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Recursive sliding DFT algorithms: A review
Abstract
This paper reviews different recursive structures of Sliding Discrete Fourier Transform (SDFT) algorithms. Normally, a SDFT algorithm is introduced to design a filter or to compute N-point DFT through subsequent iterations in a recursive manner by allowing window shift technique. The proposed paper deals with comparative analysis of different SDFT structures; rSDFT, SGDFT, rSGDFT, DnSDFT, mDFT, HDFT, mHDFT, SWIFT, oSDFT to examine their characteristics such as computational complexity, stability, filter structure, frequency behaviour, computation error, and noise performance. Finally, the important parameters and range of operation are identified for different SDFT structures to define suitable applications.
... Performing a Discrete Fourier Transform (DFT) to the time series θ [n] allows to extract φ T E S [n] as it will correspond to the phase angle of the Fourier coefficient of the fundamental component, of frequency mod . Since only the Fourier coefficient of the fundamental frequency is required, the calculation process can be simplified using the Sliding Discrete Fourier Transform (SDFT) [13,14]. When SDFT is applied, the update rate of φ T E S [n] is consistent with that of θ [n]. ...
... Using this calculation method, the sampling rate of φ T E S is consistent with that of θ , which is f s . Due to the error accumulation and instability issues inherent in the standard Sliding Discrete Fourier Transform calculation structure, we adopt the Modulated Sliding Discrete Fourier Transform (mSDFT) here [13]. The mSDFT modulates the SQUID signal to the DC component (the 0-th frequency point) using a modulation sequence, and its computational structure is as follows (shown in Fig. 1): ...
... The mSDFT has the advantages of stability, good noise performance, and low error [13]. This is our sliding flux ramp demodulation (SFRD). ...
Microwave SQUID Multiplexing (MUX) is a widely used technique in the low-temperature detectors community as it offers a high capacity for reading large-scale Transition-Edge Sensor (TES) arrays. This paper proposes a Sliding Flux Ramp Demodulation (SFRD) algorithm for MUX readout system. It can achieve a sampling rate in the order of MHz while maintaining a multiplexing ratio of about one thousand. Advancing of this large array readout technique makes it possible to observe scientific objects with improved time resolution and event count rate. This will be highly helpful for TES calorimeters in X-ray applications, such as X-ray astrophysics missions.
... The tested signal is divided by the number of intervals for th analysis. The exact Fast Fourier Transform (FFT) in the range of the reference frequency can then be calculated [19,20]. The procedure for the Goertzel algorithm is detailed below In this step, the entire audio vector is scanned to detect the variation in pitch, which can represent the data inserted in the original audio vector. ...
... The size of the block N is equivalent to th number of points in the FFT. This value controls the frequency resolution for which th Goertzel algorithm is used, which is also known as the sample interval width [19,20]. ...
... The tested signal is divided by the number of intervals for the analysis. The exact Fast Fourier Transform (FFT) in the range of the reference frequency can then be calculated [19,20]. The procedure for the Goertzel algorithm is detailed below. ...
Audio steganalysis has been little explored due to its complexity and randomness, which complicate the analysis. Audio files generate marks in the frequency domain; these marks are known as fingerprints and make the files unique. This allows us to differentiate between audio vectors. In this work, the use of the Goertzel algorithm as a steganalyzer in the frequency domain is combined with the proposed sliding window adaptation to allow the analyzed audio vectors to be compared, enabling the differences between the vectors to be identified. We then apply linear prediction to the vectors to detect any modifications in the acoustic signatures. The implemented Goertzel algorithm is computationally less complex than other proposed stegoanalyzers based on convolutional neural networks or other types of classifiers of lower complexity, such as support vector machines (SVD). These methods previously required an extensive audio database to train the network, and thus detect possible stegoaudio through the matches they find. Unlike the proposed Goertzel algorithm, which works individually with the audio vector in question, it locates the difference in tone and generates an alert for the possible stegoaudio. In this work, we apply the classic Goertzel algorithm to detect frequencies that have possibly been modified by insertions or alterations of the audio vectors. The final vectors are plotted to visualize the alteration zones. The obtained results are evaluated qualitatively and quantitatively. To perform a double check of the fingerprint of the audio vectors, we obtain a linear prediction error to establish the percentage of statistical dependence between the processed audio signals. To validate the proposed method, we evaluate the audio quality metrics (AQMs) of the obtained result. Finally, we implement the stegoanalyzer oriented to AQMs to corroborate the obtained results. From the results obtained for the performance of the proposed stegoanalyzer, we demonstrate that we have a success rate of 100%.
... Noncausal estimation techniques (including ORBE) are not typically amenable to real-time applications [43], but we circumvent this limitation by continuously updating the estimated temporal Fourier coefficients over a small window at every time step. Further, using this sliding window enables efficient recursive techniques for updating the coefficients [46]. The implementation of this technique, which has linear algorithmic complexity, differs from the streaming Fourier sums technique of Schmidt and Towne [13], which has quadratic algorithmic complexity but a smaller memory footprint. ...
... During the testing period, we employ the sliding discrete Fourier transform (SDFT) [46,62,63] to recursively update the temporal Fourier coefficients of the measurements at every time step, t i . We thereby enable efficient updates of our triplet space measurements as new data arrive. ...
... The standard SDFT algorithm suffers from marginal stability, moderate accuracy, and timeaccumulating error (such that, eventually, the fft algorithm would need to be called to refresh the error). The more recent modulated SDFT (mSDFT) [62] and observer-based SDFT (oSDFT) [63] have more desirable stability, accuracy, and robustness to noise compared to the standard SDFT and other variants [46]. However, we retain the standard SDFT due to its simple implementation and since it remains accurate and stable over sufficiently large intervals for our purposes (see Appendix B). ...
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing linear estimators using flow statistics from an initial training period and evaluating their performance during a subsequent testing period with data obtained from direct numerical simulation. We address cases where (i) no, (ii) limited, and (iii) full-field training data are available using estimators based on (i) resolvent modes, (ii) resolvent-based estimation, and (iii) spectral proper orthogonal decomposition modes. During training, we introduce blockwise inversion to accurately and efficiently compute the resolvent operator in an interpretable manner. During testing, we enable efficient streaming reconstructions by using a temporal sliding discrete Fourier transform to recursively update Fourier coefficients using incoming measurements. We use this framework to reconstruct with minimal time delay the turbulent velocity fluctuations in a minimal channel at Reτ≈186 from sparse planar measurements. We evaluate reconstruction accuracy in the context of the extent of data required and thereby identify potential use cases for each estimator. The reconstructions capture large portions of the dynamics from relatively few measurement planes when the linear estimators are computed with sufficient fidelity. We also evaluate the efficiency of our reconstructions and show that the present framework has the potential to help enable real-time reconstructions of turbulent velocity fluctuations in an analogous experimental setting.
