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

Werner, Kurt James; Germain, François G.

doi:10.3390/app6100306

Cited by 11 publications

(28 citation statements)

References 37 publications

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“…It is discussed in many publications, e.g. [15,16,18,19,21], but the results of these works are not unambiguous and they are even contradictory in some cases. The conclusions of the presented analysis explain why it is and what the principles for optimal use of suitable window functions should be.…”

Section: Ways For Minimizing Leakage Deviations From Sinc Functionmentioning

confidence: 99%

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The Causes of Leakage Deviations from sinc Function in DFT and Ways to Minimize Them

Hájek¹

2020

AiMT

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The article describes a new model for the solution of the instability problem of discrete Fourier transform (DFT) spectra leakage for the incoherent real sinusoidal signal for solving the most accurate estimation of its frequency. This paper shows this phenomenon by a new form of DFT spectrum expression. It consists mainly of the spectrum of the rectangular signal in the form of the sinc function, modulated to the frequency of the tested signal in baseband. To do this, analogous spectra from other neighboring bands formed by the sampling effect are added as aliasing. The analysis shows some ways to minimize or correct it. The paper shows a simpler and substantially lesser effect of aliasing in the DFT spectrum for a complex valued sinusoidal signal.

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Section: Ways For Minimizing Leakage Deviations From Sinc Functionmentioning

confidence: 99%

“…The attempt to estimate as accurately as possible the frequency of the harmonic component of the signal under testing is a typical example of this problem. This is dealt with in many publications, such as [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

The Causes of Leakage Deviations from sinc Function in DFT and Ways to Minimize Them

Hájek¹

2020

AiMT

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“…In literature, a large number of estimation methods for the frequency position and amplitude are available after performing a DFT or FFT, for example the interpolation or iterative interpolation between 3 to 5 discrete neighbouring spectral lines [3][4][5][6][7][8][9][10][11][12][13]. Further scientific works solve the estimation problem by means of iterative optimization methods [14][15][16][17][18][19][20] and still others use model based methods, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…These are, e.g. the Cramer-Rao lower bound (CRLB) [3][4][5][6], [27,28] and [34,35], which represents the lower limit for the MSE of an estimator and the spline interpolation of at least two spectral lines. In chapter 4, the estimator is applied to real vibration signals of a tram gearbox to evaluate its performance in practice.…”

Section: Introductionmentioning

confidence: 99%

Amplitude and frequency estimator for aperiodic multi-frequency noisy vibration signals of a tram gearbox

Wolf¹,

Rudolph²,

Kanoun³

2021

J. vibroeng.

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Sinusoidal parameter estimation for determining frequency position and amplitude is challenging for noisy short vibration signals, e.g. from machines or human vibrations. In this paper, we propose the "Trimmed Window Discrete Fourier Transform" (TWDFT) estimator, which uses for every frequency a one-point discrete Fourier transform (DFT) to determine the corresponding spectral amplitude. To avoid leakage effects, it cuts the time interval so that it corresponds to an integer number of period durations. To evaluate the estimator performance, we compare it with relevant estimators such as the Cramer-Rao lower bound (CRLB) and the spectral spline interpolation applied on a noisy mono-frequent test signal with a fractional frequency. For the estimated parameters, the mean squared errors (MSE) are calculated and compared as a function of the signal-to-noise ratio (SNR). The advantages of the TWDFT estimator can be seen over the whole SNR range. The TWDFT estimates are better than the fast Fourier transform (FFT) starting at a SNR of -6 dB. At a SNR of 30 dB, the estimator meets the real value of the frequency and reaches similar results as the CRLB. The application of the TWDFT estimator as a short-time analysis on a vibration signal of a tram gearbox shows a significantly more differentiated time-frequency analysis compared to a short-time Fourier transform (STFT).

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“…The commonly used signal frequency estimation method in recent years is a twostep method involving rough estimation followed by fine estimation. The rough estimation is achieved through discrete Fourier transform (DFT) of the signal and the fine estimation is achieved by modifying the rough estimation using the ratio method or other methods [4][5][6][7]. There are many other methods directly based on time-domain signals, such as the autocorrelation algorithm and linear prediction algorithm [8,9].…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation of weak space‐based ADS‐B signals using genetic algorithm

Tao

Liang

2020

ETRI Journal

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Space-based automatic dependent surveillance-broadcast (ADS-B) is an important emerging augmentation of existing ground-based ADS-B systems. In this paper, the problem of space-based ultra-long-range reception processing of ADS-B signals is described. We first introduce a header detection method for accurately determining the pulse position of a weak ADS-B signal. We designed a signal encoding method, shaping method, and fitness function. We then employed a genetic algorithm to perform high-precision frequency and phase estimations of the detected weak signal.The advantage of this algorithm is that it can simultaneously estimate the frequency and phase, meaning a direct coherent demodulation can be implemented. To address the computational complexity of the genetic algorithm, we improved the ratio algorithm for frequency estimation and raised the accuracy beyond that of the original ratio algorithm with only a slight increase in the computational complexity using relatively few sampling points.

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

Cited by 11 publications

References 37 publications

The Causes of Leakage Deviations from sinc Function in DFT and Ways to Minimize Them

The Causes of Leakage Deviations from sinc Function in DFT and Ways to Minimize Them

Amplitude and frequency estimator for aperiodic multi-frequency noisy vibration signals of a tram gearbox

Parameter estimation of weak space‐based ADS‐B signals using genetic algorithm

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