Accurate Frequency Estimation Research Articles

Generalized Synchroextracting-Based Stepwise Demodulation Transform and Its Application to Fault Diagnosis of Rotating Machinery

The nonstationary characteristics of time-varying signals can be characterized by time–frequency analysis (TFA) accurately, which has been widely used in fault diagnosis of rotating machinery. However, some practical signals contain complex multicomponent modes and noise interference, which will pose challenges to traditional TFA methods. In this article, a novel technique called generalized synchroextracting-based stepwise demodulation (GSET-SD) transform is proposed. GSET-SD introduces a strategy that combines synchroextracting transform (SET) with a stepwise demodulation procedure, thereby solving the problem of detecting and retrieving the amplitude- and frequency-modulated (AM-FM) components of a multicomponent signal from the time–frequency representation (TFR), while allowing the signal to be reconstructed from the TFR. Furthermore, to increase the estimation accuracy of the initial instantaneous frequency (IF) in processing the strong modulation signals, SET is extended to the second-order or higher order domain, and the IF is accurately estimated by the higher order polynomial method, which can obtain higher resolution TFR. The proposed approach has been applied to numerical simulations and application research. The experimental results verify the effectiveness and superiority of GSET-SD in processing strong modulation signals and demonstrate its promise in the field of fault diagnosis of rotating machinery under time-varying speeds.

An Efficient Digital Channelized Receiver for Low SNR and Wideband Chirp Signals Detection

Synthetic aperture radar (SAR) is essential for obtaining intelligence in modern information warfare. Wideband chirp signals with a low signal-to-noise ratio (SNR) are widely used in SAR. Intercepting low-SNR wideband chirp signals is of great significance for anti-SAR reconnaissance. Digital channelization technology is an effective means to intercept wideband signals. The existing digital channelization methods have the following problems: the contradiction of reception blind zone and signal spectrum aliasing, high computational complexity, and low estimating accuracy for chirp signals with a low SNR. This paper proposes a non-critical sampling digital channelized receiver architecture to intercept chirp signals. The receiver architecture has no blind zone in channel division and no aliasing of signal spectrum in the channel, which can provide reliable instantaneous frequency measurements. An adaptive threshold generation algorithm is proposed to detect signals without prior information. In addition, an improved instantaneous frequency measurement (IFM) algorithm is proposed, improving low SNR chirp signals’ frequency estimation accuracy. Moreover, a simple channel arbitration logic is proposed to complete the cross-channel combination of wideband signals. Simulations show that the proposed receiver architecture is reliable and robust for low SNR and wideband chirp signal detection. When the input SNR is 0 dB, the absolute frequency root-mean-square error (RMSE) of bandwidth and the center frequency is 0.57 MHz and 1.05 MHz, respectively. This frequency accuracy is great for radio frequency (RF) wideband systems.

Synchronization and Control of a Single-Phase Grid-Tied Inverter under Harmonic Distortion

Grid-connected inverters in renewable energy systems must provide high-quality power to the grid according to regulatory standards such as the IEEE 1547. To provide high-quality current control when the inverter is connected to a distorted grid, the frequency and phase information of the fundamental harmonic of the grid should be accurately obtained. This paper examines controller design for a single-phase inverter when there is distortion in the grid voltage. The control structure is designed to enhance the quality of the injected current into the grid. To this end, a frequency-locked loop (FLL) sinusoidal tracking controller which is able to reject the grid harmonics is proposed. Thus, the contribution of this paper is a new frequency-locked loop structure with adaptive notch filters that can provide accurate estimation of grid phase and frequency and improve the performance of single-phase inverters working under harmonic distortion. We also present an explanation of how the proposed adaptive nonlinear scheme can be discretized for digital implementation on a microcontroller. Experimental and simulation results are presented to demonstrate the performance of the proposed controller in eliminating distortion and enhancing the quality of the produced power.

Doppler Frequency Estimation Based on Time Diversity of Random Processes in Doubly-Selective Channels

This work introduces a new method to estimate Doppler frequency which carries important characteristics feature of time-variant multipath fading channels. The proposed method employs the time diversity (TD) of general random processes with rich correlation characteristics introduced by various time intervals, where a maximum-likelihood (ML) algorithm is utilized. A closed-form weighted least-square equation is derived with the help of basis expansion approximation. In addition, the Cram <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\acute{\text{e}}$</tex-math></inline-formula> r-Rao lower bound (CRLB) of the estimation is analyzed. The results show that the proposed method performs well in terms of Doppler frequency estimation accuracy.

