Showing papers on "Discrete Fourier transform published in 2019"

Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms

Abstract: PRELIMINARIES An Elementary Introduction to the Discrete Fourier Transform Some Mathematical and Computational Preliminaries SEQUENTIAL FFT ALGORITHMS The Divide-and-Conquer Paradigm and Two Basic FFT Algorithms Deciphering the Scrambled Output from In-Place FFT Computation Bit-Reversed Input to the Radix-2 DIF FFT Performing Bit-Reversal by Repeated Permutation of Intermediate Results An In-Place Radix-2 DIT FFT for Input in Natural Order An In-Place Radix-2 DIT FFT for Input in Bit-Reversed Order An Ordered Radix-2 DIT FFT Ordering Algorithms and Computer Implementation of Radix-2 FFTs The Radix-4 and the Class of Radix-2s FFTs The Mixed-Radix and Split-Radix FFTs FFTs for Arbitrary N FFTs for Real Input FFTs for Composite N Selected FFT Applications PARALLEL FFT ALGORITHMS Parallelizing the FFTs: Preliminaries on Data Mapping Computing and Communications on Distributed-Memory Multiprocessors Parallel FFTs without Inter-Processor Permutations Parallel FFTs with Inter-Processor Permutations A Potpourri of Variations on Parallel FFTs Further Improvement and a Generalization of Parallel FFTs Parallelizing Two-Dimensional FFTs Computing and Distributing Twiddle Factors in the Parallel FFTs APPENDICES Fundamental Concepts of Efficient Scientific Computation Solving Recurrence Equations by Substitution Bibliography

Spectrum Analysis and Convolutional Neural Network for Automatic Modulation Recognition

Abstract: Recent convolutional neural networks (CNNs)-based image processing methods have proven that CNNs are good at extracting features of spatial data. In this letter, we present a CNN-based modulation recognition framework for the detection of radio signals in communication systems. Since the frequency variation with time is the most important distinction among radio signals with different modulation types, we transform 1-D radio signals into spectrogram images using the short-time discrete Fourier transform. Furthermore, we analyze statistical features of the radio signals and use a Gaussian filter to reduce noise. We compare the proposed CNN framework with two existing methods from literature in terms of recognition accuracy and computational complexity. The experiments show that the proposed CNN architecture with spectrogram images as signal representation achieves better recognition accuracy than existing deep learning-based methods.

Learning Support Correlation Filters for Visual Tracking

Abstract: For visual tracking methods based on kernel support vector machines (SVMs), data sampling is usually adopted to reduce the computational cost in training. In addition, budgeting of support vectors is required for computational efficiency. Instead of sampling and budgeting, recently the circulant matrix formed by dense sampling of translated image patches has been utilized in kernel correlation filters for fast tracking. In this paper, we derive an equivalent formulation of a SVM model with the circulant matrix expression and present an efficient alternating optimization method for visual tracking. We incorporate the discrete Fourier transform with the proposed alternating optimization process, and pose the tracking problem as an iterative learning of support correlation filters (SCFs). In the fully-supervision setting, our SCF can find the globally optimal solution with real-time performance. For a given circulant data matrix with $n^2$ n 2 samples of $n \times n$ n × n pixels, the computational complexity of the proposed algorithm is $O(n^2\; \log n)$ O ( n 2 log n ) whereas that of the standard SVM-based approaches is at least $O(n^4)$ O ( n 4 ) . In addition, we extend the SCF-based tracking algorithm with multi-channel features, kernel functions, and scale-adaptive approaches to further improve the tracking performance. Experimental results on a large benchmark dataset show that the proposed SCF-based algorithms perform favorably against the state-of-the-art tracking methods in terms of accuracy and speed.

