Discrete Fourier Transform Approach Research Articles

Implementation of Phasor Measurement Unit Based on Phase-Locked Loop Techniques: A Comprehensive Review

The dynamic monitoring, control, and protection of modern power systems in real time require time-stamped electrical measurements to accurately estimate the bus voltage phasors using the state estimation function under normal and abnormal conditions. These measurements can be acquired by time-synchronized devices, known as phasor measurement units (PMUs). PMUs can measure bus voltage and branch current phasors of a three-phase network, as well as the frequency and the rate of change of frequency (ROCOF), with high speed, accuracy and time stamping provided by global positioning system (GPS) at the coordinated universal time (UTC). Various phasor estimation algorithms have been proposed in the literature, while most of them are concentrated in the discrete Fourier transform (DFT) algorithm, where an integer number of samples multiple of the nominal frequency is required for the computations. In cases where the frequency of the power grid deviates from its nominal value, the raw application of the DFT approach can lead to large errors during phasor estimation. Another approach of the phasor estimation is based on the phase-locked loop (PLL) techniques, widely used in grid tie inverters. PLL techniques can track dynamically (continuous time) the estimated frequency to the time-variant frequency of the power grid. A brief introduction to the basic concepts of the synchrophasor definition is provided, while the main DFT methods for synchrophasor estimation according to recent literature are mentioned. PLL-based PMU techniques are reviewed for both steady-state and dynamic conditions according to IEEE standards. In conclusion, the performance of PLL-based PMU algorithms presented in this literature review is discussed.

A fast numerical method for photomultiplier tube calibration

In this article, a new method is discussed for the calibration and monitoring of photomultiplier tubes (PMTs). This method is based on a Discrete Fourier Transform (DFT) and it is fast and general so that it can be used in cases where an analytical model of the PMT response is not available. The DFT approach is employed for the absolute calibration of the Hamamatsu R1408 photomultiplier tube. It should be noted that the R1408 PMTs do not show a sharp peak at the single photoelectron distribution and gain determination via conventional methods is often unattainable. Here, we show that the DFT technique, coupled with a gamma function model for the single photoelectron response, produces rigorous calibration results and it can be used for gain determination with a good accuracy.

Synchrophasors Determination Based on Interpolated FFT Algorithm

Within the standard IEEE C37.118 applications and proposed hardware structure of a phasor measurement unit (PMU) are described. This paper presents the concept of the system for measuring and transferring synchrophasors from a theoretical aspect. Synchrophasor algorithms are developed in MATLAB/Simulink for the purpose of easier verification and hardware deployment on today’s market available and affordable real time development kits. Analysis of the synchrophasor measurement process is performed gradually. Firstly, by defining the synchrophasor based on three-phase to αβ-transformation and then introducing a discrete Fourier transform (DFT) based on synchrophasor estimation algorithm. Later, accompanying adverse effects resulting from its application are analyzed by means of simulation. To increase accuracy and improve estimation algorithm interpolated discrete Fourier transform (IpDFT) with and without windowing technique is used. To further optimize algorithm performance convolution sum in recursive form has been implemented instead of classical DFT approach. This study was carried out in order to validate described measurement system for the monitoring of transients during island operation of a local power electric system. Finally, simulation and experimental results including error analysis are also presented.

Optimisation of Image Processing Parameters for Flame Image Velocimetry (FIV) Measurement in a Single-Cylinder, Small-Bore Optical Diesel Engine

<div class="section abstract"><div class="htmlview paragraph">High-speed soot luminosity movies are widely used to visualise flame development in optical diesel engines thanks to its simple setup and relatively low cost. Recent studies demonstrated the high-speed soot luminosity movies are not only effective in showing the overall distribution and temporal evolution of sooting flames but also flow fields within the flame through the application of combustion (or flame) image velocimetry. The present study aims to improve this imaging technique by systematically evaluating key image processing parameters based on high-speed soot luminosity movies obtained from a single-cylinder, small-bore optical diesel engine. The raw soot luminosity movies are processed using PIVlab - a Matlab-based open-source code widely used for particle image velocimetry (PIV) applications. The images are pre-processed using the Contrast-Limited Adaptive Histogram Equalization (CLAHE) filter before the velocity vectors are determined through the multi-pass Discrete Fourier Transform (DFT) approach. This is then post processed to find the optimised filter size, interrogation window size, step size and velocity limit for minimal interpolation counts. As a result, a four-step DFT approach with interrogation windows set at 32-32-16-16 pixels, CLAHE filter size at 16 pixels and velocity limit at 3 pixels/frame is determined as optimised. The derived flow fields show that the internal flame pattern change, as demonstrated by previous studies, can be used to obtain the flow vectors within the flame successfully. From a selected example movie, the processed images show the evolution of multiple vortex structures as a result of strong jet-wall and jet-to-jet interactions as well as the swirl effects.</div></div>

