Frequency Estimation Algorithm Research Articles

High-precision frequency estimation of real sinusoids with reduced computational complexity using a model-based matched-spectrum approach

Frequency-estimation algorithms devised for complex sinusoids, including the maximum-likelihood (ML) approach, when operating on real sinusoidal signals, suffer from spectral interference due to the superposition of the aliasing components at negative and positive frequencies. This paper introduces a frequency estimation ML-like algorithm, based on a spectral-matching approach, that avoids such superposition effect by incorporating it in the signal/spectrum model. As a result, the proposed method is able to generate a more precise frequency estimate in comparison to previous approaches at a comparable computational cost, as endorsed by provided computational analyses and simulation results.

Comparative Study of Influence of Noise on Power Frequency Estimation of Sine wave Using Interpolation FFT

This paper compares performances of frequency estimations provided by different interpolation fast Fourier transform (FFT) algorithms under white Gaussian noises. Firstly, accuracies of frequency estimation algorithms are evaluated by deriving analytical expressions of variances of frequency estimation. Then, theoretical results are validated by means of computer simulations. It is shown that the trade-off between biases and variances of frequency estimation is unavoidable. From both theoretical and simulation results, it can be concluded that variances of frequency estimation are proportional to the noise variance and inverse proportional to the length of FFT.

High-Efficiency Carrier Frequency Estimation Algorithm for Real-Time Multi-Domain Communication Signal Analysis

Abstract Based on real-time multi-domain communication signal analysis architecture, a high-efficiency blind carrier frequency estimation algorithm using the power spectrum symmetry of the measured modulated signal is presented. The proposed algorithm, which utilizes the moving averaged power spectrum achieved by the realtime spectrum analysis, iteratively identifies the carrier frequency in according to the power difference between the upper sideband and lower sideband, which is defined and revised by the estimated carrier frequency in each iteration. When the power difference of the two sidebands converges to the preset threshold, the carrier frequency can be obtained. For the modulation analysis, the measured signal can be coarsely compensated by the estimated result, and the residual carrier frequency error is eliminated by a following carrier synchronization loop. Compared with previous works, owing to the moving averaged power spectrum normalization and the smart iterative step variation mechanism for the two sidebands definition, the carrier frequency estimation accuracy and speed can be significantly improved without increasing the computational effort. Experimental results are included to demonstrate the outstanding performance of the proposed algorithm.

A Simple Method for Power System Harmonic Analysis

With the increasing use of non-linear electrical loads in power system, the harmonic pollution has become a severe problem. In this paper, we proposed a simple method for power system harmonic analysis. Cascaded adaptive comb filter is designed specifically to suppress the electric harmonic pollution. And a high-precision but easily implemented frequency estimation algorithm is presented based on least square estimation method. So the electric signal frequency fluctuation can be real-time tracked, and coefficients of the comb filters can be adaptively updated with this algorithm.

Joint estimation of frequency and azimuth using acoustic vector sensor signals based on sparse decomposition theory

Acoustic vector sensor can obtain more information of sound field compared with scalar hydrophone. The sparse decomposition theory was put forward in the 90s of last century, and it provides a simple, flexible, and self-adaptive representation method of signal. Through sparse decomposition theory, it can essentially reduce the cost of signal processing and improve the compression efficiency. Space-time array manifold is constructed through signal analysis of single acoustic vector sensor (AVS). Based on sparse decomposition theory, the frequency and azimuth estimation algorithm is proposed, the frequencies and azimuths of multi-targets are estimated simultaneously by the joint estimation algorithm. Results using simulated data received from single acoustic vector sensor are illustrated. The accurate estimation of multi-targets’ frequencies, azimuths, and signal amplitudes can be obtained using the estimation algorithm we deduced. Then, the influence of targets number, signal-to-noise (SNR), snapshots number on algorithm performance is analyzed.

