## AN UNBIASED PISARENKO HARMONIC DECOMPOSITION ESTIMATOR FOR SINGLE-TONE FREQUENCY

Citations: | 1 - 0 self |

### Citations

414 |
Modern Spectral Estimation: Theory and Application
- Kay
- 1988
(Show Context)
Citation Context ...he sample covariance matrix, can be derived [8] in an alternative and simpler manner with the sample covariance of x(n) with lags 1 and 2. Inspired by the modified covariance (MC) frequency estimator =-=[2]-=-, we devise an unbiased variant of the PHD estimate. The frequency variance of the unbiased PHD method is also analyzed. Numerical examples are presented in Section 3 to ©2007 EURASIP 956 corroborate ... |

405 |
Digital spectral analysis with applications
- MARPLE
- 1987
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Citation Context ...heoretical development and to demonstrate its superiority over the MC and original PHD algorithms. 1. INTRODUCTION Estimating the frequency of a sinusoid in noise has been an important research topic =-=[1]-=--[5] because of its wide applicability in control theory, signal processing, digital communications, biomedical engineering as well as instrumentation and measurement. The discrete-time signal model f... |

200 |
Spectral Analysis of Signals
- Stoica, Moses
- 2005
(Show Context)
Citation Context ...etical development and to demonstrate its superiority over the MC and original PHD algorithms. 1. INTRODUCTION Estimating the frequency of a sinusoid in noise has been an important research topic [1]-=-=[5]-=- because of its wide applicability in control theory, signal processing, digital communications, biomedical engineering as well as instrumentation and measurement. The discrete-time signal model for s... |

50 | The estimation and tracking of frequency - Quinn, Hannan - 2001 |

31 |
List of references on spectral line analysis
- Stoica
- 1993
(Show Context)
Citation Context ...inear and multimodal cost function and thus extensive computations are involved. For applications where real-time estimation is required, computationally efficient but suboptimal frequency estimators =-=[3]-=- such as notch filtering, Capon methods, linear prediction, Yule-Walker methods and subspace based approaches are widely used choices. In this work, we focus on fast frequency estimation of a real-val... |

13 |
Maximum likelihood estimation of the parameters of a tone using real discrete data
- Kenefic, Nuttall
- 1987
(Show Context)
Citation Context ...s assumed to be a zero-mean white process with unknown variance σ 2 . The task is to find ω from the N samples of {x(n)}. Under Gaussian noise assumption, the maximum likelihood estimate of frequency =-=[6]-=- is obtained by maximizing a highly nonlinear and multimodal cost function and thus extensive computations are involved. For applications where real-time estimation is required, computationally effici... |

10 |
The retrieval of harmonics by linear prediction,” Geophys
- Pisarenko
- 1973
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Citation Context ... on fast frequency estimation of a real-valued tone in white noise. The rest of the paper is organized as follows. In Section 2, we first review that the Pisarenko harmonic decomposition (PHD) method =-=[7]-=-, which exploits the eigenstructure of the sample covariance matrix, can be derived [8] in an alternative and simpler manner with the sample covariance of x(n) with lags 1 and 2. Inspired by the modif... |

9 |
On Pisarenko and constrained Yule-Walker estimator of tone frequency
- Xiao, Tadokoro
- 1994
(Show Context)
Citation Context ...er is organized as follows. In Section 2, we first review that the Pisarenko harmonic decomposition (PHD) method [7], which exploits the eigenstructure of the sample covariance matrix, can be derived =-=[8]-=- in an alternative and simpler manner with the sample covariance of x(n) with lags 1 and 2. Inspired by the modified covariance (MC) frequency estimator [2], we devise an unbiased variant of the PHD e... |

9 | An Exact Analysis of Pisarenko's Single-Tone Frequency Estimation Algorithm
- Chan, So
- 2003
(Show Context)
Citation Context ...erior to the standard ones. As a result, our proposed frequency estimate is obtained by substituting (9) and (10) into (6). To derive the variance of the modified PHD estimator, we follow the work of =-=[9]-=-. From (5), we define a quadratic function f (ρ): f (ρ) = 2r1ρ 2 − r2ρ − r1 (13) where ρ = cos( ˆω) is one of its roots. For sufficiently large N and/or signal-to-noise ratio (SNR), this root will be ... |