Multi-scale proper orthogonal decomposition of complex fluid flows

Abstract: Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

Intelligent Reflecting Surface with Discrete Phase Shifts: Channel Estimation and Passive Beamforming

Abstract: In this paper, we consider an intelligent reflecting surface (IRS)-aided single-user system where an IRS with discrete phase shifts is deployed to assist the uplink communication. A practical transmission protocol is proposed to execute channel estimation and passive beamforming successively. To minimize the mean square error (MSE) of channel estimation, we first formulate an optimization problem for designing the IRS reflection pattern in the training phase under the constraints of unit-modulus, discrete phase, and full rank. This problem, however, is NP-hard and thus difficult to solve in general. As such, we propose a low-complexity yet efficient method to solve it sub-optimally, by constructing a near-orthogonal reflection pattern based on either discrete Fourier transform (DFT)-matrix quantization or Hadamard-matrix truncation. Based on the estimated channel, we then formulate an optimization problem to maximize the achievable rate by designing the discrete-phase passive beamforming at the IRS with the training overhead and channel estimation error taken into account. To reduce the computational complexity of exhaustive search, we further propose a low-complexity successive refinement algorithm with a properly-designed initialization to obtain a high-quality suboptimal solution. Numerical results are presented to show the significant rate improvement of our proposed IRS training reflection pattern and passive beamforming designs as compared to other benchmark schemes.

Real-Time Wavelet-Based Grid Impedance Estimation Method

Abstract: This letter presents a novel method to estimate the grid impedance based on stationary discrete wavelet packet transform (SDWPT). The proposed method uses a steady-state technique, by injecting an interharmonic current into the grid and measuring the voltage response at the point of common coupling to estimate the grid impedance. The proposed method employed a standard three-phase photovoltaic system interconnected to the grid to validate its effectiveness experimentally. Comparisons with a discrete Fourier transform- and continuous wavelet transform-based impedance estimation approaches demonstrate the performance of proposed method. Besides, the proposed SDWPT-based impedance estimation provided accurate experimental results, which make it viable for real-time applications.

50 Years of FFT Algorithms and Applications

Abstract: The fast Fourier transform (FFT) algorithm was developed by Cooley and Tukey in 1965. It could reduce the computational complexity of discrete Fourier transform significantly from $$O(N^2)$$ to $$O(N\log _2 {N})$$ . The invention of FFT is considered as a landmark development in the field of digital signal processing (DSP), since it could expedite the DSP algorithms significantly such that real-time digital signal processing could be possible. During the past 50 years, many researchers have contributed to the advancements in the FFT algorithm to make it faster and more efficient in order to match with the requirements of various applications. In this article, we present a brief overview of the key developments in FFT algorithms along with some popular applications in speech and image processing, signal analysis, and communication systems.

Reduced Leakage Synchrophasor Estimation: Hilbert Transform Plus Interpolated DFT

Abstract: Synchrophasor estimation is typically performed by means of spectral analysis based on the discrete Fourier transform (DFT). Traditional DFT approaches, though, suffer from several uncertainty contributions due to the stationarity assumption, spectral leakage effects, and the finite-grid resolution. This paper addresses these limitations, by proposing a joint application of the Hilbert transform (HT) and the interpolated DFT (IpDFT) technique. Specifically, the HT enables the suppression of the spectral leakage generated by the negative image of the tones under analysis, whereas the IpDFT limits the effects of spectrum granularity. In order to relax the constraint in terms of measurement reporting latency, the proposed estimator can adopt a window length of 40 ms and yet provides a noticeable estimation accuracy with a worst-case total vector error and frequency error equal to 0.02% and 4 mHz, respectively, in steady-state conditions. In this context, this paper discusses the most suitable setting of the algorithm parameters and their effect on spurious component rejection. Moreover, a thorough metrological characterization of the algorithm estimation accuracy and responsiveness with respect to the IEEE Std. C37.118.1 is carried out in order to detect the main uncertainty sources as well as possible room for enhancement. Finally, a comparison with two consolidated IpDFT approaches shows the actual performance enhancement provided by the proposed algorithm.

Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations

Abstract: Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural priors they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the $O(N \log N)$ Cooley-Tukey FFT algorithm to machine precision, for dimensions $N$ up to $1024$. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points -- the first time a structured approach has done so -- with 4X faster inference speed and 40X fewer parameters.

Multidimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem

Abstract: We propose Multidimensional Random Slice-based Sparse Fourier Transform (MARS-SFT), a sparse Fourier transform for multidimensional, frequency-domain sparse signals, inspired by the idea of the Fourier projection-slice theorem. MARS-SFT identifies frequencies by operating on one-dimensional slices of the discrete-time domain data, taken along specially designed lines; these lines are parametrized by slopes that are randomly generated from a set at runtime. The discrete Fourier transforms (DFTs) of data slices represent DFT projections onto the lines along which the slices were taken. On designing the line lengths and slopes so that they allow for orthogonal and uniform projections of the sparse frequencies, frequency collisions are avoided with high probability, and the multidimensional frequencies can be recovered from their projections with low sample and computational complexity. We show analytically that the large number of degrees of freedom of frequency projections allows for the recovery of less sparse signals. Although the theoretical results are obtained for uniformly distributed frequencies, empirical evidence suggests that MARS-SFT is also effective in recovering clustered frequencies. We also propose an extension of MARS-SFT to address noisy signals that contain off-grid frequencies and demonstrate its performance in digital beamforming automotive radar signal processing. In that context, the robust MARS-SFT is used to identify range, velocity, and angular parameters of targets with low sample and computational complexity.

