Sliding Discrete Fourier Transform Research Articles

Tracking of cogging stiffness using the multi-bin SDFT

Due to the high power density and wide speed range, a permanent magnet synchronous motor (PMSM) is commonly used in industry. Efficient production requires optimized motion control of the mechanism driven by the PMSM. Unfortunately, designing the controller is usually based on a model of the mechanism without including parameters originating from the motor. Cogging stiffness originates from the magnetic forces between rotor magnets and stator teeth and is one of these forgotten parameters. The performance is sub-optimal when this stiffness is not considered during control design. The stiffness also changes over time due to changing load conditions such as temperature. Aiming for optimized motion control of high-speed mechanisms, this article proposes to expand the classic motion controller with an on-line stiffness tracker. The tracker is based on the sliding discrete Fourier transform (SDFT). The tracking technique is conceptually analyzed and experimentally validated on a PMSM-driven rod. The classic Welch technique having an update time of at least 100 s is used as a benchmark. With similar accuracy and a much faster update time of 1.25 ms, the stiffness is tracked on-line using SDFT. The developed stiffness tracker is implemented on the provided commercial motion controller, proving its computational efficiency.

Tracking of cogging stiffness using the multi-bin SDFT

Due to the high power density and wide speed range, a permanent magnet synchronous motor (PMSM) is commonly used in industry. Efficient production requires optimized motion control of the mechanism driven by the PMSM. Unfortunately, designing the controller is usually based on a model of the mechanism without including parameters originating from the motor. Cogging stiffness originates from the magnetic forces between rotor magnets and stator teeth and is one of these forgotten parameters. The performance is sub-optimal when this stiffness is not considered during control design. The stiffness also changes over time due to changing load conditions such as temperature. Aiming for optimized motion control of high-speed mechanisms, this article proposes to expand the classic motion controller with an on-line stiffness tracker. The tracker is based on the sliding discrete Fourier transform (SDFT). The tracking technique is conceptually analyzed and experimentally validated on a PMSM-driven rod. The classic Welch technique having an update time of at least 100 s is used as a benchmark. With similar accuracy and a much faster update time of 1.25 ms, the stiffness is tracked on-line using SDFT. The developed stiffness tracker is implemented on the provided commercial motion controller, proving its computational efficiency.

Simulation Study of Improved DDSRF-PLL under Distorted Grid Voltage

When the grid voltage is distorted and harmonic and DC components are mixed, the phase locking accuracy of decoupled double synchronous reference frame for phase-locked loop (DDSRF-PLL) will be greatly reduced. This paper proposes an improved DDSRF-PLL(IDDSRF-PLL) structure based on Frequency Adaptive Sliding Discrete Fourier Transform (FASDFT) filtering. A cascade SDFT structure is adopted for FASDFT filtering. The SDFT with fixed sliding window width at the front stage extracts the fundamental wave signal of power grid voltage to eliminate the influence of harmonics and DC components. The latter SDFT detects the sliding window width of power grid frequency update in real time through a nonlinear tracking differentiator (TD) to suppress spectrum leakage. Then DDSRFT-PLL is used to separate the positive and negative sequence of the fundamental signal and lock the phase. Finally, the simulation results in Matlab/Simulink verify the correctness and effectiveness of the proposed method.

Moth–Flame-Optimization-Based Parameter Estimation for FCS-MPC-Controlled Grid-Connected Converter With LCL Filter

The ability to model a system with high accuracy plays an important role in finite-control-set model-predictive-control (FCS-MPC)-controlled LCL-interfaced grid-connected converters (LCL-GCCs). However, the effect of aging, unmeasured noise, and temperature change on LCL-GCCs may result in parameter perturbations between the prediction model and the actual system. A model mismatch may occur, which may lead to violations of constraints, worsen the power quality of the grid current, and even threaten the system stability. This article presents a novel nature-inspired optimization paradigm named moth–flame-optimization (MFO), which applies the spiral logarithmic function to simulate the flight of a moth approaching a flame. The method is designed to efficiently identify and update the model parameters, and the fitness function for the state variables is designed and solved iteratively to minimize mismatches with the model. The advantages of the proposed method are its fast convergence and ability to determine parameters with high accuracy. These advantages effectively prevent the algorithm from converging to local optima. To achieve the harmonic rejection capability, a sliding discrete Fourier transform (SDFT) algorithm is also proposed to predict the harmonic at each sampling interval; thus, the harmonics are considered in the cost function. Experimental comparisons under different scenarios validate the effectiveness of the proposed SDFT-based MFO–MPC method.

