Windowed Discrete Fourier Transform Research Articles

A Novel Microgrid Islanding Detection Algorithm Based on a Multi-Feature Improved LSTM

Islanding detection is one of the conditions necessary for the safe operation of the microgrid. The detection technology should provide the ability to differentiate islanded operations from power grid disturbances effectively. Given that it is difficult to set the fault threshold using the passive detection method, and because the traditional active detection method affects the output power quality, a microgrid islanding detection method based on the Sliding Window Discrete Fourier Transform (SDFT)-Empirical Mode Decomposition (EMD) and Long Short-Term Memory (LSTM) network optimized by an attention mechanism is proposed. In this paper, the inverter output current and voltage at the point of common coupling (PCC) are transformed by the SDFT. The positive sequence, zero sequence, and negative sequence components of voltage and current harmonics are calculated and reconstructed by adopting the symmetrical component method (SCM). Meanwhile, the current and voltage are decomposed into a mono intrinsic mode function (IMF). The symmetric components of voltage, current, and IMFs are used as inputs to the deep learning algorithm. An LSTM with the features extracted to classify islanding and grid disturbance is proposed. By using the attention mechanism to set the weight values of the features of hidden states obtained by the LSTM network, the proportion of important features increases, which improves the classification effect. MATLAB/Simulink simulation results indicate that the proposed method can effectively classify the islanding state under different working conditions with an accuracy level of 98.4% and a loss value of 0.0725 with a maximal detection time of 66.94 ms. It can also reduce the non-detection zone (NDZ) and detection time and has a certain level of noise resistance. Meanwhile, the problem whereby the active method affects the microgrid power quality is avoided without disturbing the current or power of the microgrid.

Amplitude and frequency estimator for aperiodic multi-frequency noisy vibration signals of a tram gearbox

Sinusoidal parameter estimation for determining frequency position and amplitude is challenging for noisy short vibration signals, e.g. from machines or human vibrations. In this paper, we propose the “Trimmed Window Discrete Fourier Transform” (TWDFT) estimator, which uses for every frequency a one-point discrete Fourier transform (DFT) to determine the corresponding spectral amplitude. To avoid leakage effects, it cuts the time interval so that it corresponds to an integer number of period durations. To evaluate the estimator performance, we compare it with relevant estimators such as the Cramer-Rao lower bound (CRLB) and the spectral spline interpolation applied on a noisy mono-frequent test signal with a fractional frequency. For the estimated parameters, the mean squared errors (MSE) are calculated and compared as a function of the signal-to-noise ratio (SNR). The advantages of the TWDFT estimator can be seen over the whole SNR range. The TWDFT estimates are better than the fast Fourier transform (FFT) starting at a SNR of –6 dB. At a SNR of 30 dB, the estimator meets the real value of the frequency and reaches similar results as the CRLB. The application of the TWDFT estimator as a short-time analysis on a vibration signal of a tram gearbox shows a significantly more differentiated time-frequency analysis compared to a short-time Fourier transform (STFT).

A high-accuracy and low-complexity phasor estimation method for PMU calibration

Due to the increasing development of renewables in power systems, the requirements for phasor measurement units (PMUs) become higher. A PMU calibrator is an important tool to test and calibrate PMUs to ensure their measurement performance. This device can provide accurate reference values for error analysis of PMUs. In this paper, a phasor algorithm with low computational complexity and high accuracy is proposed for the PMU calibrator. This method reduces the processor requirements and development cost of the calibrator, thereby facilitating its popularization. At first, an enhanced discrete Fourier transform (DFT) method is put forward: 1) the frequency response of the windowed DFT method is analyzed to reveal its large measurement errors under dynamic conditions; 2) the parameter requirements of the DFT window that is regarded as a lowpass filter are analyzed, and thus a lowpass filter with better filtering performance is designed as the window coefficients to improve the estimation accuracy. Then, based on the enhanced DFT algorithm, a calibrator algorithm framework consisting of two-stage filters and signal recognition module is established. This algorithm can consider the anti-interference ability and dynamic measurement accuracy at a low reporting rate. Simulation and experimental test results show that the proposed calibrator algorithm provides high-accuracy measurements of the static and dynamic signals with low computational complexity.