Two-Stage Analog Combining in Hybrid Beamforming Systems With Low-Resolution ADCs

Abstract: In this paper, we investigate hybrid analog/digital beamforming for multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters for millimeter wave (mmWave) communications. In the receiver, we propose to split the analog combining subsystem into a channel gain aggregation stage followed by a spreading stage. Both stages use phase shifters. Our goal is to design the two-stage analog combiner to optimize mutual information (MI) between the transmitted and quantized signals by effectively managing quantization error. To this end, we formulate an unconstrained MI maximization problem without a constant modulus constraint on analog combiners, and derive a two-stage analog combining solution. The solution achieves the optimal scaling law with respect to the number of radio frequency chains and maximizes the MI for homogeneous singular values of a MIMO channel. We further develop a two-stage analog combining algorithm to implement the derived solution for mmWave channels. By decoupling channel gain aggregation and spreading functions from the derived solution, the proposed algorithm implements the two functions by using array response vectors and a discrete Fourier transform matrix under the constant modulus constraint on each matrix element. Therefore, the proposed algorithm provides a near-optimal solution for the unconstrained problem, whereas conventional hybrid approaches offer a near optimal solution only for a constrained problem. The closed-form approximation of the ergodic rate is derived for the algorithm, showing that a practical digital combiner with two-stage analog combining also achieves the optimal scaling law. Simulation results validate the algorithm performance and the derived ergodic rate.

New Measurement Algorithm for Supraharmonics Based on Multiple Measurement Vectors Model and Orthogonal Matching Pursuit

Abstract: There are many cases of electromagnetic interference caused by supraharmonics emitted by power electronic equipment. However, there is currently no effective method for measuring supraharmonics. This paper proposes a new supraharmonics high-resolution measurement algorithm based on a multiple measurement vectors (MMVs) compressive sensing (CS) model and an orthogonal matching pursuit (OMP) recovery algorithm. First, by introducing an interpolation factor, based on a spectrum array of multiple discrete Fourier transform coefficient vectors and a Dirichlet kernel matrix, an MMVs CS model is constructed. Then, by using the jointly sparse property of high-resolution spectrum array, the MMVs CS model is converted into a single-measurement vector CS model. Third, by using an OMP recovery algorithm, the support set of the high-resolution spectrum array is solved. Finally, by using least squares, the high-resolution spectrum array of supraharmonics is obtained. Simulation results and verification of the measured data show that the algorithm proposed in this paper can improve the frequency resolution by an order of magnitude without increasing the observation time, can shorten the calculation time by $100\times $ compared with the single measurement vector compressive sensing-OMP algorithm, and can compute the amplitude and phase of supraharmonics accurately. Meanwhile, the amplitude fluctuation characteristics of supraharmonics can also be analyzed accurately. This algorithm shows a good application prospect in measuring supraharmonics accurately.

A High-Flexible Low-Latency Memory-Based FFT Processor for 4G, WLAN, and Future 5G

Abstract: A high-throughput programmable fast Fourier transform (FFT) processor is designed supporting 16- to 4096-point FFTs and 12- to 2400-point discrete Fourier transforms (DFTs) for 4G, wireless local area network, and future 5G. A 16-path data parallel memory-based architecture is selected as a tradeoff between throughput and cost. To implement a hardware-efficient high-speed processor, several improvements are provided. To maximally reuse the hardware resource, a reconfigurable butterfly unit is proposed to support computing including eight radix-2 in parallel, four radix-3/4 in parallel, two radix-5/8 in parallel, and a radix-16 in one clock cycle. Twiddle factor multipliers using different schemes are optimized and compared, wherein modified coordinate rotation digital computer scheme is finally implemented to minimize the hardware cost while supporting both FFTs and DFTs. An optimized conflict-free data access scheme is also proposed to support multiple butterflies at any radices. The processor is designed as a general IP and can be implemented using a processor synthesizer (application-specific instruction-set processor designer). The electronic design automation synthesis result based on a 65-nm technology shows that the processor area is 1.46 mm2. The processor supports 972 MS/s 4096-point FFT at 250 MHz with a power consumption of 68.64 mW and a signal-to-quantization-noise ratio of 66.1 dB. The proposed processor has better-normalized throughput per area unit than the state-of-the-art available designs.

