Proposed Frequency Estimation Research Articles

Complex-Valued Noisy Sinewaves Frequency Estimator Based on DTFT Linearization and Interpolation

This paper proposes an Interpolated Discrete-Time Fourier Transform (LIpDTFT) estimator for complex-valued noisy sinewave frequency based on the Linearization of the DTFT module behavior around the spectrum peak. It belongs to a class of LIpDTFT estimators that compensate the poor Discrete Fourier Transform (DFT) frequency resolution by interpolating two DTFT samples located very close to an initial frequency estimate. As compared with other DTFT-based frequency estimators recently proposed in the literature, the proposed LIpDTFT estimator ensures a smaller interpolation error and a lower processing effort. Moreover, if the rectangular window is adopted, it almost attains the unbiased Cramér-Rao Lower Bound (CRLB) even if a very small number of samples is analyzed. The accuracies ensured in different operating conditions by the proposed frequency estimator and other state-of-the-art DTFT-based algorithms are compared to each other through computer simulations.

Phase Error Criterion Based Adaptive Algorithm for Frequency Estimation

A simple phase error criterion (PEC-)-based adaptive algorithm for estimating the frequency of a complex sinusoidal signal in additive white Gaussian and impulsive noises is proposed. The proposed technique makes use of the instantaneous phase response of a first-order complex linear predictor (CLP) as a driving function to update the frequency parameter of the CLP. The proposed PEC is attractive due to its simplicity and high impulsive noise robustness. Theoretical analysis for the mean value of the estimated frequency and the steady-state mean square error (MSE) of the frequency estimate are derived in closed forms. Computer simulations are drawn to show the performance of the proposed frequency estimator.

Frequency estimation of multiple complex sinusoids using noise suppressing predictive FIR filter

The paper presents a predictive filter based frequency estimation algorithm (PF-FE) for multiple complex sinusoids corrupted by additive white Gaussian noise. The proposed frequency estimator combines the noise suppression capability of an FIR filter with a least squares approach minimizing the sum of the squared errors of a prediction filter. The FIR filter coefficients are chosen such that the sinusoidal components are predicted with minimum distortion. Computer simulation results are given to contrast the performance of the proposed PF-FE method with six other state-of-the-art frequency-estimators and the Cramer-Rao lower bound. Furthermore, the paper provides a complexity analysis of the PF-FE method and compares it with those of the conventional MUltiple SIgnal Classification algorithm and some selected state-of-the-art methods from the literature. Performance of the proposed PF-FE method is validated with effective mean square error (EMSE) plots for model orders of three and five and under different observation lengths and signal-to-noise ratio values. Finally, the paper demonstrates how EMSE varies for the proposed method when the prediction filter length is increased from 20 to 75. After extensive simulations, it is observed that when filter length is larger than half the observation length the EMSE will start to degrade.

Joint Physical Layer Frame Optimization and Carrier Synchronization for Satellite Communications

In this paper, we discuss general data-framing and optimization, parallel frequency-phase estimation, and powerful frequency estimator for satellite communications. Based on the standard pilot-symbol-assisted-modulation (S-PSAM) frame, we design a general PSAM (G-PSAM) frame, whose corresponding data-aided & non-data-aided Cramér-Rao bound (DA&NDA CRB) is derived with respect to carrier frequency offset, time delay and phase offset, followed by its approximate form. Also, we provide a simple solution to the G-PSAM frame optimization by means of the approximate DA&NDA CRB and the control-variate method. With an unbiased auto-correlation (AC) value, we then propose a frequency-phase decoupler and develop a parallel frequency-phase estimation (PFPE) mode in terms of the serial frequency-phase estimation (SFPE) mode, where a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">serial-to-parallel</i> estimation conversion can be implemented. Furthermore, we extend the AC frequency estimator in the PFPE mode as a powerful stepwise correlation-based one aiming at the target performance. Theoretical analysis and numerical results are provided to show the superiority of the optimized frames, the robustness of the PFPE mode, and the adaptability of the proposed frequency estimator with the optimized frames under different transmission systems.

An enhanced fast fundamental frequency estimator for three-phase electric aircraft grid

This article proposes a robust and enhanced three-phase fundamental frequency estimation algorithm for the electric aircraft grid. Unlike conventional frequency-locked loops, the digital signal processing technique-based frequency estimator proposed relies on the storage of five consecutive samples of the fundamental grid voltage signal. Furthermore, the ability to successfully operate at a low sampling frequency, i.e. 8 kHz, makes it sufficiently attractive as regards reducing the memory storage in a low-cost real-time controller. The proposed frequency estimator can additionally eliminate the negative effects of the DC-offset and the fundamental negative sequence components present in the grid signal without any additional effort. Also, the tuning efforts are reduced for the frequency variation range of 350–900 Hz owing to the existence of a single tuning gain parameter. The proposed algorithm has also been found to have a fast dynamic response, which has been experimentally validated through the use of a real-time digital controller.