A critical fault detection analysis & fault time in a UPFC transmission line

This paper discusses a critical study of fault detection and fault time analysis in a Unified Power Flow Controller (UPFC) transmission line. Here the Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT) approach are used for processing the faulty current signal to obtain fundamental current signal. The extracted fault current signals from the current transformer are fed to DWT and DFT approach for computing spectral energy (SE). The differential spectral energy (DSE) of phase currents are evaluated by taking the difference of SE obtained at sending and receiving end. The DSE is the key factor for deciding the fault in any of the phase or not. The Daubechy mother wavelet (db4) is used here because of its high accuracy of detection with less processing time. The novelty of the scheme is that it can accurately detect the critical fault variation of the line. Number of simulations are validated at the extreme condition of the line and compared to other conventional existing scheme. Multi-phase fault in double circuit line, CT saturation, UPFC operating condition (series voltage and angle), UPFC location and wind speed variation including wind farm simulation are validated to verify the performance of the scheme. The advantages of the scheme is that it works effectively to detect the fault at any stage of critical condition of the line and fault detection time remains within 20 msec (less than one cycle period). This scheme protects both internal and external zone including parameter variation of the line.

Fuzzy Logic based hybrid type control implementation of a heaving wave energy converter

This study presents the results of the Fuzzy Logic based control application for a heaving wave energy converter operating in realistic sea-state conditions. It has been shown in literature that the power capture performance of a heaving wave energy converter depends on meeting the resonance condition with the incident wave frequency. In regular sea wave conditions, the task of setting the control parameters is a well-known easy task where the wave frequency is known. However, in irregular sea conditions, the wave frequency needed for control settings is not clearly defined. One of the approaches proposed in literature is to use of the dominant wave frequency that can be estimated by a model using the Discrete Fourier Transform approach. The presented model utilises the estimated wave frequency in Fuzzy Logic controller for determination of Power Take-Off control settings. This approach combines widely used fast tuning technique with a new slow tuning method. As a part of the study, the developed realistic simulation model and proposed Fuzzy Logic based controller are used to combine the fast and slow tuning techniques to form a novel hybrid control technique. The simulation results for this new control technique in realistic sea conditions are presented.

Measuring stock market resiliency with Discrete Fourier Transform for high frequency data

In this paper, we investigate market resiliency as one of the stock market liquidity dimensions. A new methodology for stock resiliency measurement based on Discrete Fourier Transform (DFT) for high-frequency intraday data is introduced. The known disadvantage of DFT is signal leakage. Therefore, the modified formula for resiliency proxy that decreases the signal leakage impact by filtering is utilized. Three alternative window functions are employed: (1) the Hamming window, (2) the Kaiser window, and (3) the SR785 Flat-Top window. Furthermore, there is provided statistical analysis of the results, including its significance and some additional properties. The findings of empirical experiments for real-data from the Warsaw Stock Exchange reveal that the results rather turn out to be robust to the choice of the window filter. Thus, the DFT approach might be considered an auspicious resiliency proxy with an intuitive base.