Improved Homomorphic Discrete Fourier Transforms and FHE Bootstrapping

Abstract: Homomorphic encryption (HE), which enables computation on ciphertexts without any leakage, rise as a most promising solution for privacy-preserving data processing, including secure machine learning and secure out-sourcing computation. Despite the extensive applicability of HE, the current constructions are sometimes considered as impractical due to its inefficiency. In this paper, we propose improvements on the linear transformation in bootstrapping, a technique allowing the infinite number of operation for HE, and homomorphic discrete Fourier transformation (DFT) using batch homomorphic encryption. We observe that the multiplication of a sparse diagonal matrix and ciphertext of a vector can be done within O(1) homomorphic computations. This observation induces the faster algorithm for linear transformation in bootstrapping and homomorphic DFT. To achieve this, we use Cooley-Tukey matrix factorization and construct a new recursive factorization of the linear transformation in bootstrapping. Our method with radix r only requires O(r log r n) constant vector multiplication and O(√r log r n) rotations by consuming O(log r n) depth when the input vector size is n. The previous method used in the library, a library that implements homomorphic encryption for approximate computation, requires O(n) and O(√n), respectively. To show the performance improvement, we implement our method on top of the library. Our implementation, along with further few techniques, of these algorithms show the significant improvements compared to the previous algorithm. New homomorphic DFT with length 2 14 only takes about 8s which results 150 times faster than the previous method. Furthermore, the bootstrapping takes about 2 minutes for ℂ 32768 plaintext space with 8-bit precision, which takes 26 hours with same bit precision using the previous method.

Performance Enhancement of Probabilistically Shaped OFDM Enabled by Precoding Technique in an IM-DD System

Abstract: Probabilistically shaped orthogonal frequency-division multiplexing (PS-OFDM) signal is proposed and experimentally demonstrated in a low-cost intensity-modulation and direct-detection (IM-DD) system for optical access networks. The concatenation of constant composition distribution matcher (CCDM) and low-density parity-check (LDPC) code sequentially implements probabilistic amplitude shaping (PAS) and channel coding. Thanks to the precoding scheme, all data subcarriers can be treated equally by one optimized probabilistic distribution. Experimental results demonstrate that constant amplitude zero autocorrelation sequence (CAZAC) precoding can offer optimal performance compared to orthogonal circulant transform (OCT) precoding and discrete Fourier transform spread (DFT-spread) in terms of increasing generalized mutual information (GMI) and reducing PAPR. Moreover, probabilistically-shaped 64-QAM OFDM signal can provide shaping gains of 1.04/0.94/0.64 dB at 4.0/3.6/3.0 bits/QAM symbol compared to traditional 64-QAM OFDM signal. Meanwhile, compared to traditional 16-QAM OFDM, it can offer shaping gains of 1.64/0.64 dB at 3.6/3.0 bits/QAM symbol. In addition, net data rate ranging from 32.66 to 43.55-Gb/s over 20-km single mode fiber (SMF) can be achieved by only adjusting the probabilistic distribution.

A Model-Driven Deep Learning Method for LED Nonlinearity Mitigation in OFDM-Based Optical Communications

Abstract: The nonlinearity of light emitting diodes (LED) has restricted the bit error rate (BER) performance of visible light communications (VLC). In this paper, we propose model-driven deep learning (DL) approach using an autoencoder (AE) network to mitigate the LED nonlinearity for orthogonal frequency division multiplexing (OFDM)-based VLC systems. Different from the conventional fully data-driven AE, the communication domain knowledge is well incorporated in the proposed scheme for the design of network architecture and training cost function. First, a deep neural network (DNN) combined with discrete Fourier transform spreading (DFT-S) is adopted at the transmitter to map the binary data into complex I-Q symbols for each OFDM subcarrier. Then, at the receiver, we divide the symbol demapping module into two subnets in terms of nonlinearity compensation and signal detection, where each subnet is comprised of a DNN. Finally, both the autocorrelation of the learned mapping symbols and the mean square error of demapping symbols are taken into account simultaneously by the cost function for network training. With this approach, the LED nonlinearity and the interference introduced by the multipath channel can be effectively mitigated. The simulation results show that the proposed scheme exhibits better BER performance than some existing methods and further accelerates the training speed, which demonstrates the prospective and validity of DL in the VLC system.

