On the Problem of Parameter Estimation in Exponential Sums |
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| Authors: | F Filbir H N Mhaskar J Prestin |
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| Institution: | 1. Institute of Biomathematics and Biometry, Helmholtz Center Munich, 85764, Neuherberg, Germany
2. Department of Mathematics, California State University, Los Angeles, CA, 90032, USA
3. Institute of Mathematics, University of L??beck, Wallstra?e 40, 23560, L??beck, Germany
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| Abstract: | Let I≥1 be an integer, ω
0=0<ω
1<⋯<ω
I
≤π, and for j=0,…,I, a
j
∈ℂ, a-j=`(aj)]a_{-j}={\overline{{a_{j}}}}, ω
−j
=−ω
j
, and aj 1 0a_{j}\not=0 if j 1 0j\not=0. We consider the following problem: Given finitely many noisy samples of an exponential sum of the form
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(x)\tilde](k) = ?j=-II ajexp(-iwjk) +e(k), k=-2N,?,2N,\tilde{x}(k)= \sum_{j=-I}^I a_j\exp(-i\omega _jk) +\epsilon (k), \quad k=-2N,\ldots,2N, |
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| Keywords: | |
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