Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform
The paper extends the idea of the analytic signal, to the case of a complex, rather than real, signal. A quaternion Fourier transform is used to construct the analogue of the analytic signal. The idea of amplitude modulation is extended to the case where the modulating and modulated signals are both complex. The two complex signals are kept separate by treating them as orthogonal (in different complex planes, realised using quaternions). The paper presents examples and compares the approach taken with a specific signal model proposed by Lilly and Olhede.
instantaneous frequency orthocomplex modulation quaternion fourier transform