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A fast realization of new Mersenne number transformation and its applications
Author(s) -
Hua Jingyu,
Liu Fei,
Xu Zhijiang,
Li Feng,
Wang Dongming
Publication year - 2019
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2614
Subject(s) - fast fourier transform , realization (probability) , convolution (computer science) , lookup table , hadamard transform , computation , multiplication (music) , algorithm , mersenne prime , computer science , matrix multiplication , circular convolution , mathematics , fourier transform , discrete mathematics , fractional fourier transform , artificial neural network , quantum , programming language , mathematical analysis , fourier analysis , statistics , physics , combinatorics , machine learning , quantum mechanics
Summary The new Mersenne number transform (NMNT) can be realized by the fast Fourier transform (FFT) with power‐of‐two length, which results in great flexibility in real‐world fixed‐point computations, such as the convolution‐based signal processing in the embedded device. Yet the FFT realization exists the truncation errors and in order to further reduce the computations, this paper puts forward a novel realization structure for the NMNT, where the Walsh‐Hadamard transform (WHT) is employed to accelerate the NMNT computation. Moreover, we also propose the refined computing structure using the matrix decomposition and multiple constant multiplication (MCM), and then all multiplications can be replaced by the shift‐addition operations without precision loss. Besides, the use of lookup table (LUT) to reduce the complexity is also discussed in our study. A typical convolution application is tested by computer simulations, while the result demonstrates that the proposed scheme produces precise computing results with reduced complexity.