... Non-causal ORBE is not typically amenable to real-time applications [43], but we circumvent this limitation by continuously updating the estimated temporal Fourier coefficients over a small window at every time step. Further, using this sliding window enables efficient recursive techniques for updating the coefficients [45]. ...
... During the testing period, we employ the sliding discrete Fourier transform (SDFT) [45,58,59] to recursively update the temporal Fourier coefficients of the measurements at every time step, . We thereby enable efficient updates of our triplet space measurements as new data arrives. ...
... The standard SDFT algorithm suffers from marginal stability, moderate accuracy, and time-accumulating error (such that, eventually, the fft algorithm would need to be called to refresh the error). The more recent modulated SDFT (mSDFT) [58] and observer-based SDFT (oSDFT) [59] have more desirable stability, accuracy, and robustness to noise compared to the standard SDFT and other variants [45]. However, we retain the standard SDFT due to its simple implementation and since it remains accurate and stable over sufficiently large intervals for our purposes (see Appendix B). ...
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing linear estimators using flow statistics from an initial training period and evaluating their performance during a subsequent testing period with data obtained from direct numerical simulation (DNS). We address cases where (i) no, (ii) limited, and (iii) full-field training data are available using estimators based on (i) resolvent modes, (ii) resolvent-based estimation, and (iii) spectral proper orthogonal decomposition modes. During training, we introduce blockwise inversion to accurately and efficiently compute the resolvent operator in an interpretable manner. During testing, we enable efficient streaming reconstructions by using a temporal sliding discrete Fourier transform to recursively update Fourier coefficients using incoming measurements. We use this framework to reconstruct with minimal time delay the turbulent velocity fluctuations in a minimal channel at from sparse planar measurements. We evaluate reconstruction accuracy in the context of the extent of data required and thereby identify potential use cases for each estimator. The reconstructions capture large portions of the dynamics from relatively few measurement planes when the linear estimators are computed with sufficient fidelity. We also evaluate the efficiency of our reconstructions and show that the present framework has the potential to enable real-time reconstructions of turbulent velocity fluctuations in an analogous experimental setting.
... That means φ T ES [n] can be calculated from θ [1] to θ[n]. We call it a Sliding Discrete Fourier Transform (SDFT) method [13]. It is easy to see that SDFT method can greatly improve the update rate of φ T ES [n] as same as the SQUID signal. ...
... Using this calculation method, the sampling rate of φ T ES is consistent with that of θ, which is f s . Due to the error accumulation and instability issues inherent in the standard Sliding Discrete Fourier Transform calculation structure, we adopt the Modulated Sliding Discrete Fourier Transform (mSDFT) here [13]. The mSDFT modulates the SQUID signal to the DC component (the 0-th frequency point) using a modulation sequence, and its computational structure is as follows (shown in Fig 1): The mSDFT has the advantages of stability, good noise performance, and low error. ...
Microwave SQUID Multiplexing (MUX) is a widely used technique in the low temperature detectors community as it offers high capacity of reading out large scale Transition-Edge Sensor (TES) arrays. In this paper, we propose a Sliding Flux Ramp Demodulation (SFRD) algorithm for MUX readout system. It can achieve a sampling rate in the order of MHz while maintaining a multiplexing ratio about one thousand. Advancing of this large array readout technique makes it possible to observe scientific objects with improved time resolution and event count rate. This will be highly helpful for TES calorimeters in X-ray applications, such as X-ray astrophysics missions.
... However, the computation of the DFT is block-oriented; thus, evaluating the method on overlapping observation windows can be inefficient and computationally exhaustive. For such purposes, the Sliding DFT (SDFT) algorithms were proposed [2]. Such sliding window transforms are used to calculate the DFT bins on a sample-by-sample basis in a recursive manner. ...
... The results show how the size of the FFT and the quantizer resolution affect the total QNP. In [2], different SDFT and HDFT algorithms were studied and compared in terms of quantization noise of the twiddle factors through simulations. In [3], the error propagation for several SDFT algorithms was studied through simulation. ...
The Discrete Fourier Transform (DFT) algorithm is widely used in signal processing and communication systems to transform the signal to the frequency-domain. As real-time signal analysis is required for fast processing, several recursive algorithms were proposed to perform the calculation with overlapping sequences in a sliding manner. One Sliding DFT (SDFT) method is the Hopping DFT (HDFT), where the DFT calculations are not evaluated sample-by-sample but with longer steps, thus further reducing the computational complexity compared to the other SDFT algorithms. This paper analyses the effect of fixed-point roundoff error in the HDFT algorithm, including the Updating Vector Transform (UVT) block. A closed-form expression for the resulting quantization noise power at the output of the HDFT algorithm is provided, which is validated through simulations. The results show that the roundoff error can be determined based on the number and size of the hops, the window size, and the number of fractional bits used in the quantization process.
... To achieve continuous analysis of signals and obtain fixed length signal spectra at different times, it is equivalent to sliding a fixed length sliding window over the signal time history. This window receives a new signal point each time and separates an old signal point, as shown in figure 2. In the sliding window, only the DFT of the window input length N needs to be calculated each time [48]. ...
Due to the influence of various factors on bridge sensors, the signals obtained often contain multiple signal components, including temperature and vehicle induced effect. It is necessary to separate and analyze individual signals in bridge health detection. In order to separate temperature and vehicle response components from complex signals, this article proposes an improved variational mode decomposition (VMD) algorithm based on recursive methods, which takes the mean value of each recursive block as the eigenvalue, fits the eigenvalues of each recursive block using the least squares method, and separates the first intrinsic mode function. The applicability of this method in the field of bridges was first verified through modal decomposition of simulated deflection and strain data. Then based on the health monitoring data of the Jingtai Expressway viaduct, the rapid separation of temperature response and vehicle response of the bridge has been achieved. The results indicate that the recursive method, in an online continuous decomposition environment, is approximately seven times faster than the traditional VMD algorithm. Moreover, when setting the same penalty factor, the mean square error obtained from separating finite element simulation data is smaller than that of VMD, and the separated actual measurement data has a higher correlation coefficient with temperature. This resolves the computational speed issue of the VMD algorithm in real-time bridge health monitoring, demonstrating the feasibility of the recursive algorithm, and effectively separates signals related to temperature and vehicles.
... It should be noted that by the moment numerous different recursive DFT algorithms have been developed and described [28,29], which remained beyond the framework of this study. However, the potential of applying a few of them to TDE problem is discussed in conclusion. ...
The article discusses the practical implementation of various methods for time delay estimation (TDE) on a Raspberry Pi single-board computer. The relevance of the research is due to the importance of the implementation of TDE methods in the tasks of object positioning and localization. The demand for real-time operation, as well as the requirement to use single-board computers as sensor nodes, imposes high demands on the efficiency of computing. The paper compares various time-domain and frequency-domain TDE methods, including those that utilize a limited set of spectral bins, applicable to problems of localization of acoustic signal sources. The paper considers various methods, their advantages, disadvantages, and computational features. In addition, we have carried out their comparative analysis as well as conducted experimental validation of theoretical estimates of the demands on computing resources. During a series of computational experiments carried out through specially developed software, the computing time and the memory usage are estimated. Based on empirical research on a single-board computer, the Raspberry Pi 4B, we reasonably advise certain methods to be employed in particular scenarios for localization of an acoustic source in space using the Raspberry Pi single boards.