Reduction of Noise in Measurements of Phasor Angles by Using Two Digital Filters

An electric power system is monitored and controlled on the basis of its phasor information, such as amplitude, phase angle, and frequency. This phasor can be measured through discrete Fourier transform (DFT) coefficients of its positive nominal frequency. Then, the frequency estimate can be calculated from time variation of the measured phasor angle. The accuracy of the phasor-angle measurement and the frequency estimation are severely affected by noise in the power system signal and the leakage of the negative fundamental frequency in DFT. This paper proposes a DFT-based phasor-angle measurement algorithm to cope with both the noise effect and the leakage effect. In addition, a frequency estimation algorithm is developed to use the same technique in the phasor-angle measurement algorithm. These algorithms introduce two digital filters for the reduction of the noise effect. The effectiveness of the proposed algorithm in the noise effect reduction is verified through simulations.

PEFAC - A Pitch Estimation Algorithm Robust to High Levels of Noise

We present PEFAC, a fundamental frequency estimation algorithm for speech that is able to identify voiced frames and estimate pitch reliably even at negative signal-to-noise ratios. The algorithm combines a normalization stage, to remove channel dependency and to attenuate strong noise components, with a harmonic summing filter applied in the log-frequency power spectral domain, the impulse response of which is chosen to sum the energy of the fundamental frequency harmonics while attenuating smoothly-varying noise components. Temporal continuity constraints are applied to the selected pitch candidates and a voiced speech probability is computed from the likelihood ratio of two classifiers, one for voiced speech and one for unvoiced speech/silence. We compare the performance of our algorithm with that of other widely used algorithms and demonstrate that it performs well in both high and low levels of additive noise.

Power System Frequency Estimation by Reduction of Noise Using Three Digital Filters

Accurate estimation of power system frequency is essential for monitoring and operation of the smart grid. Traditionally, this has been done using discrete Fourier transform (DFT) coefficients of the positive fundamental frequency. Such DFT-based frequency estimation has been used successfully in phasor measurement units and frequency disturbance recorders in North America. Frequency errors in DFT-based algorithms for single-phase signals arise mainly due to noise and the leakage effect of the negative fundamental frequency. In this paper, a DFT-based frequency estimation algorithm is proposed to introduce three digital filters for reduction of estimate error due to noise and the leakage effect. This algorithm calculates the frequency estimate from the magnitude ratios of DFT coefficients to avoid the leakage effect. It compensates the estimate error, which is induced from the DFT magnitude ratios of three filtered outputs. The enhancement of signal-to-noise ratios is verified through simulations.

Support vector regression ‐based robust frequency estimation algorithm by instantaneous phase

There are two important factors which impact the performance of phase-based frequency estimation algorithms remarkably: the approximations of noise phase model and imperfections in phase unwrapping process. Support vector regression (SVR) exits excellent capabilities for learning unknown data and forecasting the future ones, especially under the small sample condition. Therefore, the authors introduce it to predict the variation trend of instantaneous phase and unwrap phases efficiently. Even though with that being the case, errors still exist in phase unwrapping process because of its ambiguous phase characteristic. Furthermore, a SVR-based frequency estimation algorithm is proposed and makes it immune to these error phases by means of setting the SVR's parameters properly. The results show that, compared with other phased-based algorithms, not only does the proposed one maintain a wide estimation range and quality capabilities at low frequencies, but also improves accuracy at high frequencies and decreases the impact with the initial phase. The proposed algorithm is fit for not only linear phase signal but also polynomial phase signal, under both the Gaussian and non-Gaussian condition.

Performance Comparison of Windowed Interpolation FFT and Quasisynchronous Sampling Algorithm for Frequency Estimation

The DFT-based frequency estimations have inherent limitations such as spectral leakage and picket-fence effect due to asynchronous sampling. This paper focuses on comparing the windowed interpolation FFT (WIFFT) and quasisynchronous sampling algorithm (QSSA) for frequency estimation. The WIFFT uses windows to reduce spectral leakage and employs interpolation algorithm to eliminate picket-fence effect. And the QSSA utilizes quasisynchronous weighted iterations for frequency estimation. The accuracy and time complexity of WIFFT and QSSA are theoretically studied. Computer simulations of frequency estimations with noise and fluctuations by using WIFFT and QSSA are performed. Simulations results show that the wideband noise sensitivity of QSSA is lower than that of WIFFT. However, the WIFFT exhibits less time complexity than QSSA.

