of the real signal with the multidimensional complex delta distribution.< <ETX xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>></ETX>" @default.
• W2034935457 created "2016-06-24" @default.
• W2034935457 creator A5045311025 @default.
• W2034935457 date "1992-01-01" @default.
• W2034935457 modified "2023-09-23" @default.
• W2034935457 title "Multidimensional complex signals with single-orthant spectra" @default.
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• W2034935457 doi "https://doi.org/10.1109/5.158601" @default.
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