... 6,7 FFT has high accuracy in stationary signal detection, but it cannot avoid fence effects and spectrum leakage and is ineffective at detecting non-stationary signals. 8,9 WT has good local characteristics and can effectively analyze non-stationary signals. However, the mother wavelet and decomposition levels need to be pre-selected, and if they are not selected properly, the detection results will be affected. ...
Aiming at the problem of present power harmonic and inter-harmonic detection methods, which are susceptible to noise interference and have low detection accuracy for inter-harmonics, a novel power harmonic and inter-harmonic detection method based on fractional wavelet transform (FRWT) combined with variational mode decomposition (VMD) is proposed. The FRWT-VMD algorithm first preprocesses the signal with FRWT and VMD. Second, the VMD is used to extract harmonics and inter-harmonics. The method incorporates the advantages of the FRWT and VMD methods, corrects the defect that the FRWT method is difficult to detect inter-harmonics, and improves the problem that the VMD method is susceptible to noise interference. Simulation tests on various power harmonic signals have shown that under low signal-to-noise ratio conditions, the FRWT-VMD algorithm can effectively reduce the impact of noise and has high accuracy in harmonic and inter-harmonic detection. It is a powerful method for detecting harmonics and inter-harmonics in power systems.
... The latter offers an efficient means of processing the time-frequency representation by converting the infinite time series into finite time series with a time-varying window. After all these, the fractional Fourier transform is proposed for higher resolution and accuracy by improving the overlap of frequency spectrum and energy leakage [82][83][84][85][86]. Simultaneously, the Sliding Discrete Fourier Transform (SDFT) and its variants are proposed for solving the difficulties related to the loss of information or additional distortion occurring in the FFT processed data by introducing a damping factor (r) value [87][88][89][90][91]. ...
Torque is one of the mighty core parameters of rotating machinery, and it has profound implications for the success of many engineering and industrial manufacturing activities. To date, more and more torque sensors are being researched and manufactured to meet the requirements of torque measurements in all of the engineering sectors that rely on accurate measurement of torque parameters for their success. A direct implication of these constantly growing developments is the recent development of various torque sensors, which operate based on more than ten different principles. Although several measurement principles have been created, torque sensors themselves can only be divided into two categories based on whether they come into contact with the rotating objects being measured (contact sensors) or do not have any point of contact with these objects (contactless sensors). In this paper, the concept of contactless sensors for torque measurement is redefined and the major classes of torque sensors (i.e., contactless sensors based on the laser Doppler effect, laser speckle effect, and optical coherence vibrometer, etc.) are introduced outlining the main progress, challenges, and future directions involving torque measurement applications. As the key to the success of torque measurement systems, some advanced signal processing techniques that are commonly used to enhance the accuracy of the torque measurement data are also introduced.
... In particular, as a novelty, the observer's ability to reconstruct noncoherent signals was proven which to the best knowledge of the authors has not been done before in this general setting. The main area of application of the observer is the recursive implementation of the DFT [6] [7] [8] and in that special case a modified observer structure can be used which is time invariant so the analysis is different. ...
... Theoretical chemical calculations have proven crucial in elucidating the molecule's architectures, properties, processes, and reaction selectivity. The most common theoretical approaches used to calculate various molecular properties include DFT (density functional theory), optimized molecular structures, vibrational frequencies, and chemical shifts [11][12][13]. ...
The structural characterization of the 5.5",7"-trihydroxy-3,7-dimethoxy-4'-4"-O-biflavone (TDOB) molecule was done in this study. Based on the molecule's stable phase geometry, entire calculations were done by use of the detailed CAM-B3LYP and PBEPBE approach with SDD and LanL2DZ. In addition, a variety of HOMO-LUMO energy ranges, natural bond inter-orbital and inter-orbital interactions, and electro-static surface mapping operations were as well carried out. The specific binding location and mechanism of the ligand on the protein were studied using molecular docking. In the study, affinity scores for TDOB-AKR1B1 (Aldose Reductase) (PDB: 4ICC) and (PDB: 4IGS) were found to be -8.559 cal/mol and -5.461 cal/mol, respectively. 4ICC receptor binding score was found to be greater. The inhibitory properties of TDOB were investigated against the enzymes 4ICC and 4IGS, both of which showed effective inhibition.
Season length estimation (SLE) in time series data is critical for identifying cycle lengths in time series data, especially in streaming environments where data is continuously updated. Traditional SLE methods, designed for offline mode, require the entire dataset, which is challenging for real-time analysis. Adapting these methods to online mode often involves a sliding window technique, but they still incur a computational cost of O(NlogN) per timestamp, where N is the length of the sliding window. This computational cost makes them less feasible for online streaming data applications. To address this limitation, we present OnlineSLE, an online season length estimation method designed for time series streaming data. OnlineSLE utilizes the sliding discrete Fourier transform (SDFT) to reduce the computational cost to O(N) for each timestamp, which allows for faster processing. Our extensive evaluation of various synthetic and real-world datasets demonstrates that OnlineSLE not only accelerates the computational process, but also maintains high accuracy in season length estimation. The results underscore the significant advances our method achieves in online season length estimation for time series streaming data.
Vibration parameter estimation using a non-contact technique for industry applications, biomedical applications, condition monitoring of civil structures, and rotating machines.
An alpha sliding window infinite Fourier transform (SWIFT) based digital phase-locked loop (DPLL) is proposed to measure the vibration signal. The proposed DPLL is mainly comprised of a quadrature detector, which is derived from the SWIFT structure, a moving averager unit, a controller unit, and a bi-quad oscillator. The SWIFT structure provides inherent stability as the system poles always lie inside the unit circle and has high noise rejection capability due to narrow bandwidth at high values of time-constant. Further, the SWIFT structure works on an exponential window function that gives higher weight to recent samples and also reduces the leakage effects. The Pareto front multi-objective particle swarm optimization (PF-MOPSO) algorithm is introduced in the DPLL for computing the controller gains. Three non-conflicting objective functions, namely amplitude error, phase error, and total harmonic distortion (THD) are considered in the PF-MOPSO algorithm to optimize the controller parameters. The bi-quad oscillator generates the variable pulses based on the extracted signal to synchronize the remaining units.
The proposed DPLL is able to extract the multi-frequency components of the vibration parameter using a non-contact technique. The system is capable of measuring low frequencies up to 0.2 Hz and low amplitudes up to 0.06 mm. The proposed DPLL can also extract the vibration parameters up to the noise level of dB.