Unbalanced three‐phase distribution system frequency estimation using least mean squares method and positive voltage sequence

The subject of this study is a frequency estimation algorithm suitable for grid-connected power converters placed at a weak coupling point of a three-phase electrical distribution system. An upgraded version of the widely used complex least mean squares (CLMS) algorithm for frequency estimation is introduced to cope with different voltage amplitude unbalance and harmonic distortion levels, both frequently present in power system at distribution level. First, it is suggested that the CLMS algorithm uses only a positive phase-sequence component of voltage vector, the component that is inherently symmetrical and by cancelling the phase unbalance preserves the circular vector trajectory in a two-phase αβ-plane. This study shows that it is even possible to use the positive voltage phase-sequence vector extracted using a constant delay block, thus avoiding potential instability issues in the case of signal frequency feedback loop. Second, possible high signal harmonics and signal measurement noise are both removed using low-pass filters prior to CLMS algorithm deployment. Computer simulations and experiments are performed under a variety of conditions to validate the effectiveness of the proposed technique. Experimental results are achieved using the dataset sampled from the actual three-phase grid voltage at distributed level and with data processing done in the LabVIEW software environment.

Iterative Algorithm for High Resolution Frequency Estimation

Iterative Algorithm for High Resolution Frequency Estimation

Low Complexity Direction and Doppler Frequency Estimation for Bistatic MIMO Radar in Spatial Colored Noise

We investigate the algorithm of direction and Doppler frequency estimation for bistatic multiple-input multiple-output (MIMO) radar in spatial colored noise. A novel method of joint estimation of direction and Doppler frequency in spatial colored noise based on propagator method (PM) for bistatic MIMO radar is discussed. Utilizing the cross-correlation matrix which is formed by the adjacent outputs of match filter in the time domain, the special matrix is constructed to eliminate the influence of spatial colored noise. The proposed algorithm provides lower computational complexity and has very close parameters estimation compared to estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm in high signal-to-noise ratio (SNR). It is applicable even if the transmitted waveforms are not orthogonal. The estimated parameters can be paired automatically and the Cramér-Rao Bound (CRB) is given in spatial colored noise. Simulation results confirm the effectiveness of the proposed method.

A Modified Demodulation Technique for Single-Phase Grid Voltage Fundamental Parameters Estimation

This paper proposes a modified demodulation technique to provide accurate estimation of the single-phase grid voltage fundamental amplitude, frequency, and phase angle under distorted grid conditions. A quadrature oscillator is combined with a demodulation technique for rejecting oscillations at second harmonic generated by the demodulation of the fundamental voltage component; thus, it can provide more accurate estimation, as compared to a conventional one, using same-order and cutoff-frequency-based infinite-impulse-response low-pass filters after the demodulation stage. It also does not require a separate frequency estimation algorithm for adaptive demodulation as the frequency is obtained from the estimated initial phase by using a differentiation operation and an integral controller. The technique is relatively simple and can also reject the negative effects caused by harmonics under a wide range of fundamental frequency variation as specified by the standard requirements. When compared with a quadrature phase-locked loop technique, the proposed one provides improved estimation of the fundamental voltage parameters. The performance of the proposed technique is verified using both simulation and experimental results.

FEATURES OF THE INSTANTANEOUS FREQUENCY ESTIMATION ALGORITHM WITH PRE-FILTERING

Instantaneous frequency is one of the basic signal parameters which provides important information about the time-varying spectral changes in non-stationary signals. Features of the harmonic signal frequency estimation algorithm in different signal and interference situations are researched. Research methodology is a statistical modeling. Appearance of an additional harmonic considerably worsen precision of estimation because the algorithm does not have any filtering properties. For linear frequency deviation estimation approximately equals middle between initial and final frequencies in the window. Frequency estimation of a noise process, that is formed by 2nd order filters, is almost proportional to central or cut-off frequency. There is optimal formative filter frequency for different filter parameters and estimation conditions. Reasonability of using pre-filtering in order to improve estimation precision is proved. Identified positive effect of mixture pre-filtering is also useful for estimation of frequency of periodic non-harmonic signals with higher harmonics. A great feature of the algorithm is a accurate estimation at intervals equal to a period of the signal, which brings us to the actual instantaneous frequency and provides the opportunity to observe its trend over time. Distorted factors cause significant worsening of frequency estimation precision. It can be improved by pre-filtering. The 2nd order filter using is reasonable only in case of weak a priori ambiguity, in other cases the 1st order filter is more preferable.

