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Volume 19 Issue 2
Aug.  2022
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WU Yi-quan, ZHU Zhao-da. New algorithms for the radix-3 fast W transform(-Ⅱ,Ⅲ)[J]. ACTA ACUSTICA, 1994, 19(2): 122-131. DOI: 10.15949/j.cnki.0371-0025.1994.02.006
Citation: WU Yi-quan, ZHU Zhao-da. New algorithms for the radix-3 fast W transform(-Ⅱ,Ⅲ)[J]. ACTA ACUSTICA, 1994, 19(2): 122-131. DOI: 10.15949/j.cnki.0371-0025.1994.02.006
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New algorithms for the radix-3 fast W transform(-Ⅱ,Ⅲ)

  • Nanjing University of Aeronautics and Astronautics

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  • Received Date: September 20, 1992
  • Available Online: August 08, 2022
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    • Abstract
  • The discrete W transform (DWT)is a new type of real orthogonal transform.The commonly used DWT has four different versions, namely DWT-j,j=Ⅰ,Ⅱ, Ⅲ, Ⅳ. Inthis paper new radix-3 fast algorithms are proposed for the length-3m DWT(-Ⅱ,Ⅲ). First,The radix-3 fast algorithms of the DWT-Ⅱ and DWT-Ⅲ are derived respectively and theircomputational complexity is analyzed. Then,a comparison is made with the direct algorithmand radix-2 fast algorithm. Finally,the signal flowgraphs for the radix-3 fast W transform(-Ⅱ, Ⅲ)for the length N=32 are given. Compared with direct algorithms, the radix-3 fastalgorithms greatly reduce the arithmetic operations and can be comparable to the radix-2 fastalgorithm. The can allow in-place computation and are numerically stable. The simple andregular structure makes it easy to be implemented. The proposed algorithms extend theapplicability of the fast W transform algorithm.
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