A Robust Interpolation Algorithm for Spectral Analysis

We propose a robust interpolation algorithm for model-based spectral analysis. Instead of estimating the spectral model directly, the so-called half spectrum, which has a one-to-one relationship with the spectrum through standard spectral decomposition, is estimated using an interpolation approach....

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Bibliographic Details
Published in:IEEE transactions on signal processing 2007-10, Vol.55 (10), p.4851-4861
Main Authors: Mahata, K., Minyue Fu
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Autoregressive moving average (ARMA) modeling
Autoregressive processes
Derivatives
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Filtering
Filters
Frequency estimation
Information, signal and communications theory
input-to-state filtering
Interpolation
Least squares method
Mathematical analysis
Mathematical models
Maximum likelihood estimation
Nevanlinna-Pick interpolation
Noise robustness
Programming
Signal and communications theory
Signal processing algorithms
Signal representation. Spectral analysis
Signal, noise
Spectra
Spectral analysis
Telecommunications and information theory
Testing
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Summary:We propose a robust interpolation algorithm for model-based spectral analysis. Instead of estimating the spectral model directly, the so-called half spectrum, which has a one-to-one relationship with the spectrum through standard spectral decomposition, is estimated using an interpolation approach. The interpolation data consists of the values and the derivatives of the half spectrum function at a set of user-specified points, and can be easily estimated using an input-to-state filter. Our algorithm allows a large number of noisy interpolation data to be used to optimally fit a half spectrum function of a fixed order. The capability of handling large number of interpolation data makes our algorithm robust to the inherent finite sample noise in the interpolation data. The algorithm involves solving some least-squares problems and semidefinite programming problems, and is thus numerically efficient. Numerical tests show that our algorithm gives very reliable spectral estimates.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.896253