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- W2093009076 abstract "Let h ( x ) be a nonincreasing exponential sum of order M. For N given noisy sampled values h n = h ( n ) + e n ( n = 0 , ? , N - 1 ) with error terms e n , all parameters of h ( x ) can be estimated by the known ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method. The ESPRIT method is based on singular value decomposition (SVD) of the L-trajectory matrix ( h ? + m ) ? , m = 0 L - 1 , N - L , where the window length L fulfills M ? L ? N - M + 1 . The computational cost of the ESPRIT algorithm is dominated by the cost of SVD. In the case L ? N 2 , the ESPRIT algorithm based on complete SVD costs about 21 8 N 3 + M 2 ( 21 N + 91 3 M ) operations. Here we show that the ESPRIT algorithm based on partial SVD and fast Hankel matrix-vector multiplications has much lower cost. Especially for L ? N 2 , the ESPRIT algorithm based on partial Lanczos bidiagonalization with S steps requires only about 18 S N log 2 ? N + S 2 ( 20 N + 30 S ) + M 2 ( N + 1 3 M ) operations, where M ? S ? N - L + 1 . Numerical experiments demonstrate the high performance of these fast ESPRIT algorithms for noisy sampled data with relatively large error terms." @default.
- W2093009076 created "2016-06-24" @default.
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- W2093009076 date "2015-02-01" @default.
- W2093009076 modified "2023-09-25" @default.
- W2093009076 title "Fast ESPRIT algorithms based on partial singular value decompositions" @default.
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- W2093009076 doi "https://doi.org/10.1016/j.apnum.2014.10.003" @default.
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