Application of a Hybrid Method for Power System Frequency Estimation with a 0.2-second Sampled Period

The signal processing technique is one of the principal tools for diagnosing power quality (PQ) issues in electrical power systems. The Discrete Fourier Transform (DFT) is a frequency analysis technique used to process power system signals and identify PQ problems. However, the DFT algorithm may lead to spectral leakage and picket-fence effect problems for asynchronously sampled signals that contain harmonic, inter-harmonic, and flicker components. To resolve this shortcoming, a hybrid method for frequency estimation based on a second-level DFT approach and a frequency-domain interpolation algorithm to obtain the accurate fundamental frequency of a power system is proposed in this paper. This method uses a second-level DFT to compute the cosine and sine parts for the fundamental frequency components of the acquired signals. Then, a frequency-domain interpolation approach is adopted to determine the amplitude ratio for the cosine and sine parts of the system’s fundamental frequency. A set of mixed signals with harmonic, inter-harmonic, and flicker components with the fundamental frequency deviation is used. The evaluation results demonstrate the superiority of the new method over other approaches for assessing asynchronously sampled signals contaminated with noise, harmonic, inter-harmonic, and flicker components.

Image Retrieval Based on Discrete Fractional Fourier Transform Via Fisher Discriminant

Discrete fractional Fourier transform (DFrFT) is a powerful signal processing tool. This paper proposes a method for DFrFT-based image retrieval via Fisher discriminant and 1-NN classification rule. First, this paper proposes to extend the conventional discrete Fourier transform (DFT) descriptors to the DFrFT descriptors to be used for representing the edges of images. The DFrFT descriptors extracted from the training images are employed to construct a dictionary, for which the corresponding optimal rotational angles of the DFrFTs are required to be determined. This dictionary design problem is formulated as an optimization problem, where the Fisher discriminant is the objective function to be minimized. This optimization problem is nonconvex (Guan et al. in IEEE Trans Image Process 20(7):2030---2048, 2011; Ho et al. in IEEE Trans Signal Process 58(8):4436---4441, 2010). Furthermore, both the intraclass separation and interclass separation of the DFrFT descriptors are independent of the rotational angles if these separations are defined in terms of the 2-norm operator. To tackle these difficulties, the 1-norm operator is employed. However, this reformulated optimization problem is nonsmooth. To solve this problem, the nondifferentiable points of the objective function are found. Then, the stationary points between any two consecutive nondifferentiable points are identified. The objective function values are evaluated at these nondifferentiable points and these stationary points. The smallest L objective function values are picked up and the corresponding rotational angles are determined, which are then used to construct the dictionary. Here, L is the total number of the rotational angles of the DFrFTs used to construct the dictionary. Finally, an 1-NN classification rule is applied to perform the image retrieval. Application examples and experimental results show that our proposed method outperforms the conventional DFT approach.

Individually optimized uniform contrast enhancement in CT angiography for the diagnosis of pulmonary thromboembolic disease—A simulation study

To improve the diagnostic quality of CT pulmonary angiography (CTPA) by individually optimizing a biphasic contrast injection function to achieve targeted uniform contrast enhancement. To compare the results against a previously reported discrete Fourier transform (DFT) approach. This simulation study used the CTPA datasets of 27 consecutive patients with pulmonary thromboembolic disease (PE). An optimization approach was developed consisting of (1) computation of the impulse enhancement function (IEF) based on a test bolus scan, and (2) optimization of a biphasic contrast injection function using the IEF in order to achieve targeted uniform enhancement. The injection rates and durations of a biphasic contrast injection function are optimized by minimizing the difference between the resulting contrast enhancement curve and the targeted uniform enhancement curve, while conforming to the clinical constraints of injection rate and total contrast volume. The total contrast volume was limited first to the clinical standard of 65 ml, and then to the same amount used in the DFT approach for comparison. The optimization approach and the DFT approach were compared in terms of the root mean square error (RMSE) and total contrast volume used. When the total contrast volume was limited to 65 ml, the optimization approach produced significantly better contrast enhancement (closer to the targeted uniform contrast enhancement) than the DFT approach (RMSE 17 HU vs 56 HU, p < 0.00001). On average, the optimization approach used 63 ml contrast, while the DFT approach used 50 ml with four patients exceeding 65 ml. When equivalent total contrast volume was used for individual patient, the optimization approach still generated significantly better contrast enhancement (RMSE 44 HU vs 56 HU, p < 0.01). Constraints for the injection function could be easily accommodated into the optimization process when searching for the optimal biphasic injection function. The optimization approach generated individually optimized biphasic injection functions yielding significantly better contrast enhancement compared to the DFT approach. This new approach has the potential to improve the diagnostic quality of CTPA for PE.

