A single-pass algorithm for spectrum estimation with fast convergence

Han Xiao, Wei Biao Wu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.

Original languageEnglish (US)
Article number5895109
Pages (from-to)4720-4731
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Batched mean estimate
  • bias reduction
  • nonparametric estimation
  • physical dependence measure
  • recursive algorithm
  • spectral density
  • stochastic process

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