On the Fast Fractional Jacket Transform
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Motivated by the center weighted Hadamard matrix, we propose an improved algorithm for the fast fractional jacket transform (FRJT) based on eigendecomposition of the fractional jacket matrix (FRJM). Employing a matrix diagonalization transformation that decomposes a matrix of large size into products of the matrices composed of eigenvectors and eigenvalues, an FRJM of large size can be fast factored into products of several sparse matrices in a recursive fashion. To generate an FRJM of large size, an algorithm for the factorable FRJM can be conveniently designated with a reduced computational complexity in terms of additions and multiplications. Since the proposed FRJM itself concerns interpretation as a suitable rotation in the time-frequency domain, it is applicable for optics and signal processing.
KeywordsFractional jacket transform Jacket matrix Matrix decomposition Fractional Hadamard transform Hadamard transform Signal processing
This work was supported by the National Natural Science Foundation of China (61071096, 61379153), the bilateral cooperation of the science foundations between China and Korea (NSFC-NRF 61140391), and MEST 2012-0025-21, National Research Foundation, Korea.
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