On Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing

Abstract

In an earlier article (Bai et al., 1999), the problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case that some observations are missing. The number of signals is estimated with an information theoretic criterion and the frequencies are estimated with eigenvariation linear prediction. Asymptotic properties of the procedure are investigated but the Monte Carlo simulation is not performed. In this article, a slightly different but scale invariant criterion for detection is proposed and the estimation of frequencies remains the same. Asymptotic properties of this new procedure are provided. Monte Carlo Simulation for both procedures is carried out. Furthermore, comparison on the real signals is also given.

Keywords:

• Estimation
• Frequencies
• Limiting distribution
• Multiple sinusoids
• Number of signals
• Signal processing
• Strong consistency

Mathematics Subject Classification:

• 94A13
• 62J02
• 62F10
• 62F12