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• W2963297042 abstract "Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. We show that an adequate quaternion Fourier transform permits to build relevant time–frequency representations of bivariate signals that naturally identify geometrical or polarization properties. First, a bivariate counterpart of the usual analytic signal of real signals is introduced, called the quaternion embedding of bivariate signals. Then two fundamental theorems ensure that a quaternion short term Fourier transform and a quaternion continuous wavelet transform are well defined and obey desirable properties such as conservation laws and reconstruction formulas. The resulting spectrograms and scalograms provide meaningful representations of both the time–frequency and geometrical/polarization content of the signal. Moreover the numerical implementation remains simply based on the use of FFT. A toolbox is available for reproducibility. Synthetic and real-world examples illustrate the relevance and efficiency of the proposed approach." @default.
• W2963297042 created "2019-07-30" @default.
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• W2963297042 date "2019-03-01" @default.
• W2963297042 modified "2023-09-30" @default.
• W2963297042 title "Time–frequency analysis of bivariate signals" @default.
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• W2963297042 doi "https://doi.org/10.1016/j.acha.2017.05.007" @default.
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