Window Functions with Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency
Window Functions with Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency
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DOI：
10.1109/access.2022.3161543
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发表时间：
2022
期刊：
影响因子：
3.9
通讯作者：
Tsubasa Kusano;K. Yatabe;Yasuhiro Oikawa
中科院分区：
文献类型：
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作者：
Tsubasa Kusano;K. Yatabe;Yasuhiro Oikawa
在非平稳信号分析与处理领域中，短时傅立叶变换（STFT）常用于将信号转换到时频域。STFT的瞬时频率（IF）被定义为STFT相位的时间导数，并且在重新分配方法和同步压缩变换（SST）中起着重要作用。在本文中，我们提出了一个框架来设计一个窗口函数计算的短期FT的IF。计算IF需要具有窗口的STFT和具有其导数的STFT，即，IF计算取决于窗函数及其导数。为了设计一个适合计算中频的窗口，我们将窗口设计问题公式化为相应导数的旁瓣最小化问题。以旁瓣能量或最高旁瓣电平为代价函数，设计了两个窗函数，以最小化其导数的旁瓣。SST使用建议的窗口提供了一个更清晰的时间-频率表示相比，使用普通的带宽可调窗口。
In the field of nonstationary signal analysis and processing, the short-time Fourier transform (STFT) is frequently used to convert signals into the time-frequency domain. The instantaneous frequency (IF) of the STFT is defined as the time derivative of the STFT phase and plays an important role in the reassignment method and the synchrosqueezing transform (SST). In this paper, we propose a framework to design a window function for computing the IF of STFT. Computing the IF requires the STFT with a window and STFT with its derivative, i.e., the IF computation depends on both the window function and its derivative. To design a window suitable for computing the IF, we formulate the window design problem as a sidelobe minimization problem of the corresponding derivative. Two windows are designed considering the sidelobe energy or the highest sidelobe level as cost functions for minimizing the sidelobes of their derivatives. The SST using the proposed window provides a sharper time-frequency representation compared to those produced using ordinary bandwidth-adjustable windows.