An Improved CZT Algorithm for High-Precision Frequency Estimation

Estimating the frequencies of multiple superimposed exponentials in noise is an important problem due to its various applications in engineering. In order to obtain good inhibition of spectral leakage and improve the estimation accuracy, an improved Chirp-Z transform (CZT) algorithm is proposed for high-precision frequency estimation. Firstly, the proposed algorithm analyzes the characteristics of the CZT spectrum and utilizes the CZT spectrum to construct a bias correction factor for frequency bias estimation. Then, an expression between the bias correction factor and the frequency estimation error is derived to obtain a more accurate estimate of the frequency bias. Finally, the frequency estimate of the CZT is corrected by the estimated frequency bias so as to obtain a higher frequency estimation accuracy. Compared with the conventional CZT algorithm, the proposed improved CZT algorithm achieves a higher frequency estimation accuracy by correcting the frequency estimate of the CZT method using the estimated frequency bias. The proposed improved CZT algorithm is verified using simulation studies and experimental results, and the results show that it has a higher accuracy and better robustness than the existing methods.

High-order Synchrosqueezing Superlets Transform and its application to mechanical fault diagnosis

Under the condition of variable speed, the vibration signal of mechanical transmission components present the typical non-stationary characteristics. Nevertheless, some problems, such as insufficient time–frequency energy concentration and frequent noise disturbance, exist in the current signal processing methods during the extraction of time-varying fault characteristics. Different from the frequently-used time–frequency analysis (TFA) methods such as Continuous Wavelet Transform (CWT) and Synchrosqueezing Transform (SST), High-order Synchrosqueezing Superlets Transform (HSSLT) is proposed in this paper in order to obtain a clearer and more centralized time–frequency representation (TFR). Firstly, multiple groups of wavelets with increased bandwidth are combined into a super wavelet set, and then the Superlets Transform (SLT) is proposed. The single wavelet mother function in the traditional CWT is replaced by this superlets set, which has better wavelet diversity and analytical ability for complex multi-component signals. On this basis, in order to further improve the accuracy of instantaneous frequency (IF) estimation and the energy concentration of TFA, the superlets coefficients calculated by SLT are used for the high-order IF estimation and time–frequency energy rearrangement, thereby HSSLT is presented in this paper. It has obvious advantages of high-resolution TFR and strong noise robustness. Finally, through the rolling bearing fault diagnosis of test bench and the 850 kW offshore wind turbine, the good application potential of the proposed HSSLT in the mechanical fault diagnosis under variable speed conditions is verified.

Analysis of ENF Signal Extraction From Videos Acquired by Rolling Shutters

Electric network frequency (ENF) analysis is a promising forensic technique for authenticating multimedia recordings and detecting tampering. The validity of the ENF analysis heavily relies on the capability of extracting high-quality ENF signals from multimedia recordings. This paper analyzes and compares two representative methods for extracting ENF signals from visual signals acquired by cameras using the rolling-shutter mechanism. The first method proposed in prior work, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct concatenation</i> , ignores the idle period of each frame. The second method proposed in this paper, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">periodic zeroing-out</i> , inserts zeros to missing sample points instead of ignoring the idle period. Our theoretical analyses of using multirate signal processing reveal and experiments confirm that while the first method can extract ENF signals without knowing the exact value of camera read-out time, there exists some mild distortion to extracted ENF signals. In contrast, the second method taking the read-out time as the additional input is capable of extracting distortion-free ENF signals, and its frequency component of the highest strength is always located at the nominal frequency. Additionally, we examine aliased DC and negative ENF components caused by the two methods and show that their impact on the accuracy of frequency estimation is minimum. This paper facilitates the fundamental understanding of extracting ENF signals from videos. The research findings imply that the periodic zeroing-out method offers more accurate frequency estimates, but the performance improvement is not significant.