Microgrids are able to provide a more reliable and efficient energy supply than traditional grids, as they are able to operate independently from the main grid. This allows for better management of intermittent nature of renewable energy sources, such as solar and wind, and better integration of energy storage devices and electric vehicles. They are typically used to provide reliable, resilient, and cost-effective energy to a specific area. The protection design of DC microgrids is particularly difficult due to their low fault current contribution. Thus, traditional protection schemes such as over-current and short-circuit protection, may not be sufficient to protect DC network. However, the DC microgrids are more vulnerable to faults due to the lack of standard protection scheme. Therefore in this article, Hopping Discrete Fourier Transform (HDFT) based selective harmonic extraction method is used to identify the DC fault current, which is non-linear in nature, and is used to differentiate between normal and fault conditions. The proposed methodology helps to improve the accuracy of protection systems, as well as reduce the risk of false tripping. The Simulation results reveal that the proposed scheme is robust to changes in fault resistances and can be used to identify faults in grid-coupled/decoupled scenarios of microgrids. The effectiveness of the proposed protection scheme has been validated by the simulation results obtained using PSS/Sincal and MATLAB/Simulink. The proposed method is also compared to other existing methods and the results reveal that the proposed method is more accurate and reliable.
Cloud platforms, serving as fundamental infrastructure, play a significant role in developing modern applications. In recent years, there has been growing interest among researchers in utilizing machine learning algorithms to rapidly detect and diagnose faults within complex cloud platforms, aiming to improve the quality of service and optimize system performance. There is a need for online anomaly detection on cloud platform metrics to provide timely fault alerts. To assist Site Reliability Engineers (SREs) in selecting suitable anomaly detection algorithms based on specific use cases, we introduce a benchmark called StreamAD. This benchmark offers three-fold contributions: (1) it encompasses eleven unsupervised algorithms with open-source code; (2) it abstracts various common operators for online anomaly detection which enhances the efficiency of algorithm development; (3) it provides extensive comparisons of various algorithms using different evaluation methods; With StreamAD, researchers can efficiently conduct comprehensive evaluations for new algorithms, which can further facilitate research in this area. The code of StreamAD is published at https://github.com/Fengrui-Liu/StreamAD.
Fast and accurate frequency estimation is difficult for grid-interfaced inverter under distorted grid conditions with off-nominal frequency. A popular solution considers the multiple second-order generalized integrator-based frequency-locked loop yet can hardly achieve a fast dynamic response under significant phase jump and voltage sag. Another solution uses an adaptive sliding window filter with an additional frequency estimator. However, it is challenging to handle numerical instability due to the adjusting marginally-stable resonator and the accumulation error. This letter proposes a delay-tracking loop to overcome these problems. This loop allows the delay length to track the frequency with an inherent harmonics rejection at off-nominal frequency. At the same time, the fast response speed is maintained, and the marginally stable resonator is avoided. Comparative experimental results validate the above claims.
This paper presents a new multi-inverter-based compensation scheme for the harmonic and reactive influences in a micro-grid, which not only realizes the integration of renewable energy, but also combines the functions of improving power quality at the point of common coupling (PCC) simultaneously. The proposed method uses the remaining power energy in the inverter to implement local harmonic compensation, which achieves the flexible customization of power quality and economics. Specifically, an accurate and stable modulated hopping Discrete Fourier Transform (mHDFT) algorithm with merits of computation of a sparse DFT result is applied to measure the harmonic current. In addition, a proportional resonant (PR) controller selected to track the command current due to its infinite gain for a specific point ensures there is no steady-state error (ess). Besides, delay compensation and discretization by pre-swapping bilinear transformation are performed to improve the stability of the current loop and enable the controller for digital implementation respectively. The simulation results based on Matlab/Simulink are given to verify the performance of the proposed method.
In the field of digital signal analysis and processing, the ubiquitous domain transformation is the discrete Fourier transform (DFT), which converts the signal of interest within a limited time window from discrete time to the discrete frequency domain. The active use in real-time or quasi-real-time applications has been made possible by a family of fast implementations of the DFT, called fast Fourier transform (FFT) algorithms.
The proposed frequency-locked loop (FLL) utilizes the flat frequency response characteristics of the moving window filter (MWF) in closed-loop and adaptive sampling pulse adjustment for capacitance measurement. An operational amplifier (op-amp) based relaxation oscillator generates a square wave whose fundamental sine wave is extracted by MWF. Then, the fundamental sine wave is tracked by the FLL to estimate its frequency which is inversely proportional to the unknown capacitance. The FLL employs another MWF to track the center frequency and its variation due to capacitance. The MWF offers an almost flat frequency response around the center frequency in closed-loop. However, the small magnitude and phase errors observed in the flat frequency response had been corrected by adjusting the sampling pulses adaptively. Experimental investigation demonstrates the capabilities of the scheme for wider and accurate capacitance measurement.
The field of application of Phasor Measurement Units (PMUs) might be limited by the PMU measurements reporting latencies and achievable reporting rates, particularly with respect to power system protection applications that typically require very low latencies. A way to speed-up synchrophasor estimation algorithms based on the use of the Discrete Fourier Transform (DFT) refers to the usage of stable and accurate recursive processes for the DFT estimation. In this respect, this paper presents a synchrophasor estimation algorithm, called Interpolated-Modulated Sliding DFT (IpMSDFT), characterized by high accuracies and reduced latencies, enabling reporting rates up to thousands of synchrophasor per second. It is composed by two stages: (i) a guaranteed-stable technique for sample-by-sample DFT computation; (ii) an enhanced version of the classical IpDFT algorithm for synchrophasor estimation. The algorithm is analytically formulated and its digital design tailored to allow a feasible deployment on an FPGA-based PMU. The IpMSDFT-based PMU is finally validated with respect to the numerical stability of the proposed solution, its reporting latencies and the achievable reporting rates.
The simulation of Phasor Measurement Units (PMUs) into real-time simulators (RTSs) is typically limited by the complexity of the synchrophasor estimation (SE) algorithm. This is especially true when dealing with distribution network PMUs due to the more demanding accuracy requirement and, for the case of class-P PMUs, for the limited latency. In this respect, if the SE algorithm is too simplistic, the performances of the simulated PMU might not match the specific application needs. On the other hand, when higher precision of the synchrophasors estimations is required, an increased computational complexity of the SE algorithm is obtained and, as a consequence, few devices can be simulated into a RTSs at the same time. The work presented in this paper illustrates the design and the deployment of a C37.118 class-P compliant PMU into the Opal-RT RTS. The RTS-deployed PMU has demonstrated to match the requirements of both transmission and distribution networks. The simulated PMU has been experimentally validated and demonstrated to be well suited for its integration into any RTS. Index Terms—Phasor Measurement Units, synchrophasors, real-time simulation, enhanced-Interpolated Modulated Sliding Discrete Fourier Transform, IEEE Std. C37.118.
Discrete orthogonal transforms such as the discrete Fourier transform (DFT), discrete Hartley transform (DHT), and Walsh?Hadamard transform (WHT) play important roles in the fields of digital signal processing, filtering, and communications. In recent years, there has been a growing interest in the sliding transform process where the transform window is shifted one sample at a time and the transform process is repeated.
