Accurate Amplitude Estimation of Harmonic Components of Incoherently Sampled Signals in the Frequency Domain

Belega, Daniel; Dallet, Dominique; Slepička, David

doi:10.1109/tim.2010.2045144

Cited by 33 publications

(13 citation statements)

References 17 publications

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“…The superposed noise and jitter will, in simulation performed in this way, cause a relative error in detection on fundamental frequency of 0.001 %. It can be seen that the accuracy of the proposed algorithm is within the limits that are attained in processing a signal of this form, in [17,21,[23][24][25], and better then the one presented in [26]. In the time domain, the relative error between the signal and its reconstruction was 0.0025 %.…”

Section: Simulation Resultsmentioning

confidence: 69%

“…Fig.4 and 5 depict the MSE of the amplitudes and frequency after 10 5 simulations, respectively. Results clearly show that the proposed estimation schemes asymptotically reach the CRLB as in [21,22]. Additional testing of the proposed algorithm was carried out by simulation in the program package Matlab and SIMULINK.…”

Section: Simulation Resultsmentioning

confidence: 92%

“…Noisy samples are obtained by adding white noise samples to the samples of processing signal. For the estimation of deterministic parameters, a commonly used lower bound for the mean square error (MSE) is the Cramer-Rao lower bound (CRLB), given by inverse of the Fisher information [19][20][21]. Fig.4 and 5 depict the MSE of the amplitudes and frequency after 10 5 simulations, respectively.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Frequency and parameter estimation of multi-sinusoidal signal

Petrović¹

2012

Measurement Science Review

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Estimating the fundamental frequency and harmonic parameters is basic for signal modeling in a power supply system. This paper presents a complexity-reduced algorithm for signal reconstruction in the time domain from irregularly spaced sampling values. Differing from the existing parameter estimation algorithms, either in power quality monitoring or in harmonic compensation, the proposed algorithm enables a simultaneous estimation of the fundamental frequency, the amplitudes and phases of harmonic waves. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. It is proved that the estimation performance of the proposed algorithm can attain Cramer-Rao lower bound (CRLB) for sufficiently high signal-to-noise ratios. The proposed algorithm can be applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The simulation and experimental results verify the effectiveness of the proposed algorithm.

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Section: Simulation Resultsmentioning

confidence: 69%

Section: Simulation Resultsmentioning

confidence: 92%

Section: Simulation Resultsmentioning

confidence: 99%

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Frequency and parameter estimation of multi-sinusoidal signal

Petrović¹

2012

Measurement Science Review

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“…The expression of the CRLB for amplitude estimation appears in [8] based on [10]. This also means The log-log scale of Fig.…”

Section: Cramér-rao Lower Bound For Amplitude Estimationmentioning

confidence: 95%

Theoretical Limits of Parameter Estimation Based on Quantized Data

Virosztek

Kollár

2017

Period. Polytech. Elec. Eng. Comp. Sci.

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Parameter estimation of band-limited periodic signals (sine and multisine waves) is a very common task in the field IntroductionThe aim of this paper is to investigate the theoretical limits and practical properties of quantizer and signal parameter estimation in that case when parameters of the excitation signal and the quantizer has to be estimated from the same measurement record. This kind of estimation is necessary in the following scenarios:• A band-limited periodic signal has been acquired via analog-to digital conversion. The signal contains harmonic components and additive noise, and the quantization of the signal is non-ideal. However the parameters (DC offset, frequency and the Fourier components) of the signal shall be estimated paying attention to the nonidealities of the measurement channel (the quantizer). The estimated parameters can be used for multiple applications: o to determine power quality based on the harmonic content of the voltage signal of a power transmission line o to control the frequency of a power transmission network based on accurate estimation of system frequency o to qualify an audio amplifier based on the harmonic distortion and the amount of noise at the output and naturally other applications may exist.• The aim is to qualify the analog-to-digital converter using standard quality measures e.g. effective number of bits (ENOB), signal to noise and distortion ratio (SINAD), integral nonlinearity (INL) differential nonlinearity (DNL), etc. These quantities can be calculated based on the parameter estimators using elemental mathematical operations. Owing to the properties of maximum likelihood estimators [1] the quality measures calculated using the ML estimators of the signal and quantizer parameters are the ML estimators of the quality measures. This way applying a sinusoidal excitation -which necessarily contains additive noise and harmonic components depending on the quality of the sine wave generator -and then calculating the ML estimators of the quantizer and excitation signal parameters one can achieve asymptotically unbiased and asymptotically efficient estimators for the quality measures of the quantizer.

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“…sine waves with a low amplitude with respect to the measurement range of an analog-to-digital (A/D) converter) occur in many application fields ranging from aerospace to industrial processes (e.g. see [1][2][3]). The amplitude estimation of a sine wave can be performed either in the time domain or in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

On the Validity of the Noise Model of Quantization for the Frequency-Domain Amplitude Estimation of Low-Level Sine Waves

Bellan¹

2015

Metrology and Measurement Systems

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This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models.

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Accurate Amplitude Estimation of Harmonic Components of Incoherently Sampled Signals in the Frequency Domain

Cited by 33 publications

References 17 publications

Frequency and parameter estimation of multi-sinusoidal signal

Frequency and parameter estimation of multi-sinusoidal signal

Theoretical Limits of Parameter Estimation Based on Quantized Data

On the Validity of the Noise Model of Quantization for the Frequency-Domain Amplitude Estimation of Low-Level Sine Waves

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