Robust Frequency-Adaptive Quadrature Phase-Locked-Loops With Lyapunov-Certified Global Stability

This work describes and compares two phase-locked-loop (PLL) algorithms aimed at tracking a biased sinusoidal signal with unknown frequency, amplitude, and phase, with inherent robustness to dc offset. The proposed methods endow quadrature PLLs, renowned for their excellent tracking performance, with frequency-adaptation capability, while providing robust global stability certificates. The large-gain global stability, proved by Lyapunov-like arguments borrowed from adaptive control theory, represents a major benefit when compared to the conventional PLLs, whose convergence instead can be proved only locally by small-signal analysis or small-gain assumptions. In this connection, the proposed algorithms represent the first frequency-adaptive and dc-bias rejecting PLL-type architectures with Lyapunov-certified global stability. When used for signal tracking, the proposed methods are shown to outperform the adaptive observer, especially in noisy conditions. Moreover, they provide more accurate frequency estimates than existent frequency-adaptive PLLs, showing enhanced robustness in facing both phase-noise and measurement perturbations.

Multi-Vib

Vibration measurement is vital for fault diagnosis of structures (e.g., machines and civil structures). Different structure components undergo distinct vibration patterns, which jointly determine the structure's health condition, thus demanding simultaneous multi-point vibration monitoring. Existing solutions deploy multiple accelerometers along with their power supplies or laser vibrometers on the monitored object to measure multi-point vibration, which is inconvenient and costly. Cameras provide a less expensive solution while heavily relying on good lighting conditions. To overcome these limitations, we propose a cost-effective and passive system, called Multi-Vib, for precise multi-point vibration monitoring. Multi-Vib is implemented using a single mmWave radar to remotely and separately sense the vibration displacement of multiple points via signal reflection. However, simultaneously detecting and monitoring multiple points on a single object is a daunting task. This is because most radar signals are scattered away from vibration points due to their tilted locations and shapes by nature, causing an extremely weak reflected signal to the radar. To solve this issue, we dedicatedly design a physical marker placed on the target point, which can force the direction of the reflected signal towards the radar and significantly increase the reflected signal strength. Another practical issue is that the reflected signal from each point endures interferences and noises from the surroundings. Thus, we develop a series of effective signal processing methods to denoise the signal for accurate vibration frequency and displacement estimation. Extensive experimental results show that the average errors in multi-point vibration frequency and displacement estimation are around 0.16Hz and 14μm, respectively.

Estimation of Three-Dimensional Thoracoabdominal Displacements During Respiration Using Inertial Measurement Units

This article presents a wearable inertial measurement unit based system that estimates three-dimensional respiratory displacements on the thoracoabdominal surface. Such estimates can be useful in the calculation of respiratory rate, tidal volume, and for monitoring synchrony of compartments of the thoracoabdominal wall for diagnosis and physiotherapy. Challenges in estimating displacements from inertial sensors include drift due to sensor bias, errors due to the measurement of a large gravity component by accelerometers, and the need to compensate for real-time tilt angles from natural bending of the subject during breathing. An algorithm that combines double integration, high-pass filters, tilt angle estimation, and a Kalman smoother to estimate real-time gravity components along the sensor axes is utilized. The algorithm is facilitated by a special formulation of the gravity vector's kinematic model about the sensor axes. Preliminary experimental results show that the three-axes displacements are estimated with 1 mm accuracy at normal breathing frequencies of 0.25 Hz or higher, but lose some accuracy at lower breathing rates. The Kalman smoother which uses a combination of forward and backward filters is shown to provide significantly superior performance compared to a traditional Kalman filter, which only uses forward propagation. Additionally, the developed system also provides very accurate estimates of breathing frequency.

Impacts of sampling frequency on the estimation accuracy of exceedance for suspended solids and nitrates in streams in small to medium-sized watersheds

Data from a 389 km2 watershed and one of its 14.5 km2 subbasins were used to assess the effects of sampling frequency on the estimation accuracy of the exceedance frequency (EF) for suspended solids and nitrate-nitrogen in streams. Values of EF estimated from 17 subsampling schemes were compared with the actual EF (EFa) at different threshold concentrations. The coefficient of variation and relative bias were used to measure the estimation accuracy. Results indicated that the EFa of the larger watershed was much lower than that of the smaller watershed for both suspended solids and nitrate-nitrogen. We also found that EFa can be modeled as an exponential function of the threshold concentration. For the EF estimations, the coefficient of variation decreased with increasing sampling frequency and increasing EFa. The relative bias tended to be negative when EFa was low or the threshold concentration was high, reaching -75% in some cases. This result implies that reported EF values based on low-frequency data could be severely underestimated due to the high possibility of missing large events. However, there were also cases with positive relative bias, implying overestimation of EF due to over representation of large events. These findings can be used to determine adequate sampling frequencies for water-quality parameters, avoiding common observed biases (mostly negative) in the estimation of EF for extreme pollution events.