A Morlet Wavelet-Based Two-Point FIR Filter Method for Phasor Estimation

This article proposes a method of phasor estimation called the Morlet wavelet-based two-point finite-impulse response (FIR) filter (MW-FIR), showing advantages on algorithm complexity, customizability, and zero overshoot. The method focuses on amplitude and frequency estimation, while phase and rate of frequency of change (ROCOF) estimation can be performed using the standard signal processing model with an FIR filter. The mathematical principle behind the method is presented. The causes of error are discussed, and the parameter selection procedure is introduced to minimize error and adjust algorithm performance according to different application requirements. The proposed method has been discussed and compared with the three-point interpolated discrete Fourier transform (ipDFT) method and the FIR method using a flat-top (FT) windowing function, under the static and dynamic situations given by the IEC/IEEE 60255-188-1 and noise immunity evaluation. Finally, the major advantages of the proposed frequency estimation method compared with the conventional FIR-based method using the derivative of angular position are discussed. It can be concluded that this method becomes a substitute for ipDFT in most cases and shows several advantages over the FIR-based method with an FT sequence.

Algebraic estimator of Parkinson’s tremor frequency from biased and noisy sinusoidal signals

Tremor is an uncontrolled trembling movement or shakes, which are defined as an involuntary, rhythmic oscillatory movement of the body. The dominant features of Parkinsonism are the motor task and its frequency. This paper presents studies on the tremor parameter identification to be used for obtaining the frequency as a dynamical feature of the tremor. The method is based on the analysis of time-varying signals for identification of the tremor’s frequency from unknown noisy harmonic signals with an offset, using time-varying unstable filters and low-pass Butterworth filters. This approach uses an algebraic derivative method, in the frequency domain, to obtain the main frequency of tremors in the time domain. The first frequency mode of the tremor is one of the main characteristics to represent the low vibrational dynamics of Parkinson’s tremor. The proposed frequency estimation is performed in less than a period of the slower component of the measured signal. Real tremor signals were used to experimentally validate the proposed method and the algorithm proved to be fast and robust to high-frequency noises tracking the time variation of the tremor accurately.

A Memory-Reduced Frequency Estimator for the Measurement of Sinusoidal Signal

This brief presents a memory-reduced hardware architecture for acquiring the frequency of sinusoidal signal based on the interpolated discrete Fourier transform (IpDFT). By exploiting the sparsity of the sinusoidal signal in the frequency domain, a spectrum compression method that can remove the unnecessary spectral lines is proposed together with the corresponding parameter extraction scheme, which circumvents the large-point DFT computation involved in the conventional IpDFT and thereby reduces the memory consumption markedly. On this basis, a low-latency hardware architecture is designed for the proposed frequency estimator. Implementation results demonstrates the proposed work can gain satisfactory accuracy while retaining low hardware cost and latency.

Improved Fundamental Frequency Estimator for Three-Phase Application

This letter reports a digital signal processing based frequency estimation technique that relies on the storage of fundamental three-phase grid voltage samples. Unlike phase-locked loop algorithms, the proposed algorithm does not require the phase error information when estimating the grid frequency. Moreover, only four consecutive samples of the fundamental orthogonal components are required in order to estimate the deviation in the grid frequency. The proposed scheme is facilitated with an inherent nonadaptive comb filtering behavior in order to reject the dc offset and harmonics while attaining a good immunity to voltage sag and the fundamental negative sequence component. Additionally, the off-nominal harmonic rejection capability of the proposed frequency estimator is enhanced by using a postfiltering method. The experimental validations reported in this study demonstrate that the proposed frequency estimator is suitable for three-phase grid applications.

A low complexity model order and frequency estimation of multiple 2-D complex sinusoids

Model order and frequency estimation of multiple 2-D complex sinusoids in additive white Gaussian noise are addressed. Frequency estimation follows the coarse-fine search strategy. Coarse estimates, obtained by locating maxima of the 2-D discrete Fourier transform, are refined in a two-stage procedure. In both stages, frequency refinement is based on three-point periodogram maximization. In order to provide accurate model order estimation (MOE) for a wide signal-to-noise ratio (SNR) range, our approach combines two metrics for sinusoid detection in the 2-D frequency domain, one for low and the other for high SNR values. The proposed frequency estimation method attains the Cramér-Rao lower bound and it outperforms parametric methods in terms of the estimation accuracy and numerical efficiency. Compared with information criterion-based methods, the proposed MOE approach is numerically more efficient, it does not require estimation of noise variance and hence does not suffer from overestimation at high SNR.