An acoustic echo cancellation (AEC) algorithm based on minimising the mutual information between the loudspeaker and system output signals over a sliding discrete Fourier transform (DFT) window, for single AEC parameter estimation, is introduced. Unlike the conventional least-mean-square (LMS) systems, the proposed algorithm requires no double-talk detection (DTD) and its AEC parameter can be continually updated. Although it has been shown that independent component analysis (ICA) allows continual adaptation of the AEC parameters under DTD, current ICA-based algorithms estimate a filter of the same length as that of the LMS techniques. The sliding DFT window is utilised to facilitate adaptation of only one AEC parameter for deflation of the far-end signal, thereby greatly reducing the computational load.
Discrete Fourier transform (DFT) codes have been used to provide robustness against errors and erasures in various applications. This paper focuses on improving error localization of the Bose-Chaudhuri-Hocquenghem (BCH) DFT codes. First, we analyze how the subspace-based error localization outperforms the coding-theoretic one. Then, we propose an extension of the subspace-based error localization, based on additional syndrome, that improves the existing one and is naturally suitable for rate-adaptive distributed source coding (DSC). Further, we propose a new generic subspace-based algorithm to decode BCH-DFT codes. The proposed approach generalizes the encoding and decoding of this important class of DFT codes. It introduces many different decoding matrices for a DFT code; this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding. Finally, the extended and generalized approaches are combined to maximize the decoding gain. Simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace-based error localization, in the presence of quantization noise.
The discrete Fourier transform (DFT) produces a Fourier representation for finite-duration data sequences. In addition to its theoretical importance, the DFT plays a key role in the implementation of a variety of digital signal-?processing algorithms. Several algorithms including the fast Fourier transform (FFT) and the Goertzel algorithm have been introduced for the fast implementation of the DFT [1], [2].
The article deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the article providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.
Timing acquisition constitutes a major challenge in realizing ultra-wideband communications. In this paper, we propose the timing with dirty template (TDT) approach as a promising candidate for achieving rapid, accurate and low-complexity acquisition. We describe the dirty template (DT) technique, in order to develop and test timing algorithms in both modes: data-aided (DA) and non-data- aided (NDA) modes. First, we derive the Cramer–Rao lower bound, which is used as a fundamental performance limit for any timing estimator. Next, the TDT acquisition estimator is achieved by using the Maximum Likelihood concept. Then we propose a new method, based on Time-Hoping codes, to improve the performance estimation of the original dirty template algorithms. Simulation shows the estimation error results of the modified method in the DA and NDA modes. It confirms the high performance and fast timing acquisition of DA mode, compared with NDA mode, but with less bandwidth efficiency.
In this paper, we propose a novel time delay estimation approach based on sliding the discrete Fourier transform (DFT) analysis window, sample by sample, over the received short continuous wave (CW) pulse signal with the DFT evaluated successively. This approach uses the maximum magnitude of the spectrum and its corresponding phase offset to estimate the time delay (pulse echo mode) of the signal. We use the corresponding time as the first estimate, which is improved on the basis of the related phase. Examples are given of synthetic signals and simulated delays scenario, with and without added white noise. An underwater application, based on distance and speed of sound measurements using this approach in a water tank is demonstrated. The proposed method is shown to significantly outperform standard correlator-based approaches. Furthermore, the algorithm is simple to use and can be easily implemented, being based on phase detection using the sliding DFT.
In this paper, a robust technique is proposed for the estimation of fundamental frequency in unbalanced three-phase power systems. This is achieved by firstly justifying the modelling mismatch inherently overlooked in the conventional complex-valued least squares enhanced smart discrete Fourier transform method, and then applying the total least squares framework to minimise the error vectors corresponding to both the independent and dependent consecutive voltage measurements and, eventually, to achieve higher immunity to both noise and harmonic pollution. Simulations on both synthetic and real-world noisy unbalanced power systems demonstrate the performance advantage of the proposed algorithm over other smart discrete Fourier transform based ones.
Filter Bank MultiCarrier (FBMC) modulation with one of its variants, the Offset Quadrature Amplitude Modulation (OQAM) is considered as one of the most favored candidates for future 5G air interface. The transceiver architectures of FBMC-OQAM is categorized into two main design approaches: using PolyPhase Network (PPN) and using Frequency Spreading (FS). The PPN approach requires a lower complexity while the FS based architecture shows better performance when considered at the receiver. In this paper we introduce and analyze an improved FS-FBMC receiver architecture which will reduce the required computational load. The proposed structure is based on a recently introduced variant of the sliding Discrete Fourier Transform (DFT) known as Hopping DFT (HDFT). We show that by applying the HDFT, the FS complexity can be reduced.
In this paper, design of frequency-locked loop (FLL) is proposed based on computationally efficient DFT structures. In recent years, the DFT structures are evolved as sliding DFT, modulated sliding DFT, hopping DFT, modulated hopping DFT, and sliding windowed infinite Fourier transform. Considering their tuned filter characteristics, an attempt has been made to obtain a solution for the instantaneous frequency estimation problem of the input signal under varying center frequency condition. In each DFT structure, the kth bin in-phase and quadrature components are separated for instantaneous signal extraction. The feedback loop is designed around these DFT structures and it was observed that the frequency responses exhibit flat magnitude and phase interestingly, when compared to the open-loop structures. Hence, an adaptive sampling frequency adjustment scheme is proposed for these structures as frequency locked-loop to estimate the instantaneous frequency of the input signal for wide variation in center frequency. These FLLs with different DFT structures are tested for dynamic performance and wide operating range. The proposed FLLs are implemented in FPGA and experimental investigations have been carried out for frequency estimation. Further experimental investigations on these FLLs as system on chip were carried out with area and power analysis.
Purpose
This paper aims to design a tip state estimation method for a hybrid-structured flexible manipulator (HSFM) with one rotating joint and one telescopic joint in the vertical plane.
Design/methodology/approach
The HSFM model is decomposed into a static deflection model and a vibration model. The sliding discrete Fourier transform (SDFT) is used to filter the high frequency noise and obtain main vibration components to represent the vibration model. Then, a novel fuzzy logic adaptive Kalman filter (FLAKF) is designed to estimate the state of a vibrational equilibrium position. The complete tip state of the HSFM is obtained by superimposing the FLAKF filter results with the SDFT vibration analysis results.
Findings
Both the simulation results and physical experimental results verify the effectiveness of the proposed tip state estimation method. The vibration analysis based on SDFT is used to represent the vibration model and reduce the computational complexity in the process of solving differential equation. The proposed FLAKF can effectively increase the stability and robustness of the estimator.
Originality/value
In this paper, the tip state estimation problem of the HSFM in vertical plane is first proposed. The effect of gravity on the HSFM is considered by the static deflection model. A precise tip state estimator is designed by a closed loop SDFT and a novel FLAKF, which can provide an accurate feedback for the vibration control controller and make an accurate evaluation of the control effect.
