Metrology and Measurement Systems

Sienkowski, S.; Krajewski, M.

doi:10.24425/119561

Cited by 3 publications

References 23 publications

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Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

et al. 2021

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To improve frequency resolution, assignments of sub-bins within the bin interval of the conventional discrete Fourier transform are proposed by decreasing the number of sampled data. The simulated and experimental results of the basic sub-bin spectrum characteristics are presented. Using a signal oscillator, digital oscilloscope, and PC, the sub-bin line spectrum between two conventional bins is measured, and nine line spectra of sub-bins corresponding to the simulated results are measured. The linearity of the sub-bin spectrum intensity for amplitudes of 0.001–10 V of the input signal is also measured. The Doppler signals from the optical interferometer using a He–Ne laser are measured using a mixer to tune the frequency. A sub-bin spectrum of 104.89 kHz between two bin frequencies of 104.49 and 105.47 kHz is measured using 256 data points at a sampling frequency of 250 kHz and an acquisition time of 1.024 ms. The precision of displacement for the acquisition time is improved by one order to 32 nm for a full displacement of 2.342 µm. The sub-bins, as a composition of bin structure, are applicable to various fields.

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Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

et al. 2021

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Frequency resolution improvement by sub-bins and an inverse matrix in discrete Fourier transform

Sato¹,

Nakabayashi²,

Ito³

et al. 2023

Appl. Opt.

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We proposed a method to use sub-bins (SBs) and the inverse matrix to reduce the spectral leakage in discrete Fourier transform (DFT) over the conventional spectral resolution. SBs were assigned between two conventional bins. Utilizing the real signal, the process reproducing complex amplitudes at each SB was described and confirmed through simulations with the pseudo-inverse matrix. In experiments, with the 256 number of data, the frequency interval of k=107 and 108 was 4 divided by SBs. The single-peak spectrum at each SB frequency was measured clearly. Using the two signals with frequencies corresponding to two SBs within the conventional bin interval, the spectrum with two peaks was also measured. The linearity was confirmed for the input range from 0.1–5 V. The feasibility of this method to improve the frequency resolution has been shown for various optical applications.

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Metrology and Measurement Systems

Sienkowski

Krajewski

2020

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This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation(RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage(experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error(MSE) to compare the estimators. The errors were juxtaposed with the Cramér-Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR > 25 dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.

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Metrology and Measurement Systems

Cited by 3 publications

References 23 publications

Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

Frequency resolution improvement by sub-bins and an inverse matrix in discrete Fourier transform

Metrology and Measurement Systems

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