Interpolation Fast Fourier Transform Research Articles

Research on the online measuring technology of inter-turn insulation of dry air-core reactor

The fault model of the inter-turn short circuit of the dry air-core reactor is first analysed in this study, by which an online monitoring method of the reactor inter-turn insulation fault is proposed by using the change of the power angle. In order to achieve high-precision measurement, the fundamental harmonic separation algorithm improved by Hanning windowed interpolation method can effectively reduce the error of power angle measurement caused by frequency fluctuation and harmonic interference. By comparing it with the power angle measurement errors of fast Fourier transform (FFT) and Hanning window interpolation FFT, the algorithm is verified. The sensitivity and stability of the equipment are verified by the experiment of simulating and eliminating the fault in the initial stage of the inter-turn short circuit. At the same time, an online monitoring system for inter-turn insulation fault of dry-type air-core reactor based on this method is designed, including field monitoring device, the intelligent electronic device of the dry air-core reactor and expert software. The method and monitoring device proposed in this study enables the fault to be accurately monitored in the early stage, which is of great significance for the safe operation of the reactor.

High-Precision Harmonic Analysis Algorithm Based on Five-Term MSD Second-Order Self-Convolution Window Four-Spectrum-Line Interpolation

For the frequency spectrum leakage and fence effect generated in Fast Fourier Transform (FFT) during asynchronous sampling and integral period truncation affect the precision of harmonic detection, a new algorithm for harmonic analysis based on four-spectrum-line interpolation FFT with second-order self-convolution window with five-term Maximum-Sidelobe-Decay (MSD) was proposed and the polynomial fitting method was used to construct the four-spectrum-line interpolation correction formula. The simulation results showed that this algorithm could improve the detection accuracy of amplitude, phase and frequency by 1-2 orders of magnitude compared with other commonly used windowed interpolation algorithms.

Research on harmonic detection based on wavelet threshold and FFT algorithm

ABSTRACTThe fast Fourier transform (FFT) algorithm with window interpolation is the most commonly used and most effective method in harmonic analysis. However, the fast Fourier transform has a great dependence on the quality of the signal, and the existence of noise makes the detection result error. A harmonic detection method based on wavelet threshold preprocessing noise elimination and windowed interpolation FFT algorithm is proposed in this thesis. Firstly, de-noising the selected signals, and the wavelet coefficients are used to select the wavelet threshold to eliminate the noise in the signal. Then the signal after the de-noising is analysed by the Nuttall window interpolate FFT algorithm, and the calculation formula is derived by using the amplitude information content of four spectral lines. The simulation results show that the proposed method is more accurate and effective to detect the signal after de-noising.

Improved Parameter Identification Method for Envelope Current Signals Based on Windowed Interpolation FFT and DE Algorithm

Envelope current signals are increasingly emerging in power systems, and their parameter identification is particularly necessary for accurate measurement of electrical energy. In order to analyze the envelope current signal, the harmonic parameters, as well as the envelope parameters, need to be calculated. The interpolation fast Fourier transform (FFT) is a widely used approach which can estimate the signal frequency with high precision, but it cannot calculate the envelope parameters of the signal. Therefore, this paper proposes an improved method based on windowed interpolation FFT (WIFFT) and differential evolution (DE). The amplitude and phase parameters obtained through WIFFT and the envelope parameters estimated by the envelope analysis are optimized using the DE algorithm, which makes full use of the performance advantage of DE. The simulation results show that the proposed method can improve the accuracy of the harmonic parameters and the envelope parameter significantly. In addition, it has good anti-noise ability and high precision.

A Novel Through‐the‐Wall Imaging Algorithm Combined with Phase Shift Migration and NUFFT

This paper proposes a novel Through wall imaging (TWI) algorithm combined with phase compensation and Nonuniform fast Fourier transform (NUFFT). The wall effect is cancelled with phase compensation, which is implemented by multiplying the conjugated wall transmissivity with the received echoes. The NUFFT technique is implemented to calculate the imaging results. The proposed method has two merits: The phase compensation avoids a time-consuming calculation of the incidences angles; the image is reconstructed more accurately and efficiently than the conventional Interpolation-fast Fourier transform (IPFFT) method. The new method is implemented on 2D synthetic-generated data and experimental data. The results demonstrate that our method generates high quality focused images and achieves target geometrical identification within a very short time.

