Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency
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...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9739664/ |
| _version_ | 1797804914358878208 |
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| author | Tsubasa Kusano Kohei Yatabe Yasuhiro Oikawa |
| author_facet | Tsubasa Kusano Kohei Yatabe Yasuhiro Oikawa |
| author_sort | Tsubasa Kusano |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T05:44:13Z |
| format | Article |
| id | doaj.art-d9f8b28f96d649aea3b08abd0d2eab52 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T05:44:13Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-d9f8b28f96d649aea3b08abd0d2eab522023-06-13T23:00:22ZengIEEEIEEE Access2169-35362022-01-0110320753209210.1109/ACCESS.2022.31615439739664Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous FrequencyTsubasa Kusano0https://orcid.org/0000-0002-7025-2049Kohei Yatabe1https://orcid.org/0000-0002-1345-0663Yasuhiro Oikawa2https://orcid.org/0000-0002-9078-1714Department of Intermedia Art and Science, Waseda University, Tokyo, JapanDepartment of Intermedia Art and Science, Waseda University, Tokyo, JapanDepartment of Intermedia Art and Science, Waseda University, Tokyo, JapanIn 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.https://ieeexplore.ieee.org/document/9739664/Short-time Fourier transform (STFT)instantaneous frequency (IF)window derivativeadjustable windowsynchrosqueezing transform (SST) |
| spellingShingle | Tsubasa Kusano Kohei Yatabe Yasuhiro Oikawa Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency IEEE Access Short-time Fourier transform (STFT) instantaneous frequency (IF) window derivative adjustable window synchrosqueezing transform (SST) |
| title | Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency |
| title_full | Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency |
| title_fullStr | Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency |
| title_full_unstemmed | Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency |
| title_short | Window Functions With Minimum-Sidelobe Derivatives for Computing Instantaneous Frequency |
| title_sort | window functions with minimum sidelobe derivatives for computing instantaneous frequency |
| topic | Short-time Fourier transform (STFT) instantaneous frequency (IF) window derivative adjustable window synchrosqueezing transform (SST) |
| url | https://ieeexplore.ieee.org/document/9739664/ |
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