Rolling Bearing Fault Analysis by Interpolating Windowed Discrete Fourier Transform Algorithm

Rolling Bearing Fault Analysis by Interpolating Windowed Discrete Fourier Transform Algorithm

Analysis of MFCC and Multitaper MFCC Feature Extraction Methods

In speech & audio applications, short-term signal spectrum is often represented using mel-freuency cepstral coefficient (MFCC) computed from a windowed discrete Fourier transform (DFT). Windowing reduces spectral leakage but variance of the spectrum estimate remains high. An extension to windowed DFT is called multitaper method which uses multiple time domain windows which are called as tapers with frequency domain averaging. Then detailed statistical analysis of MFCC bias & variance is done. For speaker verification the extracted feature is used to design a model using classifier (GMM), which implements likelihood ratio test to decide whether to accept or deny the registered speaker.

Modulation Linearity Correction Method of LFM Signal Based on Windowed Discrete Bi-orthogonal Fourier Transform

Modulation Linearity Correction Method of LFM Signal Based on Windowed Discrete Bi-orthogonal Fourier Transform

Low-Variance Multitaper MFCC Features: A Case Study in Robust Speaker Verification

In speech and audio applications, short-term signal spectrum is often represented using mel-frequency cepstral coefficients (MFCCs) computed from a windowed discrete Fourier transform (DFT). Windowing reduces spectral leakage but variance of the spectrum estimate remains high. An elegant extension to windowed DFT is the so-called multitaper method which uses multiple time-domain windows (tapers) with frequency-domain averaging. Multitapers have received little attention in speech processing even though they produce low-variance features. In this paper, we propose the multitaper method for MFCC extraction with a practical focus. We provide, first, detailed statistical analysis of MFCC bias and variance using autoregressive process simulations on the TIMIT corpus. For speaker verification experiments on the NIST 2002 and 2008 SRE corpora, we consider three Gaussian mixture model based classifiers with universal background model (GMM-UBM), support vector machine (GMM-SVM) and joint factor analysis (GMM-JFA). Multitapers improve MinDCF over the baseline windowed DFT by relative 20.4% (GMM-SVM) and 13.7% (GMM-JFA) on the interview-interview condition in NIST 2008. The GMM-JFA system further reduces MinDCF by 18.7% on the telephone data. With these improvements and generally noncritical parameter selection, multitaper MFCCs are a viable candidate for replacing the conventional MFCCs.

Subspace-Least Mean Square Method for Accurate Harmonic and Interharmonic Measurement in Power Systems

A high-resolution method for harmonic and interharmonic measurements in power systems is proposed based on the concepts of subspace and least mean square. A subspace function is constructed by using the noise eigenvectors of the autocorrelation matrix of the test signal. The harmonic and interharmonic frequencies of the signal are derived by finding the zeros of the subspace function. A least mean square approach is introduced to compute the amplitudes and phase angles of harmonic and interharmonic components based on the computed frequencies and time-domain measurements of the signal. The proposed method is compared with some of the recently proposed harmonic/interharmonic analysis methods, including discrete Fourier transform (DFT), windowed interpolation DFT, Prony, iterative DFT, and min-norm methods. The effects of noise, fundamental frequency deviation, and subharmonics have been considered. Numerical results show that the proposed method can perform accurate harmonic/interharmonic measurements for power system signals.

Data Compression Based on DFT for Passive Location in Sensor Networks

TDOA based passive location is an important application in sensor networks. The signal data must be transferred from one sensor to another, which is used to estimate TDOA. Therefore, a data compression method has to be used for the sake of reducing the volume of data. In order to improve coding efficiency, a block-encoding method based on windowed Discrete Fourier Transform (DFT) is proposed. We design a polyphase structure to achieve windowed DFT, which can achieve real time processing of the high sampling rate. Compared with transform coding to the whole data, the block-encoding method is easy to implement in engineering with lower computation complexity, and therefore saves computational resources. Simulation results show that TDOA estimation accuracy based on data block-encoding data is close to that based on the whole encoding method for high SNR.

A WDFT-Based Channel Estimator with Non-adaptive Linear Prediction in Non-sample Spaced Channels

This letter addresses the edge effect on a windowed discrete Fourier transform (WDFT)-based channel estimator for orthogonal frequency division multiplexing (OFDM) systems with virtual carriers in non-sample spaced channels and derives a sufficient condition to reduce the edge effect. Moreover, a modified WDFT-based channel estimator with multi-step linear prediction as an edge effect reduction technique is proposed. Simulation results show that it offers around 5dB signal-to-noise ratio (SNR) gain over the conventional WDFT-based channel estimator at bit error rate (BER) of 10-3.

