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In computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHTh) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive implementation of the WHT of order would have a computational complexity of O. The FWHTh requires only additions or subtractions. The FWHTh is a divide-and-conquer algorithm that recursively breaks down a WHT of size into two smaller WHTs of size . This implementation follows the recursive definition of the Hadamard matrix : The normalization factors for each stage may be grouped together or even omitted.

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  • Transformada ràpida de Walsh-Hadamard (ca)
  • Fast Walsh–Hadamard transform (en)
  • 快速沃爾什轉換 (zh)
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  • 在計算數學中，一個與阿達馬變換有高度相關的快速沃爾什轉換（英語：fast Walsh–Hadamard transform，FWHTh）是一個十分有效率的演算法，目的是計算阿達馬變換。一個直觀且基本的沃爾什轉換，他的計算複雜度 大約是 。而快速沃爾什轉換只需要 個加法或是減法即可。 而快速沃爾什轉換是一個分而治之的演算法，是一個常見的遞迴方法，將大小為 的沃爾什轉換拆成兩個大小為 的沃爾什轉換。這樣的寫法是根據阿達馬矩陣 的遞迴定義: 其中 的正規化項可以提出或省略掉。 沃爾什矩陣，又叫沃爾什序列，快速沃爾什轉換FWHTw，就是用上面的作法計算以後，把輸出結果排成序列。 (zh)
  • In computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHTh) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive implementation of the WHT of order would have a computational complexity of O. The FWHTh requires only additions or subtractions. The FWHTh is a divide-and-conquer algorithm that recursively breaks down a WHT of size into two smaller WHTs of size . This implementation follows the recursive definition of the Hadamard matrix : The normalization factors for each stage may be grouped together or even omitted. (en)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Fast_walsh_hadamard_transform_8.svg
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  • In computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHTh) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive implementation of the WHT of order would have a computational complexity of O. The FWHTh requires only additions or subtractions. The FWHTh is a divide-and-conquer algorithm that recursively breaks down a WHT of size into two smaller WHTs of size . This implementation follows the recursive definition of the Hadamard matrix : The normalization factors for each stage may be grouped together or even omitted. The sequency-ordered, also known as Walsh-ordered, fast Walsh–Hadamard transform, FWHTw, is obtained by computing the FWHTh as above, and then rearranging the outputs. A simple fast nonrecursive implementation of the Walsh–Hadamard transform follows from decomposition of the Hadamard transform matrix as , where A is m-th root of . (en)
  • 在計算數學中，一個與阿達馬變換有高度相關的快速沃爾什轉換（英語：fast Walsh–Hadamard transform，FWHTh）是一個十分有效率的演算法，目的是計算阿達馬變換。一個直觀且基本的沃爾什轉換，他的計算複雜度 大約是 。而快速沃爾什轉換只需要 個加法或是減法即可。 而快速沃爾什轉換是一個分而治之的演算法，是一個常見的遞迴方法，將大小為 的沃爾什轉換拆成兩個大小為 的沃爾什轉換。這樣的寫法是根據阿達馬矩陣 的遞迴定義: 其中 的正規化項可以提出或省略掉。 沃爾什矩陣，又叫沃爾什序列，快速沃爾什轉換FWHTw，就是用上面的作法計算以後，把輸出結果排成序列。 (zh)
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