On Linearly Precompressed Non-Parametric Spectrum Estimation

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Extending the derivation of a maximum likelihood spectrum estimator by Stoica and Sundin, non-parametric spectrum estimation with linear pre-compression is introduced. For real-time applications, linear pre-compression allows for a scalable trade-off between data rate and accuracy of the estimate. Pre-compression is based on linear projection with a compression matrix formed from sequences with perfect periodic autocorrelation. This basis has the property of preserving the power spectrum. The derived estimator is verified with numerical simulations.