On linearly precompressed non-parametric spectrum estimation

Extending the derivation of a maximum likelihood spectrum estimator by Stoica and Sundin, non-parametric spectrum estimation with linear precompression is introduced. For real-time applications, linear precompression allows for a scalable trade-off between data rate and accuracy of the estimate. Precompression 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.