Distribution Derivative Method for Generalised Sinusoid with Complex Amplitude Modulation

The most common sinusoidal models for non-stationary analysis represent either complex amplitude modulated exponentials with exponential damping (cPACED) or log-amplitude/frequency modulated exponentials (generalised sinusoids), by far the most commonly used modulation function being polynomials for both signal families. Attempts to tackle a hybrid sinusoidal model, i.e. a generalised sinusoid with complex amplitude modulation were relying on approximations and iterative improvement due to absence of a tractable analytical expression for their Fourier Transform. In this work a simple, direct solution for the aforementioned model is presented.