Adaptive DFT-Based Interferometer Fringe Tracking

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) Observatory at Mount Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier-transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on offline data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse. One example of such an application might be to the field of thin-film measurement by ellipsometry, using a broadband light source and a Fourier-transform spectrometer to detect the resulting fringe patterns.

Optimal interpolating windowed discrete Fourier transform algorithms for harmonic analysis in power systems

An interpolating windowed discrete Fourier transform (DFT) has been used to eliminate the errors caused by the leakage and picket fence effects associated with use of a conventional DFT. An interpolating algorithm eliminates the errors caused by the picket fence effect, and the errors produced by the leakage effect are reduced by windowing the signals. The precision of the harmonic analysis and the implementation of the interpolating algorithm are both affected by the choice of window function. The leakage effect of a conventional DFT and the windowed DFT are analysed. A method to construct optimal window functions and the corresponding interpolation algorithms is presented. Simulation results show that the interpolating windowed DFT algorithms have a high accuracy and are easy to implement and they are therefore useful tools for precise and practical harmonics evaluation in power systems.

Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform

This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of the recursive moving window discrete Fourier transform (DFT) with precomputed twiddle factors. We show the strong influence of precomputation errors – both within the initial fast Fourier transform (FFT) and the recursion – on the numerical stability. Numerical simulations confirm the theoretical results.

Windows for ADC dynamic testing via frequency-domain analysis

In this paper, the frequency-domain dynamic test of analog-to-digital converters (ADCs) is considered under the assumption of noncoherent sinewave sampling. A procedure is described which is based on the windowed discrete Fourier transform (WDFT), optimized for the achievement of high estimation accuracy. With this aim, the class of windows belonging to the set of discrete prolate spheroidal sequences is adopted for the reduction of the effects of spectral leakage. Practical suggestions are given for a straightforward applicability of derived results and for an efficient estimation of ADC spectral parameters. Finally, experimental results are presented in order to validate the proposed testing approach.

Some alternatives in transform-domain suppression of narrow-band interference for signal detection and demodulation

Conventional detection and demodulation rules are not ideally suited for use with discrete Fourier transform (DFT) based narrow-band interference suppression, if the DFT incorporates time-weighting to localize the interference spectrally. Detection rules which are adapted to the time-weighting are introduced and shown to offer significant improvements in performance, but their implementation is complex. It is found that if a spectrally-contained orthogonal transform (SCOT) is employed in place of the windowed DFT however, the conventional detection rules have a level of performance comparable to that obtained with DFT based suppression and the adapted rules. In addition to yielding good interference localization, SCOTs benefit from the fact that they provide a Karhunen-Loeve like transform for each component of the observation. The primary focus of the paper is the application of interference suppression for the detection of the presence of covert signals; however, it is also demonstrated that SCOT based suppression is potentially better suited than DFT based suppression for data demodulation in commercial code-division multiple-access (CDMA) network overlays.

The use of DFT windows in signal-to-noise ratio and harmonic distortion computations

The discrete Fourier transform (DFT) can be used to compute the signal-to-noise ratio (SNR) and harmonic distortion of a waveform recorder. When the data record contains a non-integer number of cycles of the sine wave, energy leaks from the sine wave and its harmonics to adjacent frequencies. A.L. Benetazzo et al. (1992) describe a windowed DFT method for computing the RMS value of a sine wave from the magnitude of the main lobe of its DFT and recommend the use of minimum energy windows. We present criteria for choosing the DFT window. A constraint for the window coefficients is derived to insure that quantization error does not influence the estimate of the amplitude of a sine wave from the main lobe of its DFT.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recursive moving window DFT algorithm

A recursive algorithm is presented for computing the discrete Fourier transform (DFT). The algorithm is developed for a moving-window-type processing. The computational structure is fully concurrent and allows a vectorized updating of the DFT. The total time required for the updating could be as low as that of only one multiplication and two additions, regardless of the number of points. A possible structure for executing the computations is developed, and possible enhancements are analyzed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>