Fast algorithms for single frequency estimation

In this paper, some new estimators of the frequency of a single complex sinusoid are presented. The rotate-add-decimate (RAD) method of Crozier is first refined to more closely approach the Cramer-Rao Bound (CRB). An additional modification yields an unbiased estimator (ERAD) that essentially achiev...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2006-05, Vol.54 (5), p.1762-1770
Main Author: Klein, J.D.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Complexity
Computation
Computational complexity
Context
Cramer-Rao bounds
Detection, estimation, filtering, equalization, prediction
Discrete Fourier transforms
Estimators
Exact sciences and technology
Frequency estimation
Information, signal and communications theory
Maximum likelihood estimation
Radar signal processing
Signal and communications theory
Signal processing
Signal processing algorithms
Signal to noise ratio
Signal, noise
single sinusoid
Telecommunications and information theory
Thresholds
Yield estimation
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Description
Summary:In this paper, some new estimators of the frequency of a single complex sinusoid are presented. The rotate-add-decimate (RAD) method of Crozier is first refined to more closely approach the Cramer-Rao Bound (CRB). An additional modification yields an unbiased estimator (ERAD) that essentially achieves the CRB above a signal-to-noise ratio (SNR) threshold comparable to that of RAD. In addition, this estimator is proven to achieve the CRB for high SNR. The ERAD method requires approximately 2N complex multiply-adds and log/sub 2/N arctangents. A modified ERAD (MERAD) is proposed that matches the SNR threshold and computational complexity of the RAD method (approximately 3N complex multiply-adds and log/sub 2/N arctangents) but achieves the CRB for high SNR.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.870549