Rapid Extraction of the Fundamental Components for Non-Ideal Three-Phase Grid Based on an Improved Sliding Discrete Fourier Transform

In order to make an effective extraction of the fundamental components for a non-ideal three-phase grid, an improved sliding discrete Fourier transform (ISDFT) has been proposed in this paper. Firstly, the non-ideal signal characteristics are studied in detail, which reveals that there are not only typical harmonic components, but also double frequency components, that exist in dq coordinates when the three-phase grid voltages are unbalanced. Then, the structure form of the conventional sliding discrete Fourier transform (SDFT) has been redesigned to form the ISDFT algorithm, in which a special offset link is introduced to reduce the extraction time while the effectiveness is guaranteed. The experimental results show that this proposed ISDFT is suitable for types of non-ideal signals extraction and can keep a nice dynamical and steady performance in cases of grid or load disturbance. For the average extraction time, ISDFT is saving about 44.56% more of the time than SDFT and about 65.32% more than discrete Fourier transform (DFT).

Automatic seizure detection with different time delays using SDFT and time-domain feature extraction.

Automatic seizure detection is important for fast detection of the seizure because the way that the expert denotes and searches for seizure in the long signal takes time. The most common way to detect seizures automatically is to use an electroencephalogram (EEG). Many studies have used feature extraction that needs time for calculation. In this study, sliding discrete Fourier transform (SDFT) was applied for conversion to a frequency domain without using a window, which was compared with using window for feature selection. SDFT was calculated for each time series sample directly without any delay by using a simple infinite impulse response (IIR) structure. The EEG database of Bonn University was used to test the proposed method, and two cases were defined to examine a two-classifier feedforward neural network and an adaptive network-based fuzzy inference system. Results revealed that the maximum accuracies were 93% without delay and 99.8% with a one-second delay. This delay accrued because the average was taken for the results with a one-second window.

Low-Speed Sensorless Control for the Interior Permanent Magnet Synchronous Motors with Sliding Discrete Fourier Transform

An efficient estimation of the rotor position has always been a premise of the reliable operation for the interior permanent magnet synchronous motors (IPMSM), especially for low-speed conditions because of the small back electromotive force (EMF) and low signal-to-noise ratio (SNR). The commonly used observation method, e.g., sliding mode observer (SMO), is suitable for these surface mounted motors and has no great adaptability to the saliency. In this paper, a novel rotor position (including the real-time position and initial position) estimation method was proposed based on the traditional high-frequency signal injection method. Firstly, high-frequency signals were injected to induce the high-frequency current components which contain the rotor position information. Then, the sliding discrete Fourier transform (SDFT) algorithm was used to extract the amplitudes of the induced current components which could be used to get the real-time and initial rotor positions by a proportional integral (PI) regulator and a polarity identification. Lastly, with the established experiments’ platform, the estimation tests of the rotor position at a low speed have been completed to make verification of the effectiveness of the approach studied in this paper.

Improvements to the Sliding Discrete Fourier Transform Algorithm [Tips & Tricks

This article presents two networks that improve upon the behavior and performance of previously published sliding discrete Fourier transform (SDFT) algorithms. The proposed networks are structurally simple, computationally efficient, guaranteed stable networks used for real-time sliding spectrum analysis. The first real-time network computes one spectral output sample, equal to a single-bin output of an N-point DFT, for each input signal sample. The second real-time network is frequency flexible, in that its analysis frequency can be any scalar value in the range of zero to one-half the input data sample rate measured in cycles per second.

