S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function.
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| - S transform (en)
- S-преобразование (ru)
- S轉換 (zh)
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| - S轉換(s-transform)是一種時頻分析的工具。 和其他時頻分析工具一樣，透過S轉換，我們可以同時從時域以及頻域觀察一個信號的能量分布。S轉換的特別之處在它既保持與傅立葉變換的直接關係，又可在不同頻率有不同的解析度。此外，S轉換與小波轉換（wavelet transform）有密切的關係，或可視為連續小波轉換（continuous wavelet transform）的變形。S轉換的清晰度略優於加伯轉換（Gabor transform），而不如韋格納分佈（Wigner distribution function）、科恩克萊斯分佈、（Modified Wigner distribution function）。 (zh)
- S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function. (en)
- S-преобразова́ние — один из математических операционных методов отображения функции, зависящей от одной переменной, обычно от времени в частотно-временную область, разновидность оконного преобразования Фурье с гауссовской оконной функцией вида . S-преобразование имеет лучшее разрешение, чем , но уступает по разрешению преобразованию Вигнера и билинейному время-частотному преобразованию. Предложено в 1994 г. для анализа геофизических данных. (ru)
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| - S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function. A fast S transform algorithm was invented in 2010. It reduces the computational complexity from O[N2·log(N)] to O[N·log(N)] and makes the transform one-to-one, where the transform has the same number of points as the source signal or image, compared to storage complexity of N2 for the original formulation. An implementation is available to the research community under an open source license. A general formulation of the S transform makes clear the relationship to other time frequency transforms such as the Fourier, short time Fourier, and wavelet transforms. (en)
- S-преобразова́ние — один из математических операционных методов отображения функции, зависящей от одной переменной, обычно от времени в частотно-временную область, разновидность оконного преобразования Фурье с гауссовской оконной функцией вида . S-преобразование имеет лучшее разрешение, чем , но уступает по разрешению преобразованию Вигнера и билинейному время-частотному преобразованию. Предложено в 1994 г. для анализа геофизических данных. В 2008 г. найден алгоритм быстрого S-преобразования, на несколько порядков сокращающий вычислительную сложность относительно прямого вычисления. Алгоритм быстрого S-преобразования свободно доступен по свободной лицензии. (ru)
- S轉換(s-transform)是一種時頻分析的工具。 和其他時頻分析工具一樣，透過S轉換，我們可以同時從時域以及頻域觀察一個信號的能量分布。S轉換的特別之處在它既保持與傅立葉變換的直接關係，又可在不同頻率有不同的解析度。此外，S轉換與小波轉換（wavelet transform）有密切的關係，或可視為連續小波轉換（continuous wavelet transform）的變形。S轉換的清晰度略優於加伯轉換（Gabor transform），而不如韋格納分佈（Wigner distribution function）、科恩克萊斯分佈、（Modified Wigner distribution function）。 (zh)
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