The ℍ-analytic signal

We consider the extension of the analytic signal concept known for real valued signals to the case of complex signals. This extension is based on the Quaternion Fourier Transform (QFT) and leads to the so-called ℍ-analytic signal. After defining the ℍ-analytic signal and giving some of its properties, we present a new notation for quaternions, named the polar Cayley-Dickson form, which allows the extension of instantaneous phase and amplitude for the ℍ-analytic signal. Identification of the components of a complex signal are then performed through the analysis of its ℍ-analytic signal. We illustrate these new ideas on simulations.