An algebraic approach to fast perturbed sinusoidal signal parameters identification
MIC'06 Proceedings of the 25th IASTED international conference on Modeling, indentification, and control
Frequency estimation via multiple lags of correlations in the presence of broadband colored noise
Signal Processing - Special section: Distributed source coding
Estimation of the parameters of sinusoidal signals in non-Gaussian noise
IEEE Transactions on Signal Processing
Journal of Multivariate Analysis
Hi-index | 754.84 |
Based on an asymptotic analysis of the contraction mapping (CM) method of Li and Kedem (1993), a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements. The CM frequency estimates are defined as the fixed points of a contractive mapping formed by the lag-one autocorrelation coefficient calculated from the output. of a parametric filter applied to the observed time series. With bandwidth parameters judiciously chosen according to the asymptotic analysis, the algorithm is shown to be able to accommodate possibly poor initial values of precision O(n-13/) and converge to a final estimate whose accuracy is arbitrarily close to O(n-32/), the optimal error rate for frequency estimation under the Gaussian assumption. The total computational complexity of the algorithm is shown to be O(n log n), which is comparable to that of n-point fast Fourier transform (FFT). A novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n. This enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other.