The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula:
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| - Gabor transform (en)
- Transformada de Gabor (ca)
- Gabor-Transformation (de)
- Gabortransformatie (nl)
- Transformada de Gabor (pt)
- 加伯轉換 (zh)
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| - Die Gabor-Transformation (nach Dennis Gábor) ist eine spezielle (und in bestimmter Weise optimale) gefensterte Fourier-Transformation. Sie ist eng verwandt mit der Wavelet-Theorie und wird in vielen Bereichen der digitalen Signal- und Bildverarbeitung eingesetzt. Sie ist ein Spezialfall der Kurzzeit-Fourier-Transformation. (de)
- Gabortransformatie genoemd naar Dennis Gabor is een bijzonder geval van fouriertransformatie waarbij vooral frequentieveranderingen goed zichtbaar kunnen worden gemaakt. Bij gabortransformatie wordt een gaussische functie als venster (window) over het signaal gelegd. Zoals bij iedere praktische implementatie van fouriertransformatie wordt daarbij een integratie over een oneindig interval verkort tot een eindig, en in dit geval een kort tijdsinterval. Aangezien kunnen waarden buiten ±1,9143 buiten beschouwing blijven en resteert de vereenvoudiging: (nl)
- 加伯轉換是窗函數為高斯函數的短時距傅立葉變換。 (zh)
- The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula: (en)
- A transformada de Gabor, em homenagem a Dennis Gabor, é um caso especial da . É utilizada para determinar a frequência senoidal e o conteúdo da das seções locais de um sinal à medida que muda ao longo do tempo. A função a ser transformada é multiplicada primeiramente por uma função Gaussiana, que pode ser considerada como uma , e a função resultante é então transformada com uma transformada de Fourier para derivar a [[análise tempo-frequência]. A função de janela indica que o sinal próximo ao tempo analisado terá maior peso. A transformada de Gabor de um sinal x(t) é definida por esta fórmula: (pt)
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| - Die Gabor-Transformation (nach Dennis Gábor) ist eine spezielle (und in bestimmter Weise optimale) gefensterte Fourier-Transformation. Sie ist eng verwandt mit der Wavelet-Theorie und wird in vielen Bereichen der digitalen Signal- und Bildverarbeitung eingesetzt. Sie ist ein Spezialfall der Kurzzeit-Fourier-Transformation. (de)
- The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula: The Gaussian function has infinite range and it is impractical for implementation. However, a level of significance can be chosen (for instance 0.00001) for the distribution of the Gaussian function. Outside these limits of integration the Gaussian function is small enough to be ignored. Thus the Gabor transform can be satisfactorily approximated as This simplification makes the Gabor transform practical and realizable. The window function width can also be varied to optimize the time-frequency resolution tradeoff for a particular application by replacing the with for some chosen . (en)
- Gabortransformatie genoemd naar Dennis Gabor is een bijzonder geval van fouriertransformatie waarbij vooral frequentieveranderingen goed zichtbaar kunnen worden gemaakt. Bij gabortransformatie wordt een gaussische functie als venster (window) over het signaal gelegd. Zoals bij iedere praktische implementatie van fouriertransformatie wordt daarbij een integratie over een oneindig interval verkort tot een eindig, en in dit geval een kort tijdsinterval. Aangezien kunnen waarden buiten ±1,9143 buiten beschouwing blijven en resteert de vereenvoudiging: (nl)
- A transformada de Gabor, em homenagem a Dennis Gabor, é um caso especial da . É utilizada para determinar a frequência senoidal e o conteúdo da das seções locais de um sinal à medida que muda ao longo do tempo. A função a ser transformada é multiplicada primeiramente por uma função Gaussiana, que pode ser considerada como uma , e a função resultante é então transformada com uma transformada de Fourier para derivar a [[análise tempo-frequência]. A função de janela indica que o sinal próximo ao tempo analisado terá maior peso. A transformada de Gabor de um sinal x(t) é definida por esta fórmula: A função gaussiana tem um intervalo infinito e é impossível de implementar. Contudo, um nível de significância pode ser escolhido (por exemplo 0.00001) para a distribuição da função gaussiana. Fora destes limites de integração a função gaussiana é suficientemente pequena para ser ignorada. Assim, a transformada de Gabor pode ser satisfatoriamente aproximada como Esta simplificação torna a transformada de Gabor prática e viável. A largura da função de janela também pode ser variada para otimizar a troca de resolução tempo-frequência para uma aplicação específica, substituindo o por para algum alfa escolhido. (pt)
- 加伯轉換是窗函數為高斯函數的短時距傅立葉變換。 (zh)
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