Skip to Main content Skip to Navigation
Journal articles

Time-frequency analysis of bivariate signals

Abstract : Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate quantities, e.g. rotary components. 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, the quaternion embedding of bivariate signals is introduced, similar to the usual analytic signal of real 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.
Complete list of metadata

Cited literature [42 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01362586
Contributor : Julien Flamant Connect in order to contact the contributor
Submitted on : Friday, September 9, 2016 - 10:24:37 AM
Last modification on : Wednesday, November 3, 2021 - 5:11:31 AM
Long-term archiving on: : Saturday, December 10, 2016 - 12:50:22 PM

File

1609.02463v1.pdf
Files produced by the author(s)

Identifiers

Citation

Julien Flamant, Nicolas Le Bihan, Pierre Chainais. Time-frequency analysis of bivariate signals. Applied and Computational Harmonic Analysis, Elsevier, 2019, 46 (2), pp.351-383. ⟨10.1016/j.acha.2017.05.007⟩. ⟨hal-01362586⟩

Share

Metrics

Record views

608

Files downloads

734