Maximally Energy-Concentrated Differential Window for Phase-Aware Signal Processing Using Instantaneous Frequency

The short-time Fourier transform (STFT) is widely employed in non-stationary signal analysis, whose property depends on window functions. Instantaneous frequency in STFT, the time-derivative of phase, is recently applied to many applications including spectrogram reassignment. The computation of instantaneous frequency requires STFT with the window and STFT with the (time-)differential window, i.e., the computation of instantaneous frequency depends on both the window function and its time derivative. To obtain the instantaneous frequency accurately, the sidelobe of frequency response of differential window should be reduced because the side-lobe causes mixing of multiple components. In this paper, we propose window functions suitable for computing the instantaneous frequency which are designed based on minimizing the sidelobe energy of the frequency response of the differential window.