A Blind Demodulation Algorithm for Underwater Acoustic MPSK Signal

Multiple phase-shift keying (MPSK) is a common carrier modulation in underwater acoustic (UWA) communication. This paper proposes a robust blind demodulation algorithm to improve the performance and practicability of blind demodulation of MPSK signals under impulsive noise and UWA sparse multipath channels. The proposed algorithm adopts a $T$ /2-spaced blind equalizer based on quasi-affine projection, so it has strong adaptability to sparse UWA multipath channels. First, the received signal is preprocessed to suppress the impulsive interference, and the parameters are estimated. Then, timing synchronization is performed point by point based on sliding discrete Fourier transform (SDFT) to avoid equalizer performance degradation or even lock-loss caused by large clock frequency deviation and long-time error accumulation. Based on this, the over-sampling signal with two fixed sampling points per symbol is obtained. Meanwhile, following the idea of memory improved proportionate affine projection algorithm and normalized factor, the cost function of the blind equalizer is constructed by using the $l_{0}$ norm penalty on the tap coefficients. In this way, the updating formula of the tap coefficients is derived, and the blind equalization is then conducted on the signal after timing synchronization to eliminate or weaken the channel influence. Finally, the residual frequency offset and phase offset of the carrier are removed through the M-power transform and the second-order decision feedback digital phase-locked loop. Simulation experiments and practical signal demodulation results indicate that the proposed algorithm achieves higher BER performance and modulation parameter robustness for impulsive noise and UWA multipath channel.

A Digital Interfacing Circuit Based on Sliding DFT Bins for Capacitive Sensors

A digital interfacing circuit (DIC) based on sliding discrete Fourier transform (SDFT) bins has been proposed for lossy capacitive sensors. The proposed interfacing circuit consisting of an analog sensing circuit and an analog-to-digital converter (ADC)-field-programmable gate array (FPGA)-based DIC. The sliding DFT bin-1 is employed as a quadrature signal generator to obtain in-phase and quadrature signals of the input supply voltage provided to the analog sensing circuit. The output sinusoidal signal of analog sensing circuit is correlated with the in-phase and quadrature signals separately and then averaged with SDFT bin-0 for computing sensing capacitance and resistance values. The proposed method is implemented in FPGA and tested for capacitance measurement range of 11 pF–5.27 nF with the maximum relative percentage error of 1.36%. The nonlinearity error is < 0.37% FS and FSS. Moreover, the suitability of the proposed interface for humidity measurement has been explored and validated experimentally with saturated salt solutions. Furthermore, the interdigitated capacitance is fabricated and tested with the proposed digital interface for the capacitance range of 30–122 pF, which finds an application in capacitive touchpad.

A harmonics detection method based on improved comb filter of sliding discrete Fourier for grid-tied inverter

Harmonic detection plays an important role in power quality for grid-tied inverters. Among the various methods, sliding discrete Fourier transform (SDFT) based algorithms have found wide and popular applications due to advantages like simplicity and excellent selectively filtering properties. However, SDFT suffers from disadvantages like slow dynamics and large memory occupation. In this paper, the discrete transfer function of SDFT harmonic extraction method is analyzed, and the SDFT transfer function is divided into three parts: comb filter, resonance controller, and adjustment factor. It is found that the comb filter determines the harmonic component that SDFT needs to detect and the dynamic performance of SDFT. Thus, the comb filter can be improved according to the characteristics of the load current, thereby achieving faster dynamic performance while reducing the digital storage space required for the implementation of the SDFT algorithm. Therefore, a general harmonics detection is proposed, which could detect harmonics by adjusting the comb filter of SDFT according to the characteristics of the load current. Finally, the correctness and effectiveness of the proposed general harmonics detection method are verified by relevant experiments.

Sparsity-inducing frequency-domain adaptive line enhancer for unmanned underwater vehicle sonar

The radiated lines from underwater targets are a significant feature for passive sonar detection. Since the spatial and time processing gains are limited in an unmanned underwater vehicle (UUV) sonar, an adaptive line enhancer (ALE) is usually employed as a preprocessing step to enhance the signal-to-noise ratio (SNR) of the lines. However, the original time-domain ALE based on the least mean square (LMS) algorithm suffers from the weight noise in the adaptation, which limits the SNR gain severely. Inspired by the frequency-domain sparsity of the lines, a sparsity-inducing ALE is developed to break through this limitation. The proposed ALE is implemented in the frequency domain and a reweighted L1-norm sparse penalty is incorporated into the cost function of the adaptation. By means of the sparse penalty, a zero-attraction term is added in the adaptation, which results in the suppression of the weight noise. The SNR gain is thus enhanced. In the proposed ALE, the sliding discrete Fourier transform (SDFT) technique is utilized to transfer the time-domain input samples to the frequency domain, and the computational complexity of the proposed ALE is thus comparable to that of the original one, which meets the energy efficiency requirement of UUV. Simulation results demonstrate that the SNR gain of the proposed ALE is over 9 dB higher than that of the original ALE with an input SNR of −25 dB. Experimental data processing also verifies the superiority of the proposed ALE.

