Time-frequency analysis of bivariate signals

Spectral Analysis of Stationary Random Bivariate Signals

“…where U (ν), V (ν) are the standard FTs of u, v: the QFT is performing two standard FT. This may explain why this QFT shares most properties of the classical FT, see [25]. Another benefit of the QFT is that it provides a well-suited framework for bivariate signals.…”

“…This form is particularly useful for quaternion embedding of complex signals, see [25], and in the spectral description of stationary signals in Section III-G.…”

“…We review here briefly the Quaternion Fourier Transform (QFT) introduced in [29] and studied in detail recently in [25]. We refer the reader to these articles for proofs and a detailed presentation.…”

“…The above relations are directly obtained by discretizing the continuous-time QFT presented in [25], [29] using similar arguments as with the usual FT.…”

“…We propose a new approach to analyze the spectral content of stationary random bivariate signals. It is based on recent results from [25], [26] and extended to the case of stationary bivariate signals seen as complex-valued signals. This paper provides a well-suited framework for the analysis of stationary bivariate signals which naturally describes the spectral content and the "geometric" (also sometimes called polarization) content of bivariate signals.…”