A frequency estimation technique is proposed with fractional bin-index-based moving-window discrete Fourier transform (MWDFT). In order to increase the range of estimation frequencies, different MWDFTs with bin-indices k = 0.5, 1, 1.5, 2, and 2.5 are chosen and incorporated in the frequency estimator. The structure of the MWDFT is modified with the positive feedforward coefficients for fractional bin-indices and negative coefficients for integer multiples. The frequency of the input signal is estimated by adaptively adjusting the sampling pulses for MWDFT with integer and fractional bin-indices. The proposed frequency estimator is validated through field programmable gate array implementation for measuring a capacitance range of 89.201-1420.69 pF. A relaxation oscillator with a measurand as capacitance exhibits a square wave whose frequency is inversely related to the measurand. The frequency of the square wave is estimated through the proposed DFT procedure instantaneously by extracting the fundamental sinusoidal signal and tracking the same with the feedback loop. The experimental investigation on the proposed method proves to be accurate and computationally efficient, and offers a wide operating range with less acquisition time.
Nowadays, most brushless DC (BLDC) motors use Hall sensors or sensorless algorithms based on backelectromotive force (back-EMF) sensing to detect rotor position information. These methods detect the commutation moments but imply the use of rectangular stator currents which, according to recent literature, limits the energy efficiency. In this study, sinusoidal stator currents are used to increase the motor energy efficiency. As a consequence, standard control based on the feedback of the Hall sensors or based on sensorless techniques detecting the back-EMF zero-crossing cannot be used. Therefore, the authors propose a load angle control algorithm for BLDC motors without using position and speed sensors. The objective is to obtain energy-efficient sensorless control for the BLDC motor based on the measurement of only two current and one voltage signal. The energy saving potential of the proposed method is especially outspoken for fixed speed applications with varying loads, which are typical BLDC applications. Experimental results are presented to validate the proposed method. Energy efficiency measurements over the whole operating range of the BLDC motor are included and show an energy saving potential up to 9.5%.
italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sliding Goertzel DFT algorithm
in
phase-locked loop technique
is proposed for simultaneous estimation of moving-vibration parameters: amplitude, frequency, and velocity. The proposed algorithm is derived from the standard
sliding discrete Fourier transform
where its computation complexity is reduced by inserting a pole–zero pair in the system function. A damping factor is introduced in the system function to stabilize when discrete Fourier transform (DFT) is computed with limited finite word length precession. It allows the system poles to lie within unit circle of the
z
plane and confirms a stable system. Furthermore, an adaptive sampling control is achieved as the sampling pulse duration varies according to carrier frequency deviation. An appropriate figure of merit is selected for the system function to reduce the noise effects in the input signal and to accept large range of measurement. Simulation investigation confirms the capability of the proposed technique to extract information even in the presence of large noise.
An online method for amplitude and frequency estimation of exponentially decaying sinusoids is proposed with a moving-window discrete Fourier transform (MWDFT) filter and frequency-locked loop. The tuned filter characteristics of MWDFT is modified into more flat characteristic around the center frequency with negative feedback, which increases the bandwidth of the filter. An adaptive sampling pulse adjustment mechanism is incorporated in the proposed structure for online estimation of frequency. Hence, the frequency error was exploited to achieve synchronization between in-phase component of MWDFT and input signal of estimation. The amplitude is estimated in online from the in-phase and quadrature-phase components of MWDFT. The performance of the proposed method is compared with the existing techniques and experimentally validated on single-link flexible manipulator system for the online estimation of frequency and amplitude of tip deflection signal. The experimental investigation prove that the proposed online technique performs well over the existing techniques.
The discrete Fourier transform (DFT) is the standard tool for spectral analysis in digital signal processing, typically computed using the fast Fourier transform (FFT). However, for real-time applications that require recalculating the DFT at each sample or over only a subset of the N center frequencies of the DFT, the FFT is far from optimal.
The Discrete Fourier transform (DFT) is the most widely used technique for determining the frequency spectra of digital signals. However, in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated, the use of DFT becomes difficult due to its heavy computational burden. This paper proposes an optimal sliding DFT (oSDFT) algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding DFT algorithms. The proposed oSDFT algorithm directly computes the DFT bins of the shifted window by simply adding (or subtracting) the bins of a previous window and an updating vector. We show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario. Our simulations demonstrate that the proposed algorithm outperforms the existing sliding DFT algorithms in terms of computational accuracy and processing time.
Cyclostationary feature (CSF) detection plays an important role in spectrum sensing for cognitive radio systems, since it has low requirements on a-priori knowledge about the primary user signals and high robustness to noise and interferences. Existing CSF detecting technologies depend on full-size Fast Fourier Transform (FFT), which leads to high implementation cost in case of high carrier frequency and high spectral resolution. Here in this work, we introduce Sliding Discrete Fourier Transform (SDFT) to reduce the computational complexity of CSF detection while enhancing its performance simultaneously.
The Fourier transform is widely used to diagnose induction motor faults through the monitoring of fault signatures from measured signals such as stator currents. For a good frequency resolution, Fourier transform needs a long signal acquisition time and that increases the probability of speed fluctuations what leads to fault signatures variations. In addition, limited acquisition time and acquired points generate unwanted sidelobes leakage phenomenon, caused by step frequency resolution. In signal processing, the use of window functions allows the avoidance of this phenomenon with the cost of losing a part of signal information. In this paper, the authors propose a new method for the diagnostic of induction motor broken bar fault based on sliding window DFT and the effect of sidelobes of sideband frequencies on the fundamental component amplitude of stator current. The main advantage of the proposed method is that, one can detect the amplitude of the fault indicator frequency in vicinity of the fundamental one in shorter time and with good precision even if the motor turns at no-load when compared to used methods, as FFT, ZFFT, MUSIC and ZMUSIC. The simulation and experimental results validate the effectiveness of the proposed method.
A proper real-time system identification method is of great importance in order to acquire an analytical model that sufficiently represents the characteristics of the monitored system. While the use of different time-domain online identification techniques has been widely recognized as a powerful approach to system diagnostics, the frequency-domain identification techniques have primarily been considered for offline commissioning purposes. This paper addresses issues in the online frequency-domain identification of a mechanical system with varying dynamics; particular attention is paid to detect the changes in the system dynamics. A closed-loop online identification method is presented that is based on a sliding discrete Fourier transform at a selected set of frequencies. The method is experimentally validated by a closed-loop controlled servomechanism with a limited stroke and time-varying parameters.