A novel coriolis mass flowmeter signal processing method based on adaptive notch filter and Hilbert transform

Coriolis mass flowmeter has been widely used in the energy field, and the key of mass flowrate measurement is to calculate the frequency and phase difference of the signal accurately. Aiming at the poor measurement precision problem in Coriolis mass flowmeter, a novel Coriolis mass flowmeter signal processing method is presented based on adaptive notch filter and Hilbert transform. Firstly, the long time continuous frequency tracking and accuracy problem of adaptive notch filter is effectively solved, by introducing the idea of negative feedback control. Then, the frequency estimation results are used to judgment whether the whole data will be extended or not, which makes the length of data sequence close to or equal to an integer multiple of the period. And then, Hilbert transform is conducted to the extended signals. Finally, the phase difference can be obtained by utilizing the sinusoidal functions. Simulation results show that the proposed method has high frequency and phase difference estimation accuracy, and it can be used for real time flowrate measurement of flowmeter. Experimental tests validate that the precision of this method is less than 3‰, which is more than 2 times of that of the traditional method.

Robust estimation of fundamental frequency positive-sequence component for grid-integration applications in energy systems

This article studies the problem of fundamental frequency positive-sequence component separation in unbalanced three-phase systems for grid-integration applications. We propose a-simple-to-implement approach involving a modified delayed signal cancellation method and moving average filtering. A delay-based linear-regression framework is considered to make the sequence component separation frequency-adaptive, providing fast and accurate frequency estimation. Comparative experimental results demonstrate the suitability of the proposed method over conventional approaches.

A Simple Structure for Accurate Estimation of Single-Phase Grid Frequency Under DC Offset and Both Odd and Even Harmonics

This article proposes an enhanced frequency-locked loop method for the single-phase grid frequency estimation under dc offset and both odd and even harmonics conditions. The proposed method relies on an adaptive recursive discrete Fourier transform-based frequency error detector and an integral controller. It offers a relatively simple structure and computationally efficient method. It can provide accurate frequency estimation at steady state under grid disturbances and takes a dynamic time of around one and half cycles of the fundamental frequency. The improved performance of the proposed method is verified by comparing it with the results of several existing methods reported in the technical literature. The efficacy of the proposed method is proved using simulated and real-time experimental results.

Accurate Frequency Estimator for Real Sinusoid Based on DFT

An accurate frequency estimator for real sinusoid based on Discrete Fourier Transform (DFT) is proposed. The proposed estimator is based on the interpolation of the maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) spectral lines and can operate with both the rectangular window and the maximum sidelobe decay (MSD) window. In the coarse estimation step, the proposed estimator with the MSD window is used. According to the value of the coarse estimate, the negative frequency spectral component is removed. In the fine estimation step, the proposed estimator with the rectangular window is utilized to achieve the Cramer–Rao lower bound (CRLB). Simulation results show that the performance of this algorithm is better than that of the AM algorithm, Candan algorithm, Djukanovic algorithm, and FDIAM algorithm.

Roll Eccentricity Signal Detection and Its Engineering Application Based on SFFT-IAA

The roll eccentricity signal is a weak and complex periodic signal that is difficult to be identified. To improve the detection accuracy of the roll eccentricity signal and to compensate effectively, this study proposed a roll eccentricity signal detection method by combining the sparse fast Fourier transform (SFFT) and the iterative adaptive approach (IAA). The proposed method can rapidly determine the frequency range of the roll eccentricity signal by using the SFFT. Then, it divides the frequency range into several small frequency bands. In each small frequency band, the frequency, amplitude, and phase angle of each harmonic component of the roll eccentricity signal were estimated by using IAA. The simulation results show that the proposed method can find all frequency components, and the frequency estimation accuracy is higher than 99.88%. Finally, the engineering application of this method and the eccentricity compensation control were investigated. In engineering applications, the proposed method can reduce the thickness fluctuation of the finished strip by 89.2%, and the product quality is improved significantly. The simulation results and engineering experiments show that the proposed method has an excellent effect on detecting and compensating roll eccentricity signals.

