The Gabor transform, named after Dennis Gabor, and the Wigner distribution function, named after Eugene Wigner, are both tools for time-frequency analysis. Since the Gabor transform does not have high clarity, and the Wigner distribution function has a "cross term problem" (i.e. is non-linear), a 2007 study by S. C. Pei and J. J. Ding proposed a new combination of the two transforms that has high clarity and no cross term problem.Since the cross term does not appear in the Gabor transform, the time frequency distribution of the Gabor transform can be used as a filter to filter out the cross term in the output of the Wigner distribution function.
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| rdfs:label
| - Transformada de Gabor-Wigner (ca)
- Gabor–Wigner transform (en)
- Transformada Gabor-Wigner (pt)
- 加伯–韋格納轉換 (zh)
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| rdfs:comment
| - The Gabor transform, named after Dennis Gabor, and the Wigner distribution function, named after Eugene Wigner, are both tools for time-frequency analysis. Since the Gabor transform does not have high clarity, and the Wigner distribution function has a "cross term problem" (i.e. is non-linear), a 2007 study by S. C. Pei and J. J. Ding proposed a new combination of the two transforms that has high clarity and no cross term problem.Since the cross term does not appear in the Gabor transform, the time frequency distribution of the Gabor transform can be used as a filter to filter out the cross term in the output of the Wigner distribution function. (en)
- A Transformada Gabor, em homenagem a Dennis Gabor, e a função de distribuição de Wigner, em homenagem a Eugene Wigner, são ferramentas para . Uma vez que a Transformada de Gabor não possui clareza e a tem um problema de "termo cruzado" (ou seja, é não-linear), um estudo de 2007 por S. C. Pei e J. J. Ding propôs uma nova combinação das duas transformadas que possui alta clareza e nenhum problema de termo cruzado. Uma vez que o termo cruzado não aparece na transformada de Gabor, a distribuição de frequência-tempo da Transformada Gabor pode ser usada como um filtro para remover o termo cruzado na saída da função de distribuição de Wigner. (pt)
- 加伯–韋格納轉換（Gabor Wigner Transform）是一種時頻分析的工具，由加伯轉換（Gabor Transfrom）及（Wigner Transform）兩種時頻分析工具所組合而成，加伯轉換根據丹尼斯·蓋博所命名，而韋格納轉換則是根據尤金·維格納，原名維格納·帕爾·耶諾所命名。加伯轉換是一窗函數為高斯函數的短時距傅立葉變換，由於傳統短時距傅立葉變換的窗函數常為一矩形函數，由於矩形函數的傅立葉變換為一個Sinc函數，所以在做時頻分析的時候容易會有Side lobe（页面存档备份，存于互联网档案馆）的現象，所以加伯轉換嘗試利用高斯函數來當作窗函數，三角波為兩個矩形函數卷積而來，高斯函數則為無限多個矩形函數卷積而來所以在頻域上代表無限多個Sinc函數相乘而來，這樣相乘原先Sinc函數小於1的數值越乘越小，Side lobe（页面存档备份，存于互联网档案馆）的影響也跟著變小，但它必須遵守海森堡測不準原理，所以它的清晰度有它的極限。而韋格納轉換由於是對訊號的自相關函數做傅立葉轉換，所以清晰度可以成功超越測不準原理所規範的極限。但它的缺點在於當一個訊號有兩個以上的成分(component)所組成，分析出來的時頻圖就會產生嚴重的cross-term的現象。為了結合兩者的優點所以S.C Pie和J.J.Ding在2007年提出了加伯-韋格納轉換。 (zh)
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| - The Gabor transform, named after Dennis Gabor, and the Wigner distribution function, named after Eugene Wigner, are both tools for time-frequency analysis. Since the Gabor transform does not have high clarity, and the Wigner distribution function has a "cross term problem" (i.e. is non-linear), a 2007 study by S. C. Pei and J. J. Ding proposed a new combination of the two transforms that has high clarity and no cross term problem.Since the cross term does not appear in the Gabor transform, the time frequency distribution of the Gabor transform can be used as a filter to filter out the cross term in the output of the Wigner distribution function. (en)
- A Transformada Gabor, em homenagem a Dennis Gabor, e a função de distribuição de Wigner, em homenagem a Eugene Wigner, são ferramentas para . Uma vez que a Transformada de Gabor não possui clareza e a tem um problema de "termo cruzado" (ou seja, é não-linear), um estudo de 2007 por S. C. Pei e J. J. Ding propôs uma nova combinação das duas transformadas que possui alta clareza e nenhum problema de termo cruzado. Uma vez que o termo cruzado não aparece na transformada de Gabor, a distribuição de frequência-tempo da Transformada Gabor pode ser usada como um filtro para remover o termo cruzado na saída da função de distribuição de Wigner. (pt)
- 加伯–韋格納轉換（Gabor Wigner Transform）是一種時頻分析的工具，由加伯轉換（Gabor Transfrom）及（Wigner Transform）兩種時頻分析工具所組合而成，加伯轉換根據丹尼斯·蓋博所命名，而韋格納轉換則是根據尤金·維格納，原名維格納·帕爾·耶諾所命名。加伯轉換是一窗函數為高斯函數的短時距傅立葉變換，由於傳統短時距傅立葉變換的窗函數常為一矩形函數，由於矩形函數的傅立葉變換為一個Sinc函數，所以在做時頻分析的時候容易會有Side lobe（页面存档备份，存于互联网档案馆）的現象，所以加伯轉換嘗試利用高斯函數來當作窗函數，三角波為兩個矩形函數卷積而來，高斯函數則為無限多個矩形函數卷積而來所以在頻域上代表無限多個Sinc函數相乘而來，這樣相乘原先Sinc函數小於1的數值越乘越小，Side lobe（页面存档备份，存于互联网档案馆）的影響也跟著變小，但它必須遵守海森堡測不準原理，所以它的清晰度有它的極限。而韋格納轉換由於是對訊號的自相關函數做傅立葉轉換，所以清晰度可以成功超越測不準原理所規範的極限。但它的缺點在於當一個訊號有兩個以上的成分(component)所組成，分析出來的時頻圖就會產生嚴重的cross-term的現象。為了結合兩者的優點所以S.C Pie和J.J.Ding在2007年提出了加伯-韋格納轉換。 (zh)
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