This paper presents a three-phase harmonic and sequence components measurement method based on modulated sliding discrete Fourier transform (mSDFT) and a variable sampling period technique. The proposal allows measuring the harmonic components of a three-phase signal and computes the corresponding imbalance by estimating the instantaneous symmetrical components. In addition, an adaptive variable sampling period is used to obtain a sampling frequency multiple of the main frequency. By doing so, DFT typical errors, known as spectral leakage and picket-fence effect, are mitigated in steady state. The proposal is tested with different disturbances by simulation and experimental results. Some results obtained with a power quality monitor implemented with the proposed system are also presented. The high rejection to distortion in the electrical network, frequency adaptability, flexibility, and good performance in power quality monitor application render the proposed method a promising alternative for signal processing from the mains.
An efficient procedure for frequency estimation is proposed in this paper to alleviate the computational complexity. Grounded on the fact that the frequency of a target signal usually lies in a known range in practical applications, two fundamental steps in the frequency estimation, i.e., the discrete Fourier transform (DFT) and the interpolation of the DFT samples, are modified accordingly. Unlike the previous works focusing on either the DFT or the interpolation, this paper does not decouple the two steps but optimizes the whole procedure comprehensively by considering the interrelationship between the two steps. As a result, the number of operations required for the estimation is remarkably diminished while the performance remains competitive with the recent works.
This brief presents the feedforward short-time Fourier transform (STFT). This new approach is based on reusing the calculations of the STFT at consecutive time instants. This leads to significant savings in hardware components with respect to fast Fourier transform based STFTs. Furthermore, the feedforward STFT does not have the accumulative error of iterative STFT approaches. As a result, the proposed feedforward STFT presents an excellent tradeoff between hardware utilization and performance.
The sliding discrete Fourier transform-based phase locking scheme (SDFT-PLL) has been adapted for the extraction of message signals from mono-component amplitude modulation–frequency modulation (AM–FM) signals. In the proposed scheme, the SDFT-PLL is designed to track a carrier signal, which has been modulated by sinusoidal message signals both in amplitude and frequency. The sliding DFT filter is prone to windowing effect if input signal frequency drifts from centre carrier frequency. The amplitude and phase errors caused by this effect have been utilised to achieve locking condition by adaptive sampling frequency control. The SDFT-PLL is modified in such a way that the numerically controlled oscillator produces sampling pulses suitable for SDFTbin-1 and SDFT bin-0 for the retrieval of frequency and amplitude modulation signals, respectively. Hence, the frequency and amplitude variation of monocomponent AM–FM could be retrieved simultaneously. Furthermore, Bessel function-based analysis provides an insight to the removal of unwanted spectral components present in error signal. Simulation results prove the capability of PLL in message signal retrieval for large variation in frequency and amplitude. The proposed scheme is implemented in field programmable gate array to validate the performance of SDFT-PLL in decomposition of the mono-component AM–FM signal.
The standard method for spectrum analysis is the Discrete Fourier Transform(DFT), typically implemented using a Fast Fourier Transform (FFT) algorithm. However, certain applications require an on-line spectrum analysis only on a subset of M frequencies of an N-point DFT . In such cases, the use of Single-bin Sliding DFT (Sb-SDFT) is preferred over the direct application of FFT. Along these lines, the most popular algorithms are the Sliding Discrete Fourier Transform (SDFT), the Sliding Goertzel Transform (SGT), the Modulated Sliding Discrete Fourier Transform (mSDFT), and the S. Douglas and J. Soh algorithm (D&S). Even though these methods seem to differ, they are derived from the conventional DFT using distinct approaches and properties. To better understand the advantages, limitations and similarities each of them have, this work thoroughly evaluates and compares the four Sb-SDFT methods. What is more, the direct application of these Sb-SDFTs may lead to inaccuracies due to spectral leakage and picket-fence effects, common pitfalls inherited by every DFT-based method. For this reason, a unified model of the Sb-SDFT methods is proposed, whose aim is to design a frequency adaptive control loop. This frequency adaptability allows to mitigate the problems associated with improper sampling frequency. By using this unified model, the election of the Sb-SDFT algorithm is independent of the controller design and all the methods are equivalent. Theoretical results are validated by simulations and a DSP implementation of the four frequency adaptive Single-bin Sliding DFT methods.
An estimation method based on sliding discrete Fourier transform (SDFT) integrated with phase-locked loop is introduced for vibration mode estimation of single-link flexible manipulator (SLFM). Based on Euler-Lagrangian state space model and first vibration mode frequency, SDFT PLL is designed to estimate first vibration mode and harmonics that appear in tip deflection. Instantaneous change in tip deflection due to payload conditions is tracked by adaptive sampling frequency control. State-space model, estimated amplitudes and frequencies of tip deflection including harmonics are validated through experiments. Furthermore, experimental investigation on SLFM demonstrates the effectiveness of online vibration mode estimation method in presence of noise and offset.
A power-line interference (PLI) removal method is proposed based on a previously published sliding discrete Fourier transform (SDFT) phase locking scheme (PLL), which extracts the nonstationary sinusoids from the electrocardiogram (ECG) signal. The proposed PLI canceler consists of SDFT PLL as a vital element, which can track the variation in center frequency of the PLI either 50 or 60 Hz. The PLI canceler involves the adaptive sampling frequency control in which the sampling frequency of SDFT filter is adaptively adjusted according to the center frequency variation of the interference. Since the in-phase and quadrature components of SDFT filter can provide instantaneous sinusoidal and cosinusoidal interference signals, the SDFT PLL is capable of tracking amplitude, phase, and frequency of the interference. Additional resonators of different bin indices are augmented with SDFT PLL to handle the dominant odd harmonics of PLI. Furthermore, the SDFT PLL is cascaded with another SDFT bin to eliminate the baseline wander present in the real-time ECG signal. The adaptive PLI canceler based on SDFT PLL offers the tracking capability of variant PLI, attenuation of 40 dB, less acquisition time of 0.2 s for a variant PLI of ±5 Hz, removal of dominant odd harmonics, and baseline wander with expense of sampling frequency. Experimental results prove the efficacy of the proposed method in nonstationary sinusoidal interference extraction. Experimental investigation on SDFT PLL using field programmable gate array demonstrates the feasibility of digital implementation of the proposed algorithm.
A new modulated hopping Discrete Fourier Transform (mHDFT) algorithm which is characterized by its merits of high accuracy and constant stability is presented. The proposed algorithm, which is based on the circular frequency shift property of DFT, directly moves the k-th DFT bin to the position of k = 0, and computes the DFT by incorporating the successive DFT outputs with arbitrary time hop L. Compared to previous works, since the pole of mHDFT precisely settles on the unit circle in the Z-plane, the accumulated errors and potential instabilities, which are caused by the quantization of the twiddle factor, are always eliminated without increasing much computational effort. The numerical simulation results verify the effectiveness and superiority of the proposed algorithm.
