Derivative Features of Short-Time Holomorphic Fourier Transform

A short-time holomorphic Fourier transform is introduced, which is holomorphic regardless of the chosen window function. Based on the holomorphic properties and the Wirtinger derivative approach, we delve into the derivatives of the power-spectrum-based functions. Power-spectrum-based weighting of the amplitude or phase derivatives is reasonably introduced during the power-spectrum differentiation. Additionally, we explore the linkage between these introduced derivatives and the group delay or instantaneous frequency.