A fast and precise power system frequency estimation method without iterations

The conventional power system frequency estimation methods based on the Discrete Fourier Transform (DFT) normally require iterative calculations to eliminate the errors due to spectral leakage in off-nominal frequencies. It cannot provide both fast response and good accuracy under a system disturbance. In this paper, a fast and precise frequency estimation method is presented. The theoretical analysis shows the angle difference of the positive sequence voltage is exactly linear to the frequency deviation. Based on this angle characteristic, this method is able to precisely calculate the frequency deviation from angle differences between the continuous DFT calculations without the need for any iteration. Even if there is only one single phase voltage input available, the simulated positive sequence voltages can be derived by constructing the remaining two phase-voltages utilizing an appropriate phasor shift. To effectively restrain the harmonic interferences, a two-cycle Hanning window is applied as a filter. One method to detect the phase angle jump is proposed to avoid transient frequency errors by using the 2nd order derivative of the frequency. The simulation compares the frequency estimation performance between the proposed non-iterative method and the conventional iterative method. The simulation results show the frequency response is faster and the accuracy is reliable within the range 40–70 Hz, even if there are harmonic interferences or three-phase unbalances. This proposed frequency estimation method is easy to implement, and it can be widely applied in the intelligent electronic devices within the power system.

Closed-Form Estimator for Frequency Estimation of Complex Sinusoidal Signals in Multiplicative and Additive Noise

In this paper, a new method is proposed for estimating the frequency of a complex sinusoidal signal in multiplicative and additive noise. The proposed method is based on the linear prediction property of the signals’ autocorrelation function. This frequency estimation method is a closed-form algorithm which can directly estimate the frequency without peak searching. The performance of the proposed frequency estimator is investigated by computer simulations. Simulation results demonstrate that the performance of the proposed technique is reasonable and is close to Cramer–Rao bound.

Estimation of Grid Frequency in Disturbed Converter-Based Power Systems by PLL State Variable Feedback

Fast real-time estimation of the grid frequency is essential for stable operation of renewable converter-based sources in future power systems. Therefore this paper presents a new phase-locked loop for the estimation of time-dependent frequencies in unbalanced power systems with harmonics. The proposed frequency estimation method consists of two signal processing steps: In the first step, a least mean square estimator reconstructs the fundamental sinusoidal signal from the measured three-phase grid voltage and splits it into positive, negative and zero sequence components. In the second step, the resulting first harmonic three-phase positive sequence is converted into the synchronous reference frame in the form of a phase-locked loop using a state feedback controller scheme to reconstruct the current grid frequency. Here the controller output is equivalent to the signal to be reconstructed. The feedback controller design is based on linear matrix inequalities where the requirements are explicitly considered. The capability of proposed state feedback phase-locked loop is demonstrated by full scaled electro magnetic transient simulations.

Frequency Estimation Based on Moving-Window DFT With Fractional Bin-Index for Capacitance Measurement

A frequency estimation technique is proposed with fractional bin-index-based moving-window discrete Fourier transform (MWDFT). In order to increase the range of estimation frequencies, different MWDFTs with bin-indices $k = 0.5$ , 1, 1.5, 2, and 2.5 are chosen and incorporated in the frequency estimator. The structure of the MWDFT is modified with the positive feedforward coefficients for fractional bin-indices and negative coefficients for integer multiples. The frequency of the input signal is estimated by adaptively adjusting the sampling pulses for MWDFT with integer and fractional bin-indices. The proposed frequency estimator is validated through field programmable gate array implementation for measuring a capacitance range of 89.201–1420.69 pF. A relaxation oscillator with a measurand as capacitance exhibits a square wave whose frequency is inversely related to the measurand. The frequency of the square wave is estimated through the proposed DFT procedure instantaneously by extracting the fundamental sinusoidal signal and tracking the same with the feedback loop. The experimental investigation on the proposed method proves to be accurate and computationally efficient, and offers a wide operating range with less acquisition time.

Development of a tuning algorithm for a dynamic vibration absorber with a variable stiffness property

In this study, we propose a frequency estimation method based on an adaptive line enhancer algorithm to be used for changing the property of the frequency-tunable dynamic vibration absorber. This method estimates the frequency from the time series of the delayed input signal, focusing on the fact that the autocorrelation function of noise converges rapidly to zero when the phase difference for several sampling periods is set. An elastomer composite with controllable stiffness, known as a magnetorheological elastomer, is used in a dynamic vibration absorber whose natural frequency is tuned adaptively to the disturbance frequency through the application of an external magnetic field. Firstly, we explain the structure of a variable-stiffness absorber and the mechanism of the proposed frequency tuning algorithm. Secondly, the test result of the absorber properties, namely, the natural frequency and damping ratio, is shown. By taking full advantage of the frequency adjustability of the proposed vibration absorber, we then evaluated the real-time vibration control performance for an acoustically excited plate having multiple resonant peaks. The sweep excitation tests show that the vibration of the structure can be effectively reduced with an improved performance by using the adaptive-tuned dynamic vibration absorber to be used with the proposed frequency estimation algorithm.