Efficient Stolt Migration for Large Nonuniform Single Borehole Radar Surveys

In this paper, the formulation of Stolt migration is modified for impulse borehole radar imaging in large nonuniform subsurface scenarios. By applying the nonuniform fast Fourier transform (FFT) to the acquisition of the frequency–wavenumber spectrum (FWS), the efficiency of Stolt migration for nonuniform surveys is improved. First, each nonuniform exponent basis in Fourier transform is approximated with a weighted summation of several uniform exponent bases. Then, the nonuniform samples with the same uniform exponent basis are accumulated to generate a larger virtual uniform sample set. The FWS of nonuniform samples is approximated with the virtual sample set by FFT. Finally, angular frequency interpolation and inverse FFT are performed over a sample FWS to reconstruct the reflectivity map of the imaging area. The selection of approximation parameters is discussed to make a tradeoff between approximation error and computational cost. The improved Stolt migration technique is compared with the conventional backprojection method and the Kirchhoff migration method on synthetic data and validated by a single borehole radar experiment in a subsurface scenario. The results show that the developed Stolt migration is superior to the conventional methods in terms of computational cost, cross-range resolution, and the ability to reconstruct the targets.

A Harmonic Analysis Method Based on Harris Window for Digital Substation

Accurate and efficient harmonics detection is an important premise and basis for controlling the harmonics. The sampling frequency of the grid voltage and current in digital substation normally must be kept constantly as required by the standard of IEC61850, thus the asynchronous sampling caused by the fluctuating grid frequency and this constant sampling frequency will result in spectral leakage and aliasing which would affect the accuracy of harmonic analysis. In this paper, a double-spectrum-line interpolation Fast Fourier Transform approach based on multi-term Harris window for grid frequency and harmonic measurement was proposed, and the simple and practical adjustment formulas for the frequency, amplitude and phase angle were derived by curve fitting. The correctness and effectiveness of the proposed method were validated by simulation and field test.

Rife-Vincent (I) Window Interpolated FFT Algorithm Based on Cubic Spline Function

In order to further improve the precision of harmonics measurement, the paper provides a new interpolation fast Fourier transform (FFT) algorithm based on RifeVincent (I) window. By using the cubic spline function to approach the ninth multinomial of frequency modification coefficient and the function of harmonic amplitude correction of the interpolation FFT algorithm based on RifeVincent (I) window, the computing speed has been improved. It can solve the contradiction between calculation accuracy and computational speed of windowed and interpolated FFT algorithm. The simulative results show that RifeVincent (I) window interpolation algorithm by using cubic spline function has the amplitude error less than 0.00001 %, the frequency error less than 0.000001 Hz, and the phase error less than 0.01%.

Composite Interpolated Fast Fourier Transform With the Hanning Window

The composite interpolated fast Fourier transform (IpFFT) with the Hanning window is investigated to decrease the estimation variance. This form of composite IpFFT makes use of four consecutive spectral lines around a spectral peak. These four consecutive lines render three estimators using the complex spectrum-based interpolation. The three estimators can be averaged to decrease the variance, and their weighting coefficients are established to produce the minimum variance. Theoretical analysis shows that this composite IpFFT has its best performance under noncoherent sampling conditions, achieving a minimum frequency variance of 1.8 folds of the Crame?r-Rao bound (CRB). The worst case occurs in the situation of coherent sampling, with a maximum variance of 2.6 folds of the CRB. Theoretical analysis was validated by numerical experiments on three types of noise-contaminated signals, cisoids, real-valued sine waves, and double-tone complex-valued signals. The cisoid case shows that the empirical variance very well matches the theoretical expression. Insofar as simulation is concerned (signal-to-noise ratio down to -2 dB), the empirical variance deviating from the theoretical expression is no more than 25%. All three experiments show that the empirical variance of the IpFFT is almost independent of the initial phase, whereas the bias is the opposite.

A Note on Optimality of Analytical Leakage Compensation at Boundary Frequencies

The interpolated fast Fourier transform (IFFT) was one of the first methods for the highly accurate estimation of sine wave parameters, and its first successful descendant was analytical leakage compensation [which is commonly called analytical solution (AS)]. The AS estimate of frequency is a whole class of solutions whose variance depends on a free parameter K. Thus, to extract the minimum variance solution from a theoretically infinite set, we have to find the optimal value K opt. This paper clarifies the mathematical background of AS and proposes two new solutions for K opt, which reduce the variance of AS estimates of low and high frequencies close to an integer. All inferences are justified by simulations, which confirm the validity of theoretical considerations.

