What question did this study set out to answer?

To develop robust, high-resolution approximation methods for extracting sinusoidal processes from noisy measurement data using state-space representations and singular-value decomposition.

December 1, 1983Journal of the Optical Society of America

State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem

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Authors

SKSun‐Yuan Kung KAK.S. Arun DRD. V. Bhaskar Rao

Discussion

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Overview

Simulation study demonstrates improved resolution in noisy sinusoidal retrieval using singular-value decomposition and state-space modeling, indicating robust spectral estimation.

Key Points

To develop robust, high-resolution approximation methods for extracting sinusoidal processes from noisy measurement data using state-space representations and singular-value decomposition.
Applied singular-value decomposition to noisy data and covariance matrices to construct low-rank factored approximants.
Derived least-squares parameter estimates within a state-space framework to formulate the covariance-based Toeplitz approximation method and a direct-data approximation method.
Evaluated algorithm resolution using numerical simulations and extended the modeling principles to two-dimensional signals.
The Toeplitz approximation method provided robust Pisarenko-like spectral estimates from covariance sequences despite noise-induced rank perturbations.
Direct-data approximation enabled effective harmonic retrieval directly from time-series measurements without prior covariance estimation.
Simulations demonstrated superior resolution capability compared with conventional spectral retrieval methods.

Cite This Study

Kung et al. (1983) studied this question.

synapsesocial.com/papers/6a6fcf2387f9210571275488 https://doi.org/10.1364/josa.73.001799

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December 1, 1983Journal of the Optical Society of America

State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem

View Full Paper

Ask AI

Bookmark

Authors

SKSun‐Yuan Kung KAK.S. Arun DRD. V. Bhaskar Rao

Discussion

Member takes

Overview

Simulation study demonstrates improved resolution in noisy sinusoidal retrieval using singular-value decomposition and state-space modeling, indicating robust spectral estimation.

Key Points

To develop robust, high-resolution approximation methods for extracting sinusoidal processes from noisy measurement data using state-space representations and singular-value decomposition.
Applied singular-value decomposition to noisy data and covariance matrices to construct low-rank factored approximants.
Derived least-squares parameter estimates within a state-space framework to formulate the covariance-based Toeplitz approximation method and a direct-data approximation method.
Evaluated algorithm resolution using numerical simulations and extended the modeling principles to two-dimensional signals.
The Toeplitz approximation method provided robust Pisarenko-like spectral estimates from covariance sequences despite noise-induced rank perturbations.
Direct-data approximation enabled effective harmonic retrieval directly from time-series measurements without prior covariance estimation.
Simulations demonstrated superior resolution capability compared with conventional spectral retrieval methods.

Cite This Study

Kung et al. (1983) studied this question.

synapsesocial.com/papers/6a6fcf2387f9210571275488 https://doi.org/10.1364/josa.73.001799

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