On-line harmonic signal denoising from the measurement with non-stationary and non-Gaussian noise

Harmonic denoising is one of the important preprocessing steps before extracting harmonic signal characteristics. Several signal processing techniques have been developed and applied for denoising the harmonics, which assume that the noise follows a Gaussian distribution and is stationary. However, the noise is often not so simple as a Gaussian distribution, and it could be non-Gaussian and non-stationary in most practical scenarios. A novel online denoising method for the harmonic signal with non-stationary complex noises based on the Bayesian Maximum a Posteriori (MAP) framework is proposed in this paper. The measured signal is divided equally into several frames. Then these frames are transformed into the time-frequency domain by the Short-Time Fourier transform (STFT) and are assumed to be the sum of a low-rank matrix and a noise matrix. The online model of the low-rank matrix and the noise matrix is then constructed between the frames. The online Gaussian mixture model (GMM) and low-rank matrix factorization are performed on the measurement matrix in the complex number domain to reconstruct the harmonic signal. The performance of the proposed method is validated in the simulations. The non-Gaussian and non-stationary noise can be removed more effectively, and the proposed algorithm can improve the frequency estimation accuracy.

Micro-Doppler Curves Extraction of Space Target Based on Modified Synchro-Reassigning Transform and Ridge Segment Linking

The micro-movement feature is recognized as one of the practical features of space target recognition in academic circles. The separation of the micro-Doppler curve of the scattering center is the key to feature extraction and parameter estimation, which depends on the time–frequency analysis method. The existing techniques have low separation accuracy and adaptability when there are overlap and noise in the time–frequency domain. This paper proposes a micro-Doppler feature extraction algorithm of a space target based on the modified synchro-reassigning transform (MSRT) and ridge segment linking. The MSRT can eliminate repeated assignment problems, has more accurate micro-Doppler frequency estimates than the synchro-reassigning transform, and has lower computational complexity than second-order synchronous compression and synchronous extraction transforms. The re-linking of the ridge realizes the correct connection of the micro-Doppler curves of each scattering center. The simulation data and the electromagnetic calculation data verify the method’s effectiveness.

A Novel Frequency Estimator for Protection Applications in Active Distribution Networks

Frequency is a useful parameter for ensuring the proper functioning of the power system operation, control, and protection. In this article, a fast and accurate frequency estimator (FE) is developed using a zero crossing and a peak, occurring in the buffered data, unlike the commonly used two zero crossings. Prior to this, the signal is preprocessed using the sliding Goertzel filter (SGF) that mitigates the impact of undesirable features such as harmonics, noise, etc., from the signal. The two FEs, with and without SGF, then work in tandem to form the hybrid estimator and are named as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z_{C}P_{k}$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{HFE}}$</tex-math></inline-formula> . The estimated frequency is chosen based on the minimum error computed from the two parallel estimators. The performance of the estimator is, then, validated using the simulated signals polluted with harmonics, noise, transients, etc. The article also discusses the protection-oriented applications of the proposed FE in active distribution network (ADN). Moreover, the evaluation results with the real-time field data and the IEEE-13 ADN incorporated with photovoltaic using dSPACE1104 and real-time digital simulator show its capability to estimate the real-time frequency with satisfactory output.

Pilot-Tone Assisted Successive Interference Cancellation for Uplink Power- and Frequency-Division Multiplexing Passive Optical Network

Frequency division multiplexing (FDM) passive optical network (PON) is considered as a competitive solution for 5G-advanced and 6G mobile fronthaul (MFH) to support multiple radio units (RUs) with shared trunk fiber and distributed unit (DU). However, it is likely to cause uplink signal overlapping by laser wavelength drift, and guard bands should be reserved between FDM channels, which limits the spectral efficiency (SE). In this work, we propose to aggregate multiple uplink FDM channels using power division multiplexing and jointly adopt successive interference cancellation (SIC) at the receiver to improve the uplink SE. We first theoretically derive the SE of such power- and frequency-division multiplexing (PFDM) PON with both guard band and SIC together, and reveal that PFDM PON can achieve higher SE than the pure FDM PON with guard band only. Focusing on the case of two overlapped uplink signals, we propose a pilot-tone assisted SIC to improve the estimation accuracy of frequency offset and phase noise in heavily overlapped uplink signals. In the proof-of-concept experiments, compared to the orthogonal case without considering the guard band, 0.29 bit&#x002F;s&#x002F;Hz SE penalty due to the residual interference after SIC is observed when two uplink signals are completely overlapped. The results showed that, in the presence of laser drift, PFDM PON becomes more spectrally-efficient than FDM PON when the relative wavelength drift exceeds 20&#x0025; of the signal bandwidth.