Improved synchrophasor measurement to capture sub/super-synchronous dynamics in power systems with renewable generation

Abstract: The existing phasor-measurement unit (PMU) and wide-area measurement system (WAMS) based on the fundamental synchrophasors are insufficient to accurately capture the dynamics of sub/super-synchronous resonance or oscillation (SSR/SSO). To address this issue, this study proposes a new method for the simultaneous and precise measurement of the fundamental and multiple sub/super-synchronous harmonic phasors. It improves the classic discrete Fourier transform (DFT)-based method by adding adaptive frequency detection, modal filtration and phasor correction and compensation. Thus, in the context of SSR/SSO, the phasors of both fundamental and interharmonic components can be precisely obtained at local PMUs and the control/data centre of WAMS. The basic procedures and the prototype implementation of the method have been elaborated, and the performance has been examined with simulation signals as well as the field data recorded from an actual SSO incident. The results have verified its high precision, noise immunity and fast response.

Rate of Change of Frequency Estimation for Power Systems Using Interpolated DFT and Kalman Filter

Abstract: This paper presents a new method for estimating the rate of change of frequency (RoCoF) of voltage or current signals measured using instrument transformers. The method is demonstrably superior to currently available methods in the literature, in terms of estimation latency and estimation error. The estimation is performed in two steps. In the first step, the analog voltage or current signal obtained from an instrument transformer is statistically processed using interpolated discrete Fourier transform (IDFT) in order to obtain the means and variances of the signal parameters. These means and variances are then given as inputs to the second step, in which Kalman filtering (KF) is used to find the final RoCoF estimate. Accurate mathematical expressions for the means and variances of signal parameters have been derived and used in the second step, which is the main reason behind the superior performance of the method. The applicability of the method has been demonstrated on a benchmark power system model.

Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations

Abstract: Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural priors they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the O(N log N) Cooley-Tukey FFT algorithm to machine precision, for dimensions N up to 1024. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points-the first time a structured approach has done so-with 4× faster inference speed and 40× fewer parameters.

Generalized Channel Estimation and User Detection for Massive Connectivity With Mixed-ADC Massive MIMO

Abstract: This paper aims to provide a partial discrete Fourier transform (DFT) pilot sequence assisted joint channel estimation and user activity detection scheme for massive connectivity, in which a large number of devices with sporadic transmission communicate with a base station (BS) in the uplink. The joint channel estimation and device detection problem can be formulated as a compressed sensing single measurement vector or multiple measurement vector (MMV) problem depending on whether the BS is equipped with single or large number of antennas. Due to high hardware cost and power consumption in massive multiple-input multiple-output (MIMO) systems, a mixed analog-to-digital converter (ADC) architecture is considered. In order to accommodate a large number of simultaneously transmitting devices, the joint channel estimation and active user detection are formulated as an MMV problem for the massive connectivity scenario; and the proposed GTurbo-MMV algorithm can precisely estimate the channel state information and detect active devices with relatively low overhead. Furthermore, we study the state evolution (SE) for the MMV problem to obtain achievable bounds on channel estimation and device detection performance, in which both the missing and false detection probabilities can be made tend to zero in the massive MIMO regime. The simulation results confirm the theoretical accuracy of our analysis.

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

Abstract: 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.