Study on frequency estimation based on weighted least square method with three Fourier coefficients

In this paper, a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method. Based on the idea of Provencher, three biggest Fourier coefficients in the maximum periodogram are considered, the Fourier coefficients can be written as three equations about the amplitude, phase, and frequency, and the frequency is estimated by solving equations. Because of the error of measurement, weighted least square method is used to solve the frequency equation and get the signal frequency. It is shown that the proposed estimator can approach the Cramer-Rao Bound (CRB) with a low Signal-to-Noise Ratio (SNR) threshold and has a higher accuracy.

Multidimensional rare event probability estimation algorithm

This work contains Monte–Carlo Markov Chain algorithm for estimation of multi-dimensional rare events frequencies. Logits of rare event likelihood we are modeling with Poisson distribution, which parameters are distributed by multivariate normal law with unknown parameters – mean vector and covariance matrix. The estimations of unknown parameters are calculated by the maximum likelihood method. There are equations derived, those must be satisfied with model’s maximum likelihood parameters estimations. Positive definition of evaluated covariance matrixes are controlled by calculating ratio between matrix maximum and minimum eigenvalues.

A widely linear least mean phase algorithm for adaptive frequency estimation of unbalanced power systems

A robust technique for online estimation of the fundamental frequency of both balanced and unbalanced three-phase power systems is proposed. This is achieved by introducing a widely linear least mean phase (WL-LMP) frequency estimator, based on Clarke’s transformation and widely linear complex domain modelling. The proposed method makes use of the full second-order information within the complex-valued system voltage, making it possible to eliminate otherwise unavoidable oscillations in frequency estimation. In this way, the WL-LMP inherits the advantages of the phase-only approach, such as its high angle estimation accuracy and immunity to voltage and harmonics variations, while accounting for the noncircularity of Clarke’s voltage in unbalanced conditions. Simulations over a range of unbalanced conditions, including those caused by voltage sags and higher order harmonics, and case studies for real-world unbalanced power systems support the analysis.

잡음영향의 저감을 위한 두 디지털 필터들의 사용에 의한 DFT 기반의 계통주파수 추정

The power system frequency plays an important role in monitoring and controlling the power system. The frequency can be measured through discrete Fourier transform (DFT) coefficients of its positive fundamental frequency. The accuracy of the frequency estimate is severely affected by noise in the power system signal and the leakage effect of the negative fundamental frequency in DFT. This paper proposes a DFT-based frequency estimation algorithm to cope with the noise as well as the leakage effect. In this algorithm, two suitable digital filters are introduced to reduce efficiently frequency estimate error due to the noise. These filters are designed to use a digital bandpass filter and a second-degree integrator. The effectiveness of the proposed algorithm in reduction of frequency estimate error is verified through simulations on noise, harmonics and frequency deviation.

최소자승법과 후보군 선택 기법을 이용한 2-18GHz 디지털 주파수 변별기 설계

Based on the conventional 2-6GHz digital frequency discriminator (DFD) using the phase unwrapping and least-squares techniques, we propose a new 2-18GHz DFD. To compensate for lowered-precision frequency estimation due to the expanded bandwidth, the proposed DFD design employs more delay lines, accordingly accompanying high complexity. Thus, a new computationally efficient frequency estimation algorithm is also presented to overcome such high computational burden. More specifically, the proposed frequency estimation algorithm is basically based on the conventional phase unwrapping technique, along with a new candidates selection for the unwrapped phases under the condition that the phase margin is known. As a result, the computational burden required for the least-squares technique can be reduced. Finally, simulation results are provided to demonstrate the effectiveness of the proposed approach, compared with those of the conventional DFD`s.