Combining the Hanning windowed interpolated FFT in both directions

The interpolated fast Fourier transform (IFFT) has been proposed as a way to eliminate the picket fence effect (PFE) of the fast Fourier transform. The modulus based IFFT, cited in most relevant references, makes use of only the 1st and 2nd highest spectral lines. An approach using three principal spectral lines is proposed. This new approach combines both directions of the complex spectrum based IFFT with the Hanning window. The optimal weight to minimize the estimation variance is established on the first order Taylor series expansion of noise interference. A numerical simulation is carried out, and the results are compared with the Cramer–Rao bound. It is demonstrated that the proposed approach has a lower estimation variance than the two-spectral-line approach. The improvement depends on the extent of sampling deviating from the coherent condition, and the best is decreasing variance by 2/7. However, it is also shown that the estimation variance of the windowed IFFT with the Hanning is significantly higher than that of without windowing.

Interharmonics Analysis Based on Interpolating Windowed FFT Algorithm

The interharmonics, which are the same as integer harmonics, have serious impacts on the design of harmonics compensation equipment. Therefore, it is important to measure interharmonics accurately. The interharmonics cannot be obtained accurately by using fast Fourier transform (FFT) for an unsynchronized sample sequence analysis because of large errors in such cases. To reduce the errors caused by using FFT for an unsynchronized sample sequence analysis and to improve the measuring precision of interharmonics in electric power systems, an interharmonics estimation method based on the interpolation FFT algorithm is proposed. An algorithm for estimating interharmonics parameters based on the Blackman-Harris window, Rife-Vincent (I) window, and Rife-Vincent (III) window is given. Simulation results demonstrate that by using the proposed algorithm for the unsynchronized sample sequence analysis, the estimated interharmonics frequency, amplitude, and phase are highly accurate

Sensorless Speed Measurement of Induction Motor Using Hilbert Transform and Interpolated Fast Fourier Transform

A new scheme based on the Hilbert transform and the interpolated fast Fourier transform (IFFT) is proposed to improve the estimation accuracy of induction motor speed from motor current signals. The phase and amplitude fluctuation associated with the eccentricity harmonics is first demodulated by the Hilbert transform. IFFT is then performed to estimate the speed of induction motors running under constant speed and transient conditions. Simulations have shown considerable improvement in estimation accuracy using IFFT as compared to the FFT technique. An experimental study has further confirmed good agreement between the estimated motor speed using the proposed scheme and the measured speed using an encoder.

ADC testing using interpolated fast Fourier transform (IFFT) technique

An ideal transfer characteristic of an analogue-to-digital converter (ADC) is simulated and an arbitrary nonlinearity error is introduced. A full-scale sine wave is also simulated and applied to ADC input. The interpolated fast Fourier transform (IFFT) technique is used to determine accurately fundamental and other harmonics in the output spectrum of the ADC. The signal-to-noise ratio and the effective number of bits (ENOB) are computed on the basis of FFT and IFFT for different resolutions of ADC and test conditions. The effects of rectangular and Hanning time window functions on the determination of frequency components are reported. The proposed method of dynamic testing of the ADC is useful for users as well as manufacturers.

A COMPARATIVE STUDY OF HIGH-ACCURACY FREQUENCY ESTIMATION METHODS

This paper presents a comparative study of three high-accuracy frequency estimation methods for application in vibration analysis of rotating machinery. The first two techniques are non-parametric methods based on the fast Fourier transform (FFT) : the interpolated fast Fourier transform (IFFT) and the iterative weighted phase averager (IWPA). The third method is a parametric high-resolution technique known as ESPRIT. The FFT-based methods combine techniques to reduce the effects of windowing with an iterative procedure which, at each iteration, detects the strongest peak and subtracts its effect (to reduce the interference resulting from spectral leakage). The paper compares their variance, resolution and computational requirements by means of simulation examples and also using end winding vibration data taken from a hydroelectric turbogenerator. It is found that, in situations with a moderate or high level of spectral interference, the IWPA method outperforms the IFFT and is even competitive with ESPRIT. Moreover, the IWPA has the ability to separate sinusoids more closely spaced than the periodogram's resolution limit. The IFFT method, on the other hand, has the lowest computational cost.