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Fast and Accurate Generalized Harmonic Analysis and Its Parallel Computation by GPU

Hisayori Noda, Akinori Nishihara
Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550 Japan
IEICE Trans. Fundamentals, Vol.E92-A, No.3 March 2009

@article{noda2009fast,

   title={Fast and Accurate Generalized Harmonic Analysis and Its Parallel Computation by GPU},

   author={Noda, H. and Nishihara, A.},

   journal={IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences},

   volume={92},

   number={3},

   pages={745–752},

   issn={1745-1337},

   year={2009}

}

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A fast and accurate method for Generalized Harmonic Analysis is proposed. The proposed method estimates the parameters of a sinusoid and subtracts it from a target signal one by one. The frequency of the sinusoid is estimated around a peak of Fourier spectrum using binary search. The binary search can control the trade-off between the frequency accuracy and the computation time. The amplitude and the phase are estimated to minimize the squared sum of the residue after extraction of estimated sinusoids from the target signal. Sinusoid parameters are recalculated to reduce errors introduced by the peak detection using windowed Discrete-Time Fourier Transform. Audio signals are analyzed by the proposed method, which confirms the accuracy compared to existing methods. The proposed algorithm has high degree of concurrency and is suitable to be implemented on Graphical Processing Unit (GPU). The computational throughput can be made higher than the input audio signal rate.
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