Two approaches to the blind phase shift extraction for two-step electronic speckle pattern interferometry

A two-step electronic speckle pattern interferometry (ESPI) method with blind phase shift of a reference wave, in which the phase shift extraction is fulfilled by using both a correlation and a discrete Fourier transform (DFT) approaches, is presented here. In the correlation approach, the blind phase shift is calculated via the correlation coefficient between two similar speckle interferograms (SI) differing only by the reference wave phase shift. The DFT approach is based on the blind phase shift extraction from frequency components of SI Fourier spectra. Comparative analysis of these approaches has testified to their high performance. Moreover, it is shown that the correlation approach is more preferable for blind phase shift extraction from SIs with a rough surface than from interferograms with a smooth surface; hence, it is more convenient for ESPI than for phase-shifting interferometry. In addition, this approach provides a lesser level of systematic error of extracted phase shift in comparison with the DFT. The correlation approach was used for experimental definition of Poisson’s ratio for duralumin constructional material by the two-step ESPI method.

WE-C-103-12: Individually Optimized Contrast Injection in CT Angiography for the Diagnosis of Pulmonary Thromboembolic Disease

Purpose: To improve the diagnostic quality of CT angiography (CTPA) for pulmonary thromboembolic disease by individually optimizing a bi-phasic contrast injection function to achieve uniform target contrast enhancement. To compare the results against a previously reported discrete Fourier transform (DFT) approach. Methods: This simulation study uses a retrospective dataset of 27 consecutive patients. We developed an optimization approach consists of two steps: 1. Compute the impulse enhancement function (IEF) based on the test bolus scan; 2. Optimize the contrast injection function using the IEF in order to achieve uniform target enhancement. We chose a bi-phasic contrast injection function in which the injection rates and durations are optimized by minimizing the difference between its contrast enhancement curve and the uniform target enhancement curve. The contrast volume is limited either to the clinical standard of 65 mL or to the same amount used in the DFT approach. The optimization approach is compared against the DFT approaches in terms of the root mean square errors (RMSE) from the uniform target contrast enhancement curve and the contrast volume used. Results: When the contrast volume is limited to 65 mL, the optimization approach produces contrast enhancement significantly (p<.00001) closer to the uniform target contrast enhancement (mean RMSE 17 HU) than the DFT approach (mean RMSE 56 HU), for which the contrast volume is not even limited. When the contrast volume is limited to be the same amount used in the DFT approach, the optimization approach still generate significantly improved contrast enhancement than the DFT approach (RMSE 44 HU vs. 56 HU, p<.0099). Conclusion: The optimization approach generates individually optimized bi-phasic injection functions yielding significantly improved contrast enhancement than the DFT approach. Its implementation in clinic has great potential to improve the diagnostic quality of CTPA. This work is supported in part by Philips Healthcare, Inc.

A discrete fourier transform approach searching for compatible sequences and optimal designs

A Discrete Fourier Transform Approach Searching for Compatible Sequences and Optimal Designs

Recursive algebraic method of computing power system harmonics

AbstractEnsuring power quality in power systems demands fast calculation of harmonics. In this paper, a recursive algebraic approach to the calculation of current transformer (CT)‐derived current signal frequency and harmonics is proposed that is based on a fast but accurate recursive algorithm whereby in any stage of sampling in a given cycle the variables are calculated on the basis of their values in the previous stage. Comparison with the discrete Fourier transform (DFT) approach shows the superiority of the proposed approach. It is shown that when the number of samples used in the DFT approach is increased, the results obtained approach those of the proposed recursive algebraic method. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Cluster expansion and the configurational theory of alloys

A rigorous mathematical foundation for the cluster-expansion method is presented. It is shown that the cluster basis developed by Sanchez et al. [Physica A 128, 334 (1984)] is a multidimensional discrete Fourier transform while the general formalism of Sanchez [Phys. Rev. B 48, 14013 (1993)] corresponds to a multidimensional discrete wavelet transform. For functions that depend nonlinearly on the concentration, it is shown that the cluster basis corresponding to a multidimensional discrete Fourier transform does not converge, as it is usually assumed, to a finite cluster expansion or to an Ising-type model representation of the energy of formation of alloys. The multidimensional wavelet transform, based on a variable basis cluster expansion, is shown to provide a satisfactory solution to the deficiencies of the discrete Fourier-transform approach. Several examples aimed at illustrating the main findings and conclusions of this work are given.

