On Detection of Frequencies Using Single Measurement of Data
Qi Cheng, Yingbo Hua · Control 95: Meeting the Challenge of Asia Pacific Growth; Preprints · 1995
In this paper, we study the large sample and high SNR consistency of four methods for detection of frequencies using a single measurement. They are the Bayesian and the MAP (maximum a posteriori) criteria proposed by Djuric, the EDC (efficient detection criterion) criterion by Zhao et al., and the ANPA (alternating notch periodogram approach) method by Huang and Chen. We show that (1) the EDC criterion and the ANPA method are large sample strongly consistent and the Bayesian and the MAP criteria are large sample weakly consistent; (2) the ANPA method does not work properly in certain scenarios. The total failure of the ANPA method for noiseless case leads to a poor performance at medium or high SNR for certain number of samples. We propose an improved detection algorithm, called the Pencil-EDC method, which has an almost correct detection in the case for which the ANPA method fails.