This text provides a basic treatment of modern electric machine analysis that gives readers the necessary background for comprehending the traditional applications and operating characteristics of electric machines-as well as their emerging applications in modern power systems and electric drives, such as those used in hybrid and electric vehicles.Through the appropriate use of reference frame theory, Electromagnetic Motion Devices, Second Edition introduces readers to field-oriented control of induction machines, constant-torque, and constant-power control of dc, permanent-magnet ac machines, and brushless dc machines. It also discusses steady-state and transient performance in addition to their applications. Electromagnetic Motion Devices, Second Edition presents:The derivations of all machine models, starting with a common first-principle approach (based upon Ohm's, Faraday's, Ampere's, and Newton's/Euler's laws)A generalized two-phase approach to reference frame theory that can be applied to the ac machines featured in the bookThe influences of the current and voltage constraints in the torque-versus-speed profile of electric machines operated with an electric driveThoroughly classroom tested and complete with a supplementary solutions manual, Electromagnetic Motion Devices, Second Edition is an invaluable book for anyone interested in modern machine theory and applications.
Accurate harmonics estimation has become a key issue in power quality assessment. This paper deals with a discrete Fourier transform (DFT)-based measurement technique, which can be easily employed to accurately determine the harmonic components of a distorted signal, i.e., voltage or current. The proposed method is based on a modulated sliding DFT algorithm, which is unconditionally stable and does not accumulate errors due to finite precision representation, and a variable sampling period technique (VSPT) to achieve a frequency adaptive mechanism. It is worth noting that the VSPT changes the sampling period for a variable grid frequency condition, leading to a constant sampling frequency under steady-state conditions. The proposed method provides: 1) high degree of accuracy; 2) structural/performance robustness; and 3) frequency adaptability. Given the modular nature of the method, it is implemented on a field programmable gate array. Simulations and experimental tests are shown to verify the performance of the proposed method.
A new frequency demodulation scheme based on sliding discrete Fourier transform (SDFT) and a phase locking scheme (PLL) is proposed for extracting message signal from sinusoidal frequency modulated signals. A wide operating range of the PLL, especially the pull-in range is utilized in extracting modulation signal from the large deviation FM signals. As fundamental frequency SDFT bin is involved in the design, the SDFT PLL scheme is suitable for demodulating linear FM signals of frequency range between d.c. and second harmonic of the carrier. Simulation and experimental results prove the fast acquisition behavior and competence of the SDFT PLL in modulation signal retrieval.
This paper proposes a novel scheme that jointly employs a sliding-window ESPRIT and DFT for estimating harmonic and interharmonic components in power system disturbance data. In the proposed scheme, separate stages are utilized to estimate the voltage fundamental component, harmonics and interharmonics. This includes the estimation of the fundamental component from lowpass filtered data using a sliding-window ESPRIT, of harmonics from a sliding-window DFT with a synchronized window, and of interharmonics from the residuals by applying the sliding-window ESPRIT. Main advantages of the approach include high resolution and accuracy in parameter estimation and significantly reduced computational cost. Experiments and comparisons are made on both synthetic and measurement data. Results have shown the effectiveness and efficiency of the proposed scheme.
Islanding refers to a condition of a distributed generator (DG) in that it continues to power a location even though power from the grid is no longer present. This condition can be dangerous to grid workers who may not realize that the load is still powered even though there is no power from the grid. Adverse effects of islanding are low power quality, grid-protection interference, equipment damage, and personnel safety hazards. For these reasons, DG systems must detect an islanding condition and immediately stop producing power; this is referred to as anti-islanding. Islanding detection methods can be categorized into two major approaches: the passive and active methods. The passive methods are based on measurement of the natural effects of islanding. The active methods use intentional transients or harmonic effects. When the power generated by the DG matches the load power consumption, passive methods fail due to the small natural effects of islanding. Therefore, the passive methods have a nondetection zone (NDZ). The active methods can reduce the NDZ size. However, these methods reduce the grid power quality. In this paper, a novel anti-islanding method (AIM) is proposed. A single-phase DG using the proposed AIM injects the output current with a little harmonic current into the grid and monitors the harmonic components of the voltage at the point of common coupling using the Goertzel algorithm. The Goertzel algorithm is a kind of discrete Fourier transform. It extracts the magnitude and phase of the desired frequency from the input signal, with a minimum computation. The proposed islanding detection algorithm resolves the NDZ but also the bad effects on the grid power quality due to injecting harmonic components qualified by the interconnection standard. The proposed islanding detection method was verified using PSIM (see www.powersimtech.com) simulations and experimental results.
Time and frequency review of acoustic heart signals in children is given in this paper. The following sound recordings were compared: Still’s innocent heart murmur (Still), pathologic murmur of the congenital ventricular septal defect (VSD) and the recording without the murmur (Normal). Goertzel algorithm was used, for the first time, to determine the spectral energy of the heart signals. The aim of this study is to show that this algorithm is very suitable to analyze the heart sound signals as well as suitable for heart murmurs recognition. Still’s murmur is analyzed in more detail because it is incorrectly diagnosed by many doctors. Analysis of Still’s murmur shows that it is, actually, a realistic musical tone of low frequency similar to glissando tone played on a bass guitar.
An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices, where m is proportional to log N. This results inma procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form. Attention is given to the choice of N. It is also shown how special advantage can be obtained in the use of a binary computer with N = 2' and how the entire calculation can be performed within the array of N data storage locations used for the given Fourier coefficients. Consider the problem of calculating the complex Fourier series N-1 (1) X(j) = EA(k)-Wjk, j = 0 1, * ,N- 1, k=0
The fast Fourier transform (FFT), a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained. Examples and detailed procedures are provided to assist the reader in learning how to use the algorithm. The savings in computer time can be huge; for example, an N = 210-point transform can be computed with the FFT 100 times faster than with the use of a direct approach. Copyright © 1967 by The Institute of Electrical and Electronics Engineers, Inc.
This paper presents a novel, simple pattern synthesis procedure for linear equispaced arrays which can be characterized by a generalized scattering matrix (GSM) and whose radiated field can be expressed as a weighted sum of shifted spherical waves. It can be viewed as an extension of the classic design techniques of the Fourier series (FS) method or the Woodward-Lawson frequency sampling method, to the case in which the individual antenna elements' patterns and all interelement couplings are taken into account. The design procedure, which yields the excitations needed to achieve the desired pattern, is based on either the FS or the discrete Fourier transform (DFT) of the spherical mode expansion of the array radiated field, as well as on various properties associated to the FS or DFT coefficients. In this work, to compute the GSM of the array and the spherical mode expansion of the field, a validated hybrid full-wave methodology, based on the finite element method and rotation and translation properties of spherical waves, is used. Numerical results of different synthesized array patterns are presented for different arrays made up of dielectric resonator antennas and cavity-backed microstrip circular patches.
This article presented a novel method of computing the SDFT that we call the modulated SDFT (mSDFT). The sliding discrete Fourier transform (SDFT) is a recursive algorithm that computes a DFT on a sample-by-sample basis. The accumulated errors and potential instabilities inherent in traditional SDFT algorithms are drastically reduced in the mSDFT. We removed the twiddle factor from the feedback in a traditional SDFT resonator and thus the finite precision of its representation is no longer a problem.