First-Fault Detection in DC Distribution With IT Grounding Based on Sliding Discrete Fourier-Transform

Since dc distribution minimizes the number of power conversion stages, it lowers the overall cost, power losses, and weight of a power system. Critical systems use IT grounding because it is tolerant to the first-fault. Hence, this is an attractive option for hybrid electric aircraft (HEA), which combines gas engines with electric motors driven by power electronic converters. This letter proposes an accurate implementation for the procedure of first-fault detection with IT grounding. The ac component injection along with the sliding discrete Fourier transform (SDFT) is used to estimate the fault impedance. The procedure is very accurate due to the heavy filtering of the implicit moving average filter. Further computation savings are obtained by using the double look-up tables, and the Goertzel algorithm for the SDFT. Results are validated by simulations and experiments.

COMPLEXITY REDUCTION OF CYCLOSTATIONARY SENSING TECHNIQUE USING IMPROVED HYBRID SENSING METHOD

In cognitive radio system, the spectrum sensing has a major challenge in needing a sensing method, which has a high detection capability with reduced complexity. In this paper, a low-cost hybrid spectrum sensing method with an optimized detection performance based on energy and cyclostationary detectors is proposed. The method is designed such that at high signal-to-noise ratio SNR values, energy detector is used alone to perform the detection. At low SNR values, cyclostationary detector with reduced complexity may be employed to support the accurate detection. The complexity reduction is done in two ways: through reducing the number of sensing samples used in the autocorrelation process in the time domain and through using the Sliding Discrete Fourier Transform (SDFT) instead of the Fast Fourier Transform (FFT). To evaluate the performance, two versions of the proposed hybrid method are implemented, one with the FFT and the other with the SDFT. The proposed method is simulated for cooperative and non-cooperative scenarios and investigated under a multipath fading channel. Obtained results are evaluated by comparing them with other methods including: cyclostationary feature detection (CFD), energy detector and traditional hybrid. The simulation results show that the proposed method with the FFT and the SDFT successfully reduced the complexity by 20% and 40% respectively, when 60 sensing samples are used with an acceptable degradation in the detection performance. For instance, when Eb/N0 is 0 dB , the probability of the detection of Pd is decreased by 20 % and 10% by the proposed method with the FFT and the SDFT respectively, as compared with the hybrid method existing in the literature.

Two-Stages Sliding Fourier Transform for High Performance Phase Angle and Frequency Tracking

Sliding discrete Fourier transform (SDFT) gives excellent performance at nominal frequency operation. However, at off-nominal frequency, it generates errors in both magnitude and phase angle due to spectral leakage. Moreover, its harmonic rejection ability is greatly impaired in this case. This paper introduces a method to apply sliding Fourier transform under off-nominal frequency at fixed sampling rate while fixing the defects associated with it off-nominal frequency operation. This method involves the use of two stages sliding Fourier transform (SFT). A fixed window-width SFT in the first stage is used to drive the variable window-width SFT in the second stage. The proposed technique (SFT–SFT) is tested in real time on dSPACE MicroLabBox using pre-generated voltage vectors to simulate the most inconvenient grid conditions. The testing scenarios proved its superior performance compared to the decoupled stationary reference frame PLL method.

Synchronous reference frame single‐phase phase‐locked loop (PLL) algorithm based on half‐cycle DFT

In single-phase power and energy applications, sliding discrete Fourier transform (SDFT) filter based quadrature signal generation is a well-known tool for designing advanced phase-locked loops (PLLs), particularly for applications where high disturbance rejection ability is demanded. The SDFT-based PLL, nevertheless, has a limited ability in achieving fast response (a response time more than one cycle of the nominal frequency). To deal with this problem, a synchronous reference frame PLL based on half-cycle DFT (HCDFT) is proposed, enabling a fast and accurate synchronisation even in distorted grid. In this study, the fundamental voltage of the PLL input signal is obtained by a HCDFT filter. Then, phase, frequency and amplitude can be detected by the improved synchronous reference frame phase-locked loop (SRF-PLL). Besides, in order to solve the phase error when the frequency changes, a phase compensator is used. The HCDFT-based SRF-PLL method proposed in this study is compared, through experimental results, with a number of conventional methods, showing that the phase can be estimated under grid voltage disturbances accurately and quickly, which verifies the effectiveness and superiority of the proposed algorithm.

