Fast Walsh-Hadamard-Fourier Transform Algorithm

An efficient fast Walsh-Hadamard-Fourier transform algorithm which combines the calculation of the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT) is introduced. This can be used in Walsh-Hadamard precoded orthogonal frequency division multiplexing systems (WHT-OFDM) to incre...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-11, Vol.59 (11), p.5627-5631
Main Authors: Hamood, M. T., Boussakta, S.
Format: Article
Language:English
Subjects:
algorithm
Algorithm design and analysis
Algorithms
Applied sciences
Computers
Delay
Detection, estimation, filtering, equalization, prediction
Discrete Fourier transform (DFT)
Discrete Fourier transforms
Exact sciences and technology
Factorization
fast Walsh-Fourier transform (FWFT)
Fourier transforms
Information, signal and communications theory
Mathematical analysis
Multiplexing
Orthogonal Frequency Division Multiplexing
Peak to average power ratio
Signal and communications theory
Signal, noise
Sparse matrices
Telecommunications and information theory
Transforms
Walsh-Hadamard transform (WHT)
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Summary:An efficient fast Walsh-Hadamard-Fourier transform algorithm which combines the calculation of the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT) is introduced. This can be used in Walsh-Hadamard precoded orthogonal frequency division multiplexing systems (WHT-OFDM) to increase speed and reduce the implementation cost. The algorithm is developed through the sparse matrices factorization method using the Kronecker product technique, and implemented in an integrated butterfly structure. The proposed algorithm has significantly lower arithmetic complexity, shorter delays and simpler indexing schemes than existing algorithms based on the concatenation of the WHT and FFT, and saves about 70%-36% in computer run-time for transform lengths of 16-4096.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2162836