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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2024.3441834