Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones

Macleod, M.D.

doi:10.1109/78.651200

Cited by 249 publications

(159 citation statements)

References 19 publications

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“…The problem of detecting multiple sinusoids in a musical signal is often framed as a successive search for a single sinusoid in the Short-Time Fourier Transform (STFT) domain [8]. Framing the problem in this way essentially ignores the effect of interferers-nearby sinusoids whose sidelobes may tilt magnitude spectrum peaks slightly so that they no longer correspond exactly to sinusoidal components.…”

Section: Introductionmentioning

confidence: 99%

“…Despite this, the approach of a successive search for sinusoids allows a complex problem to be broken down into many manageable simple problems without, e.g., any assumption of harmonic structure in the signal. Therefore, in this article, we formalize the problem as the search for a single sinusoid-in practical situations the search will be repeated in each frame until all sinusoids of interest are detected and their parameters estimated [8].…”

Section: Introductionmentioning

confidence: 99%

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Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Werner

Germain

2016

Applied Sciences

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Abstract:The magnitude of the Discrete Fourier Transform (DFT) of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude) of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Werner

Germain

2016

Applied Sciences

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“…However, this is not explored any further in this paper. The normal approximation of p(ω|x, g, l) is p(ω|x, g, l) ≈ N 2 (ω;ω, s l (ω|g)) (54) whereω is the mode of p(ω|x, g, l) corresponding to the MAP estimate of the fundamental frequency, and…”

Section: B the Distribution On The Fundamental Frequencymentioning

confidence: 99%

“…To get the MAP estimate in (58), the approximate MAP estimate in (59) may be used as the starting point of a local optimisation using the exact cost-function in (58). The local optimisation can also be substituted for faster and approximate techniques based on, e.g., interpolation [54]. In order to find the variances s l (ω|g) and s l (ω), the second order derivatives of ln p(ω|x, g, l) and ln p(ω|x, l) must be found and evaluated at the modeω.…”

Section: B the Distribution On The Fundamental Frequencymentioning

confidence: 99%

Default Bayesian Estimation of the Fundamental Frequency

Nielsen

Christensen

Jensen

2013

IEEE Trans. Audio Speech Lang. Process.

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Abstract-Joint fundamental frequency and model order estimation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real-and complex-valued discrete-time signals which may have missing samples or may have been sampled at a non-uniform sampling frequency. The observation model and prior distributions corresponding to the prior information are derived in a consistent fashion using maximum entropy and invariance arguments. Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance of the approximations are evaluated in a small-scale simulation study on both synthetic and real world signals. The simulations indicate that the proposed algorithm yields more accurate results than previous algorithms. The simulation code is available online.

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“…A multitude of methods for determining the frequency of a monochromatic pulse have been developed (Pisarenko, 1973;Chan et al, 1981;Kay and Marple, 1981;McMahon and Barett, 1986;Quinn, 1994Quinn, , 1997MacLeod, 1998;Aboutanios and Mulgrew, 2005;Provencher, 2010;Candan, 2011). The method used in this paper is explained in Appendix A.…”

Section: Frequency Determinationmentioning

confidence: 99%

High-precision measurement of satellite velocity using the EISCAT radar

Nygrén

Markkanen²,

Aikio

et al. 2012

Ann. Geophys.

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Abstract. This paper presents a method of measuring the velocity of a hard target using radar pulses reflected from the target flying through the radar beam. The method has two stages. First, the Doppler shifts of the echo pulses are calculated at a high accuracy with an algorithm which largely improves the accuracy given by the Fourier transform. The algorithm also calculates the standard deviations of the Doppler frequencies with Monte Carlo simulation. The second step is to fit the results from a sequence of radar pulses to a velocity model allowing linear variation of the second time derivative of target range. The achieved accuracies are demonstrated using radio pulses reflected by a satellite passing through the beam of the EISCAT UHF radar working at 930-MHz frequency. At high SNR levels, the standard deviations of the frequency from a single pulse reach typically down to 0.2 Hz. The best standard deviations of velocity fit are below 5 mm s −1 while those of the second time derivative of range are below 1 cm s −2 .

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Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones

Cited by 249 publications

References 19 publications

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Default Bayesian Estimation of the Fundamental Frequency

High-precision measurement of satellite velocity using the EISCAT radar

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