Efficient Computation for Discrete Fractional Hadamard Transform

This paper introduces a new fast algorithm for the discrete fractional Hadamard transform (FHT). The proposed algorithm demonstrates superior computational efficiency. For data lengths ranging from <inline-formula> <tex-math notation="LaTeX">2 \leq N \leq 1024 </tex-math>...

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Published in:	IEEE transactions on circuits and systems. I, Regular papers Vol. 71; no. 10; pp. 4698 - 4706
Main Authors:	Fan, Zi-Chen, Li, Di, Rahardja, Susanto
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.10.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Computational complexity Computational efficiency Computing time Discrete fractional Hadamard transform Eigenvalues and eigenfunctions Fans fast algorithms matrix factorization multiplication reduction Signal processing algorithms Symmetric matrices Transforms
ISSN:	1549-8328, 1558-0806
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Abstract	This paper introduces a new fast algorithm for the discrete fractional Hadamard transform (FHT). The proposed algorithm demonstrates superior computational efficiency. For data lengths ranging from <inline-formula> <tex-math notation="LaTeX">2 \leq N \leq 1024 </tex-math></inline-formula>, our algorithm achieves a reduction in the number of multiplications by up to 96.53%, 81.82%, 33.33%, and 90% compared to four existing fast algorithms for the FHT. Additionally, we compare the execution times with those of existing fast algorithms, and the results show that the proposed algorithm has better performance. The reduced computational complexity makes the proposed algorithm a potential candidate for calculating the FHT.
AbstractList	This paper introduces a new fast algorithm for the discrete fractional Hadamard transform (FHT). The proposed algorithm demonstrates superior computational efficiency. For data lengths ranging from [Formula Omitted], our algorithm achieves a reduction in the number of multiplications by up to 96.53%, 81.82%, 33.33%, and 90% compared to four existing fast algorithms for the FHT. Additionally, we compare the execution times with those of existing fast algorithms, and the results show that the proposed algorithm has better performance. The reduced computational complexity makes the proposed algorithm a potential candidate for calculating the FHT. This paper introduces a new fast algorithm for the discrete fractional Hadamard transform (FHT). The proposed algorithm demonstrates superior computational efficiency. For data lengths ranging from <inline-formula> <tex-math notation="LaTeX">2 \leq N \leq 1024 </tex-math></inline-formula>, our algorithm achieves a reduction in the number of multiplications by up to 96.53%, 81.82%, 33.33%, and 90% compared to four existing fast algorithms for the FHT. Additionally, we compare the execution times with those of existing fast algorithms, and the results show that the proposed algorithm has better performance. The reduced computational complexity makes the proposed algorithm a potential candidate for calculating the FHT.
Author	Rahardja, Susanto Li, Di Fan, Zi-Chen
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SubjectTerms	Algorithms Computational complexity Computational efficiency Computing time Discrete fractional Hadamard transform Eigenvalues and eigenfunctions Fans fast algorithms matrix factorization multiplication reduction Signal processing algorithms Symmetric matrices Transforms
Title	Efficient Computation for Discrete Fractional Hadamard Transform
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