Direct Power Control of DFIG System Without Phase-Locked Loop Under Unbalanced and Harmonically Distorted Voltage

This paper proposes an improved direct power control (DPC) strategy for the rotor-side converter (RSC) and grid-side converter (GSC) of the doubly fed induction generator under unbalanced and distorted voltage conditions. The proposed scheme is implemented in a synchronous reference frame with the fixed angular speed, so that the phase-locked loop can be removed and relevant potential instability issues can be avoided. Besides, the sequential separations and complex calculations of the power compensating items can be eliminated with the direct-resonant method based on a dual-frequency frequency adaptive vector PI. Thus, the negative and harmonic components can be directly eliminated, achieving balanced and sinusoidal current injected into the power grid. Meanwhile, the control strategy can achieve self-adaptive to the grid frequency variation in the practical situation with the proposed frequency estimation scheme. Finally, the experimental results validate the availability of the proposed DPC strategy.

High accuracy frequency extraction based on sigma-delta ADC applied in resonant dew point sensor

One of the design challenges for the resonant dew point measurement was optimizing the rapidity and accuracy of frequency extraction to meet the requirements. We have developed a 1-bit second-order sigma-delta (ΣΔ) analog-to-digital (ADC) to be applied in it, which was anticipated to have a highest resolution and design flexibility than traditional ADC. Based on the Butterworth filter, the design of ΣΔ modulator was modeled firstly to evaluate the performance of filters scheme before the hardware implementation. Furthermore, the design and implement of the digital decimation filters was presented to extend the design flexibility and application. To improve the accuracy and instantaneous of frequency estimation, we developed a new frequency estimation algorithm, which combined the Fast Fourier transform (FFT) and the chirp-Z transform. We built a complete hardware implementation system. We tested the performance of the designed ΣΔ ADC and found that has 11-bit resolution and the high flexibility. The experiment results showed the root mean square (RMS) error of frequency estimation was 0.0917 Hz with minimum error 0.01 Hz, and the SNR can achieve 123.04 dB. Results showed the proposed frequency estimation error decreases approximately 35 times under the premise of the same computation with FFT. Moreover, every completion of the frequency estimation only takes less than 1 s. Finally, the experiment of dew point measurement was carried out. The results indicated that the proposed measurement system was feasible for the frequency extraction of the resonant dew point sensor.

Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples

A flexible and accurate frequency estimator is first proposed for frequency estimation of a complex sinusoid weighted with a rectangular window function in additive white Gaussian noise. This proposed frequency estimator can be operated in the application of an arbitrary length discrete Fourier transform where the original input data is padded with any zeroes, which makes it more flexible in practice. The proposed frequency estimator utilizes the maximum sample value and its two adjacent samples in the frequency domain to perform the fine frequency estimation with unbiased results obtained. Then a modified frequency estimator is proposed to estimate the frequency when the complex sinusoid signal is weighted with different nonrectangular window functions. Although the modified frequency estimator is nonanalytic and biased, it can still improve the estimation performance for certain applications. Simulation results demonstrate that both of the proposed frequency estimators are effective to achieve the high frequency estimation accuracy. And the root mean square errors of the proposed frequency estimators approach the Cramer-Rao bound when the signal-to-noise ratio is large enough to make the coarse frequency estimation work effectively.

Off-Road Motorbike Performance Analysis Using a Rear Semiactive EH Suspension

The topic of this paper is the analysis of a control system for a semiactive rear suspension in an off-road two-wheeled vehicle. Several control methods are studied, as well as the recently proposed Frequency Estimation Based (FEB) algorithm. The motorcycle dynamics, as well as the passive, and semiactive dampers, and the algorithm controlled shock absorber models are loaded into BikeSim, a professional two-wheeled vehicle simulation software, and tested in several road conditions. The results show a detailed comparison of the theoretical performance of the different control approaches in a novel environment for semiactive dampers.

Computationally effective sampling frequency‐offset estimation for OFDM‐based LTE downlink systems

AbstractIn this paper, we present a low‐complexity sampling frequency‐offset (SFO) estimation scheme suitable for the 3GPP long‐term evolution (LTE) downlink system. First, a novel SFO estimation method for a pilot‐aided orthogonal frequency division multiplexing system is proposed providing a good performance with reduced complexity. To achieve low complexity, the proposed estimation scheme uses a central conjugate‐symmetric primary synchronisation signal specified in the LTE standard, which eases the SFO estimation at the receiver. For performance evaluation, we derive the mean square error expression of the proposed frequency estimation scheme. Simulations show that the proposed frequency estimation scheme can detect the SFO with higher accuracy and much lower complexity, compared with the conventional estimation schemes. Copyright © 2014 John Wiley &amp; Sons, Ltd.