Quadrature Sampling for Built-In Analog/RF IC Spectrum Test

The frequency-domain testing of analog and radio-frequency integrated circuits usually requires full-blown discrete Fourier transform (DFT) engines for spectrum analysis. However, the built-in spectrum analysis is prohibited due to the excessive computation requirement. This brief proposes a novel built-in frequency-domain testing algorithm based on quadrature sampling, which allows the evaluation of the interested frequency components with more than 90% reduction in computation complexity and only two locations of memory occupation. Theoretical analysis in the frequency domain of the quadrature sampling algorithm is provided to demonstrate that the results it obtained are equivalent to that of the standard DFT approach. The simplified calculation enables the on-chip implementation of the proposed algorithm with minor additional circuits and more than 90% savings of power consumption and evaluation time. The circuit architecture for the test setup is proposed and applied for the filter response and the third-order intermodulation test. Simulation results on a 450-MHz low-noise amplifier reveal accurate gain and phase evaluation with only 5.6% the amount of computation of the DFT.

Amplitude Estimation by a Multipoint Interpolated DFT Approach

This paper focuses on the amplitude estimation by a multipoint interpolated discrete Fourier transform (DFT) method. Accurate results are obtained using the weighted multipoint interpolated DFT (WMIpDFT) method with maximum sidelobe decay windows. In addition, using the WMIpDFT method with maximum sidelobe decay windows, it is mathematically proven that the systematic errors affecting the amplitude estimation decrease as the number of interpolation points and/or the window order increases. Computer simulations confirm the accuracy of the derived expressions. Moreover, the influence of white Gaussian noise on the amplitude estimations has been analyzed by means of computer simulations.

Channel estimation for OFDM systems in non-sample-spaced multipath channels

A discrete Fourier transform (DFT)-based channel estimator for orthogonal frequency division multiplexing (OFDM) systems is proposed. In multipath channels with non-sample-spaced time delays, the conventional DFT approach will cause power leakage and result in an error floor. Proposed is a novel symmetric extension DFT method to reduce the leakage power efficiently. Numerical results show that the proposed channel estimator can eliminate the error floor substantially.

Single- and multi-sine DFT demodulation with an application to precision capacitive sensors

This paper presents a comparative study of digital methods to improve the signal to noise ratio in ac bridge measurements and other applications requiring demodulation of amplitude-modulated signals. Three types of discrete Fourier transform (DFT) based algorithms are analyzed. The algorithms considered are single-sine conventional DFT, single-sine running DFT, and multi-sine running DFT. We report on a case study using a field programmable gate array (FPGA) to monitor the output signal from a typical ac bridge with variable capacitive sensors in two arms. Theoretically, both the single- and multi-sine running DFT algorithms are shown to provide improved ripple noise performance over the conventional single-sine DFT approach. Additionally, in the presence of a high noise background, theoretical calculations indicate that the multi-sine running DFT provides a factor of 2 improvement in signal to noise ratio compared to the single-sine conventional DFT. Experimental results also show a moderate improvement in ripple noise, but not at the level predicted by the theory. Finally, the method for running multi-sine reported can be used for any periodic basis function. As a result, higher complex basis functions, particularly those with orthogonal properties, such as those that can be generated from a Fourier series or functions that contain continuous spectra (wavelets for example), could also be used.

Root Counting, the DFT and the Linear Complexity of Nonlinear Filtering

The method of root counting is a well established technique in the study of the linear complexity of sequences. Recently, Massey and Serconek [11] have introduced a Discrete Fourier Transform approach to the study of linear complexity. In this paper, we establish the equivalence of these two approaches. The power of the DFT methods are then harnessed to re-derive Rueppel‘s Root Presence Test, a key result in the theory of filtering of m-sequences, in an elegant and concise way. The application of Rueppel‘s Test is then extended to give lower bounds on linear complexity for new classes of filtering functions.