Tracking abrupt frequency changes

Li, Ta‐Hsin; Kedem, Benjamin

doi:10.1111/1467-9892.00077

Cited by 9 publications

(8 citation statements)

References 10 publications

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“…In the Fourier domain this represents a single peak (from the sinusoid) and a large noisy background. The Quinn-Fernandes technique [22,43] introduces two filters, one IIR filter and one FIR filter. The IIR filter has a pole which enhances one particular frequency B(e iω ) = 0.…”

Section: Appendix B: Notch Filtering and The Quinn-fernandes Methodsmentioning

confidence: 99%

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Frequency tracking and parameter estimation for robust quantum state estimation

2011

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In this paper we consider the problem of tracking the state of a quantum system via a continuous weak measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency.

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Section: Appendix B: Notch Filtering and The Quinn-fernandes Methodsmentioning

confidence: 99%

“…The Quinn-Fernandes technique belongs to a class called adaptive notch filters [22,43]. The general idea is to introduce a filter than removes a particular frequency from the signal, the "notch" frequency.…”

Section: The Quinn-fernandes Techniquementioning

confidence: 99%

Frequency tracking and parameter estimation for robust quantum state estimation

2011

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“…To prove this assertion, consider the expressions of the contraction coefficient C n (α,α n ) given in Tables 1 and 2. According to (19) and (20),…”

Section: B a Three-step Algorithmmentioning

confidence: 99%

“…A typical IF algorithm repeats the steps of enhancing the sinusoids with a bandpass filter and estimating the frequencies on the basis of the filtered data. Since recursive filters are often employed by IF algorithms, the frequency estimates can be easily updated upon the arrival of new observations in order to track possible frequency changes (e.g., [16]- [19]). The general premise of the IF approach is that as the frequency estimates become more accurate, the filter, which depends on the frequency estimates, would enhance the sinusoids more effectively and thus further improve the precision of frequency estimation in the subsequent cycle of iteration.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation

Song

2002

IEEE Trans. Inform. Theory

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Based on an asymptotic analysis of the contraction mapping (CM) method of Li and Kedem (IEEE Trans. Inform. Theory, vol. 39, pp. 989-998, 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 judiciously chosen bandwidth parameters according to the asymptotic analysis, the algorithm is shown to be able to accommodate possibly poor initial values of precision O(n −1/3) and converge to a final estimate whose accuracy is arbitrarily close to O(n −3/2), 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 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.

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“…An alternative approach is to utilize an autoregressive (AR) approximation. The AR procedure has well-established statistical properties (see [14][15][16][17][18][19][20][21][22] and [39]) and allows a simple and accurate iterative estimation of unknown frequency. However, the AR-based frequency estimates are asymptotically biased when the order k of an approximating AR model is fixed (see [15]).…”

Section: Introductionmentioning

confidence: 99%

Autoregressive frequency detection using Regularized Least Squares

Chen

Gel²

2010

Journal of Multivariate Analysis

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a b s t r a c tTracking of an unknown frequency embedded in noise is widely applied in a variety of applications. Unknown frequencies can be obtained by approximating generalized spectral density of a periodic process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure and its parameters can be easily estimated iteratively, which is crucial for online (real-time) applications. Typically, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size, model order may change, which leads to re-estimation of all model parameters. We propose a new iterative procedure for frequency detection based on a regularization of an empirical information matrix. The suggested method enables to avoid the repeated model selection as well as parameter estimation steps and therefore optimize computational costs. The asymptotic properties of the proposed regularized AR (RAR) frequency estimates are derived and performance of RAR is evaluated by numerical examples.

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Tracking abrupt frequency changes

Cited by 9 publications

References 10 publications

Frequency tracking and parameter estimation for robust quantum state estimation

Frequency tracking and parameter estimation for robust quantum state estimation

Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation

Autoregressive frequency detection using Regularized Least Squares

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