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Abstract
An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we propose an iterative algorithm for the estimation of the analytic eigenvalues. Since these are generally transcendental, we find a polynomial approximation with a defined error. Our approach operates in the discrete Fourier transform (DFT) domain and for every DFT length generates a maximally smooth association through EVDs evaluated in DFT bins; an outer loop iteratively grows the DFT order and is shown, in general, to converge to the analytic eigenvalues. In simulations, we compare our results to existing approaches.
Original language | English |
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Pages (from-to) | 722-737 |
Number of pages | 16 |
Journal | IEEE Transactions on Signal Processing |
Volume | 69 |
Early online date | 8 Jan 2021 |
DOIs | |
Publication status | E-pub ahead of print - 8 Jan 2021 |
Keywords
- eigenvalue
- eigenfunctions
- matrix decomposition
- covariance matrices
- approximation algorithms
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Projects
- 1 Active
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Signal Processing in the Information Age (UDRC III)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 30/06/23
Project: Research