Accurate Frequency Estimation for Real Harmonic Sinusoids

Chan, K.W.; So, Hing Cheung

doi:10.1109/lsp.2004.830115

Cited by 79 publications

(45 citation statements)

References 22 publications

(29 reference statements)

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“…In this Section, we will derive the WLS frequency estimator with monic constraint based on (24). With the constraint of , we partition as (27) where (28) The data matrix is then partitioned accordingly as (29) . .…”

Section: Weighted Least Squares Frequency Estimation With Monic Cmentioning

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 Monic Cmentioning

confidence: 99%

“…In the following, we will derive the bias and variance for the monic constraint estimator, and the results should hold for the unit-norm constraint method as . Partitioning and into and as in (29), and expressing in terms of with the use of , (31) …”

Section: Relationship Between Estimators and Performance Analysismentioning

confidence: 99%

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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“…We can obtain the following error function for the orthogonal decomposition approach (23) Compared to the classical filtering approach, the orthogonal decomposition approach has an extra noise term, namely the residual interference [12]. Moreover, the desired signal is different from the desired signal in the classical filtering approach.…”

Section: A Orthogonal Decompositionmentioning

confidence: 99%

Non-Causal Time-Domain Filters for Single-Channel Noise Reduction

Jensen

Benesty

Christensen

et al. 2012

IEEE Trans. Audio Speech Lang. Process.

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Abstract-In many existing time-domain filtering methods for noise reduction in, e.g., speech processing, the filters are causal. Such causal filters can be implemented directly in practice. However, it is possible to improve the performance of such noise reduction filtering methods in terms of both noise suppression and signal distortion by allowing the filters to be non-causal. Non-causal timedomain filters require knowledge of the future, and are therefore not directly implementable. If the observed signal is processed in blocks, however, the non-causal filters are implementable. In this paper, we propose such non-causal time-domain filters for noise reduction in speech applications. We also propose some performance measures that enable us to evaluate the performance of non-causal filters. Moreover, it is shown how some of the filters can be updated recursively. Using the recursive expressions, it is also shown that the output SNRs of the filters always increase as we increase the length of the filter when the desired signal is stationary. From both the theoretical and practical evaluations of the filters, it is clearly shown that the performance of time-domain filtering methods for noise reduction can be improved by introducing non-causality.Index Terms-Linearly constrained minimum variance (LCMV) filter, maximum signal-to-noise ratio (SNR) filter, minimum variance distortionless response (MVDR) filter, noise reduction, non-causal filters, performance measures, time-domain filtering, Wiener filter.

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“…It occurs in many speech and audio applications, where it plays an important role in the characterization of such signals, but also in radar and sonar. Many different methods have been invented throughout the years to solve this problem, with some examples being the following: linear prediction [2], correlation [3][4][5][6][7], subspace methods [8][9][10], frequency fitting [11], maximum likelihood [12][13][14][15][16], cepstral methods [17], Bayesian estimation [18][19][20], and comb filtering [21][22][23]. Note that several of the listed methods can be interpreted in several ways, as we will also see examples of in this paper.…”

Section: Introductionmentioning

confidence: 99%

Joint fundamental frequency and order estimation using optimal filtering

Christensen

Jensen

Jakobsson

et al. 2011

EURASIP J. Adv. Signal Process.

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In this paper, the problem of jointly estimating the number of harmonics and the fundamental frequency of periodic signals is considered. We show how this problem can be solved using a number of methods that either are or can be interpreted as filtering methods in combination with a statistical model selection criterion. The methods in question are the classical comb filtering method, a maximum likelihood method, and some filtering methods based on optimal filtering that have recently been proposed, while the model selection criterion is derived herein from the maximum a posteriori principle. The asymptotic properties of the optimal filtering methods are analyzed and an order-recursive efficient implementation is derived. Finally, the estimators have been compared in computer simulations that show that the optimal filtering methods perform well under various conditions. It has previously been demonstrated that the optimal filtering methods perform extremely well with respect to fundamental frequency estimation under adverse conditions, and this fact, combined with the new results on model order estimation and efficient implementation, suggests that these methods form an appealing alternative to classical methods for analyzing multi-pitch signals.

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Accurate Frequency Estimation for Real Harmonic Sinusoids

Cited by 79 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

Non-Causal Time-Domain Filters for Single-Channel Noise Reduction

Joint fundamental frequency and order estimation using optimal filtering

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