Enhanced DFT-Based Controller for Selective Harmonic Compensation in Active Power Filters

Abstract: Among the various selective harmonic current controllers, the traditional repetitive-based discrete Fourier transform controller (DFTRC) is increasingly favored thanks to its unique merits of excellent selectivity and simplicity. However, the traditional approach suffers from disadvantages like slow dynamic responses, defective control structure, and sensitivity to frequency fluctuation. In order to alleviate aforementioned shortcomings, an enhanced discrete Fourier transform-based controller is proposed. The proposed controller is based on the generalized discrete Fourier transform to improve the overall control performances of dynamic responses, structure flexibility, and control robustness. The proposed controller provides individual positive-feedback path and gain coefficient for each harmonic component. Therefore, it not only maintains the advantage of excellent selectivity but also realizes the individual control parameters tuning for each harmonic frequency, which is impossible in traditional DFTRC owing to the congenital defects of control structure. In addition, a correction function is embedded in the forward path to provide the overall phase compensation and correct the plant for better characteristic. The Lagrange interpolation method is adopted to realize the fractional-order delay and its adaption to frequency variations with fixed sampling frequency. Detailed mathematical model along with optimized design principle is given to make full use of the advantages of the enhanced control structure. Extensive experimental results validate the effectiveness of the theoretical analysis and the improvement achieved by the proposed controller.

Velocity Estimation From a Single Linear Motion Blurred Image Using Discrete Cosine Transform

Abstract: There is a growing trend to use a digital camera as an instrument to measure velocity instead of a regular sensor approach. This paper introduces a new proposal for estimating kinematic quantities, namely, the angle and the relative speed, from a single motion blur image using the discrete cosine transform (DCT). Motion blur is a common phenomenon present in images due to the relative movement between the camera and the objects, during sensor exposure to light. Today, this source of kinematic data is mostly dismissed. The introduced technique focuses on cases where the camera moves at a constant linear velocity while the background remains unchanged. 2250 motion blur pictures were shot for the angle experiments and 500 for the speed estimation experiments, in a light and distance controlled environment, using a belt motor slider driven at angles between 0° and 90° and 10 preset speeds. The DCT Hough and DCT Radon results were compared to discrete Fourier transform (DFT) Hough and DFT Radon algorithms for angle estimation. The mean absolute error of the DCT Radon method for direction estimation was 4.66°. In addition, the mean relative error for speed estimation of the DCT Pseudocepstrum was 5.15%. The innovative DCT frequency analysis proposals were more accurate than all competitors evaluated for the reconstruction of the point spread function that enables calculation of relative velocity and motion direction. These results demonstrate that cameras as an instrument can be used to measure velocity even using a single linear motion blur degraded image.

Multidomain Multimodal Fusion for Human Action Recognition Using Inertial Sensors

Abstract: One of the major reasons for misclassification of multiplex actions during action recognition is the unavailability of complementary features that provide the semantic information about the actions. In different domains these features are present with different scales and intensities. In existing literature, features are extracted independently in different domains, but the benefits from fusing these multidomain features are not realized. To address this challenge and to extract complete set of complementary information, in this paper, we propose a novel multidomain multimodal fusion framework that extracts complementary and distinct features from different domains of the input modality. We transform input inertial data into signal images, and then make the input modality multidomain and multimodal by transforming spatial domain information into frequency and time-spectrum domain using Discrete Fourier Transform (DFT) and Gabor wavelet transform (GWT) respectively. Features in different domains are extracted by Convolutional Neural networks (CNNs) and then fused by Canonical Correlation based Fusion (CCF) for improving the accuracy of human action recognition. Experimental results on three inertial datasets show the superiority of the proposed method when compared to the state-of-the-art.

Combined DFT and Fuzzy Based Faulty Phase Selection and Classification in a Series Compensated Transmission Line

Abstract: The conventional distance protection scheme malfunctions sometimes in case of a fixed series capacitor compensated transmission line due to the change in relaying impedance of the protected line during faulty conditions. In order to mitigate this problem, a combined discrete Fourier transform and fuzzy (CDFTF) based algorithm has been proposed in this paper. This method has been tested on a 400 km, 735 kV series compensated transmission line network and WSCC 3-machine 9-bus system for all fault types using MATLAB/Simulink and PSCAD platforms, respectively. A fixed series capacitor is located at the middle of the protected line. The fundamental components of phase currents, phase voltages, and zero-sequence current are fed as inputs to the proposed scheme. The fault detection, faulty phase selection, and fault classification are achieved within 1/2–1 cycle of power frequency. The proposed CDFTF-based scheme is less complex and is better than other data mining techniques which require huge training and testing time. Test results corroborate the proposed scheme reliability with wide variations in fault location, fault resistance, fault inception angle, evolving faults, compensation level, and heavy load interconnection. The results discussed in this work indicate that the proposed technique is resilient to wide variations in fault and system conditions.