Yuxiang Yang

Harmonic Estimation Using Symmetrical Interpolation FFT Based on Triangular Self-Convolution Window

Harmonic estimation is an important topic in power system signal processing. Windowed interpolation fast Fourier transformation (WIFFT) is an efficient algorithm for power system harmonic estimation, which can eliminate the errors caused by spectral leakage and picket fence effect. However, the fitting polynomial in the interpolation procedure contains both even and odd terms, and this increases the computational burden. This paper proposes a simple symmetrical interpolation FFT algorithm, where the even terms are removed from the fitting polynomial based on the triangular self-convolution windows (TSCW). The polynomials for frequency and amplitude computations are provided. Considerable leakage errors and harmonic interferences can be suppressed by the TSCW. Accurate estimations of harmonic parameters can be obtained via the fitting polynomial and the TSCW, both with adjustable order to fulfill different accuracy and speed requirements of practical power harmonic measurement. Simulation results and measurements have validated the proposed method.

Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach

This paper focuses on the accurate frequency estimation of power signals corrupted by a stationary white noise. The noneven item interpolation FFT based on the triangular self-convolution window is described. A simple analytical expression for the variance of noise contribution on the frequency estimation is derived, which shows the variances of frequency estimation are proportional to the energy of the adopted window. Based on the proposed method, the noise level of the measurement channel can be estimated, and optimal parameters (e.g., sampling frequency and window length) of the interpolation FFT algorithm that minimize the variances of frequency estimation can thus be determined. The application in a power quality analyzer verified the usefulness of the proposed method.

Improved Cole parameter extraction based on the least absolute deviation method

The Cole function is widely used in bioimpedance spectroscopy (BIS) applications. Fitting the measured BIS data onto the model and then extracting the Cole parameters (R0, R∞, α and τ) is a common practice. Accurate extraction of the Cole parameters from the measured BIS data has great significance for evaluating the physiological or pathological status of biological tissue. The traditional least-squares (LS)-based curve fitting method for Cole parameter extraction is often sensitive to noise or outliers and becomes non-robust. This paper proposes an improved Cole parameter extraction based on the least absolute deviation (LAD) method. Comprehensive simulation experiments are carried out and the performances of the LAD method are compared with those of the LS method under the conditions of outliers, random noises and both disturbances. The proposed LAD method exhibits much better robustness under all circumstances, which demonstrates that the LAD method is deserving as an improved alternative to the LS method for Cole parameter extraction for its robustness to outliers and noises.

An improved crest factor minimization algorithm to synthesize multisines with arbitrary spectrum.

Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.

Optimized Trapezoid Convolution Windows for Harmonic Analysis

The new window class, which is generated by multiple time-convolution of optimized trapezoid windows, is presented. It is shown that the trapezoid windows can achieve different sidelobe and main lobe behaviors by adjusting the lengths of the lower and upper bases of an isosceles trapezoid. This is to say, in order to obtain the good sidelobe behaviors and narrow main lobe width, the optimization procedure can be applied by adjusting the normalized ratio between the lengths of the upper and lower bases of a trapezoid. Thus, a new window class having both an extremely narrow main lobe width and high sidelobe behavior is generated with the optimized trapezoid windows being the parent windows. The estimators of the frequency, amplitude, and phase for harmonic analysis is provided by using the classical interpolation fast Fourier transform algorithm based on the proposed windows. The efficiency of new windows in high-accuracy harmonic analysis is demonstrated through computer simulations.

Multi-frequency simultaneous measurement of bioimpedance spectroscopy based on a low crest factor multisine excitation

Bioimpedance spectroscopy (BIS) is becoming a powerful diagnostic tool for a wide variety of medical applications, and the multi-frequency simultaneous (MFS) measurement of BIS can greatly reduce measurement time and record the transient physiological status of a living body compared with traditional frequency-sweep measurement technology. This paper adopts the Van der Ouderaas multisine, which has 31 equidistant and flat amplitude spectra and a low crest factor of 1.405 as the broadband excitation, and realizes the MFS measurement of BIS by means of spectral analysis using the fast Fourier transform algorithm. The approach to implement the multisine based on a field-programmable gate array and a digital to analog converter is described in detail, and impedance measurement experiments are performed on three resistance-capitance three-element phantoms. Experimental results show a commendable accuracy with a mean relative error of 0.55% for the impedance amplitudes, and a mean absolute error of 0.20° for the impedance phases on the 31 frequencies ranging linearly from 32 to 992 kHz. This paper validates the feasibility of the MFS technology for BIS measurement based on the multisine excitation.

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.

Broadband Bioimpedance Spectroscopy Based on a Multifrequency Mixed Excitation and Nuttall Windowed FFT Algorithm

Bioimpedance spectroscopy (BIS) has become an important clinical indicator for monitoring the pathological status of biological tissues, and multifrequency simultaneous measurement of BIS may provide more accurate diagnostic information compared with the traditional frequency-sweep measurement technology. This paper proposes a BIS multifrequency simultaneous measurement method based on multifrequency mixed (MFM) signal excitation and a Nuttall windowed interpolation FFT algorithm. Firstly, the excitation source adopts the nine-frequency MFM signal , which has excellent spectral characteristic and is very suitable for BIS measurement. On this basis, a Nuttall window is adopted to truncate sample data, and an interpolation FFT algorithm based on Nuttall window is built to perform spectral analysis, in which the parameter correction formula is provided based on polynomial approximation. A BIS measurement simulation experiment is performed on an RC three-element equivalent circuit, and results on the 9 primary harmonic frequencies ranging from 3.9 kHz to 1 MHz show a high accuracy with the impedance amplitude relative error , and the phase absolute error . This paper validates the feasibility of BIS multifrequency simultaneous measurement method and establishes an algorithm foundation for the development of practical broadband BIS measurement system.

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.

Development of a Stair-Step Multifrequency Synchronized Excitation Signal for Fast Bioimpedance Spectroscopy

Wideband excitation signal with finite prominent harmonic components is desirable for fast bioimpedance spectroscopy (BIS) measurements. This work introduces a simple method to synthesize and realize a type of periodical stair-step multifrequency synchronized (MFS) signal. The Fourier series analysis shows that the p-order MFS signal f(p, t) has constant 81.06% energy distributed equally on its p  2nth primary harmonics. The synthesis principle is described firstly and then two examples of the 4-order and 5-order MFS signals, f(4, t) and f(5, t), are synthesized. The method to implement the MFS waveform based on a field-programmable gate array (FPGA) and a digital to analog converter (DAC) is also presented. Both the number and the frequencies of the expected primary harmonics can be adjusted as needed. An impedance measurement experiment on a RC three-element equivalent model is performed, and results show acceptable precision, which validates the feasibility of the MFS excitation.