Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency

In the field of nonstationary signal analysis and processing, short-time Fourier transform (STFT) is frequently used to convert signals into time-frequency domain. The instantaneous frequency (IF) STFT defined as time derivative phase plays an important role in reassignment method synchrosqueezing (SST). this paper, we propose a framework design window function for computing IF STFT. Computing requires with its derivative, i.e., computation depends on both derivative. To suitable IF, formulate problem sidelobe minimization corresponding Two windows are designed considering energy or highest level cost functions minimizing sidelobes their derivatives. SST using proposed provides sharper representation compared those produced ordinary bandwidth-adjustable windows.