Title :
A Family of Fast Hadamard–Fourier Transform Algorithms
Author :
Su, Teng ; Yu, Feng
Author_Institution :
Dept. of Instrum. Eng., Zhejiang Univ., Hangzhou, China
Abstract :
In this letter, we present a family of fast Hadamard-Fourier transform algorithms which combined Walsh Hadamard and discrete Fourier transforms into one single algorithm. These family algorithms can be computed in butterfly structure, and have similar sparse matrix factorization in each stage, and have less computation stages than the sum of Walsh Hadamard and discrete Fourier transforms. We factorize the algorithms with regular sparse matrices for every stage in radix-R mode, where R is power of 2.
Keywords :
Hadamard transforms; discrete Fourier transforms; matrix decomposition; Walsh Hadamard transform; butterfly structure; discrete Fourier transforms; fast Hadamard-Fourier transform algorithms; radix-R mode; sparse matrix factorization; Discrete Fourier transforms; Error correction; Error correction codes; Materials; Multiaccess communication; Sparse matrices; Discrete Fourier transform (DFT); Kronecker; Walsh Hadamad transform (WHT); sparse matrix;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2012.2207452
