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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1999 Sep 28;96(20):11106–11110. doi: 10.1073/pnas.96.20.11106

The simultaneous estimation of the number of signals and frequencies of multiple sinusoids when some observations are missing: I. Asymptotics

Zhidong Bai *, Calyampudi R Rao , Yuehua Wu , Mei-Mei Zen §, Lincheng Zhao
PMCID: PMC17994  PMID: 10500137

Abstract

The problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case when some observations are missing. The number of signals is estimated with an information theoretic criterion, and the frequencies are estimated with eigenvariation linear prediction. The strong consistency of the estimates of the number of signals and the frequencies is established and the rate of convergence of these estimates is provided. Besides, the limiting distributions of various estimates are given.

Keywords: strong consistency, limiting distribution, rate of convergence, signal processing, undamped exponential signal model


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