Reformulation of Pisarenko Harmonic Decomposition Method for Single-Tone Frequency Estimation

So, Hing Cheung; Chan, K.W.

doi:10.1109/tsp.2004.823473

Cited by 67 publications

(35 citation statements)

References 22 publications

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“…Using the method of Lagrange multipliers, the problem of minimizing (6) subject to (12) can be solved as follows. Define the Lagrangian (13) where is the Lagrange multiplier. Differentiating with respect to and then setting the resultant expression to zero yields (14) where is the estimate of up to a scalar, and is given by [22] the generalized eigenvector corresponding to the smallest generalized eigenvalue of ( , ).…”

Section: Weighted Least Squares Frequency Estimation With Generamentioning

confidence: 99%

“…The motivation of this paper is to investigate if the LP approach can attain optimum frequency estimation performance for multiple real sinusoids. In our previous work [13], a simple frequency estimator for a single real tone is devised based on the framework of Pisarenko [14], who was the first to exploit the eigenstructure of the covariance matrix in frequency estimation. Although it is an improvement to the original Pisarenko harmonic decomposition (PHD) method, the algorithm does not give efficient estimates and cannot be extended to multiple frequency estimation.…”

Section: Introductionmentioning

confidence: 99%

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Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Chan

et al. 2005

IEEE Trans. Signal Process.

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100

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Abstract-Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Cramér-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.

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Section: Weighted Least Squares Frequency Estimation With Generamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Chan

et al. 2005

IEEE Trans. Signal Process.

Self Cite

100

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“…In Fig. 4, the curve "c" shows the simulation results of the reformed Pisarenko harmonic decomposition (RPHD) frequency estimator, proposed recently [12], as a frequency estimator for single real sinusoids. This estimator is essentially obtained replacing the AC lags in (12) with some data dependent statistic which can be considered as perturbed AC lag estimates.…”

Section: Trade-off Between Signal Power and Variance Lower Boundmentioning

confidence: 99%

Phase dependence mitigation for autocorrelation-based frequency estimation

Altınkaya

Anarım

Sankur

2008

Digital Signal Processing

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The sinusoidal frequency estimation from short data records based on Toeplitz autocorrelation (AC) matrix estimates suffer from the dependence on the initial phases of the sinusoid(s). This effect becomes prominent when the impact of additive noise vanishes, that is at high signal-to-noise ratios (SNR). Based on both analytic derivation of the AC lag terms and simulation experiments we show that data windowing can mitigate the limitations caused by the phase dependence. Thus with proper windowing, the variance of the frequency estimate is no more eclipsed by phase dependence, but it continues to decrease linearly with increasing SNR. The study covers both the cases of a single sinusoid and two sinusoids closely spaced in the frequency with the Pisarenko frequency estimator, MUSIC and principal component autoregressive frequency estimators. The trade-offs between the spectral broadening and the achieved minimum variance level due to the data window are analyzed in detail.

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Section: Introductionmentioning

confidence: 99%

“…So and Chan [4] have shown that the PHD estimation performance can be improved if the data matrix is employed instead of the covariance matrix. By incorporating the technique of weighted least squares (WLS) into [4], the resultant algorithm [5] can provide optimum accuracy. Recently, Elasmi-Ksibi et al [6] have also extended [3] with the use of a normalized second-order infinite impulse response notch filter, whose frequency variance can attain Cramér-Rao lower bound (CRLB) [1] when ω is close to 0.5π.…”

Section: Introductionmentioning

confidence: 99%

Efficient frequency estimation of a single real tone based on principal singular value decomposition

Chan

Sun

2012

Digital Signal Processing

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The problem of single-tone frequency estimation for a discrete-time real sinusoid in white Gaussian noise is addressed. We first show that the frequency information is embedded in the principal singular vectors of a matrix which stores the observed data with no repeated entry. The technique of weighted least squares is then utilized for finding the frequency from the singular vectors. It is proved that the variance of the frequency estimate approaches Cramér-Rao lower bound when the data observation length tends to infinity. The computational efficiency and estimation accuracy are demonstrated via computer simulations.

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Reformulation of Pisarenko Harmonic Decomposition Method for Single-Tone Frequency Estimation

Cited by 67 publications

References 22 publications

Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Phase dependence mitigation for autocorrelation-based frequency estimation

Efficient frequency estimation of a single real tone based on principal singular value decomposition

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