An Observer-Based Adaptive Fourier Analysis [Tips &amp; Tricks

Recently, an observer-based algorithm was reviewed that is able to perform recursive sliding discrete Fourier transform (SDFT) [1]. DFT is the basic algorithm used for Fourier analysis [2], but it provides unbiased estimates only if the sampling is coherent, i.e., the ratio of the sampling frequency fs and the input signal frequency fin is a rational number. Coherent sampling of real-life periodic signals (e.g., mains voltage) can only be achieved if fin and fs are synchronized.

Improved ASM-TER Training Sequence Detection and Fine Doppler Frequency Estimation Methods from a Satellite

To detect terrestrial application-specific messages (ASM-TER) signals from a satellite, a novel detection method based on the fast computation of the cross ambiguity function is proposed in this paper. The classic cross ambiguity function’s computational burden is heavy, and we transform the classic cross ambiguity function to a frequency domain version to reduce the computational complexity according to Parseval’s theorem. The computationally efficient sliding discrete Fourier transform (SDFT) is utilized to calculate the frequency spectrum of the windowed received signal, from which the Doppler frequency could be estimated coarsely. Those subbands around the Doppler frequency are selected to calculate the ambiguity function for reducing the computational complexity. Furthermore, two local sequences with half length of the training sequence are utilized to acquire a better Doppler frequency tolerance; thus, the frequency search step is increased and the computational complexity could be further reduced. Once an ASM-TER signal is detected by the proposed algorithm, a fine Doppler frequency estimation could be obtained easily from the correlation peaks of the two local sequences. Simulation results show that the proposed algorithm shares almost the same performance with the classic cross ambiguity function-based method, and the computational complexity is greatly reduced. Simulation results also show that the proposed algorithm is more resistant to cochannel interference (CCI) than the differential correlation (DC) algorithm, and the performance of fine Doppler frequency estimation is close to that of the Cramér–Rao lower bound (CRLB).

Online Tracking of Varying Inertia using a SDFT Approach

The mechanical dynamics of modern machines very often depend on the angular position of the driven axis. To obtain optimal control, such applications typically require an advanced control structure such as an adaptive controller. Moreover, the variation in the dynamics like changing inertia, load torque, and viscous friction limits the performance and reduces the energy efficiency. Energy savings can be obtained by using so-called trajectory optimization techniques combined with feedforward control. However, both optimization and adaptive control require the knowledge of the position dependency of the mechanical parameters. In the case of reciprocating mechanisms, for instance, this position dependency is significant. Consequently, the mechanical parameters change rapidly at high operating speed of the machine. This paper thus contributes towards fast and accurate estimation of rapidly varying mechanical parameters. A sliding discrete Fourier transform (SDFT) approach is proposed to track the inertia variation of a reciprocating mechanism online. The feasibility is verified with experiments on an industrial pick and place unit. Both the results on the real machine and its CAD equivalent, modelled in a multibody dynamics software package, are considered. In addition, the developed inertia tracking algorithm is proven to be implementable in standard commercial drive components.

Air–Fuel Ratio Imbalance Diagnostic of Spark-Ignited Engines With Modulated Sliding Discrete Fourier Transform

Abstract This paper presents the novel on-board air–fuel ratio (AFR) imbalance diagnostic of spark-ignited (SI) engines. Because of the reciprocating nature of internal combustion engines, while this fault is present, it is known that the exhaust gas oxygen (EGO) sensor signal is accompanied by the oscillating disturbance of which frequency depends on the engine speed, such that it can be represented by the superposition of multiharmonic and DC signals. Motivated from this inherent feature, the novel diagnostic for detection and location of AFR imbalance is developed with modulated sliding discrete Fourier transform (mSDFT) and angular domain sampling. The feasibility is demonstrated with the simulated and measured AFR signals. It turns out that the developed diagnostic is able to identify fault types such as lean or rich imbalance and locate a single cylinder or multiple cylinders having abnormal AFR. It is robust to measurement noise at the expense of slow convergence rate. Spectral leakage is reduced with crank domain sampling such that accuracy in spectral analysis is improved. Finally, the diagnostic has great potential for broad reciprocating machinery.