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The recognition, decoding and tracking of vortex patterns is of increasing importance in many fields, ranging from the astronomical observations of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. A recently introduced combination of polar mapping and Fast Fourier Transform (FFT) was extended to novel sampling configurations and applied to the quantitative analysis of the spiral interference patterns of OAM beams. It is demonstrated that specific information on topological parameters in non-uniform arrays of OAM beams can be obtained from significantly distorted and noisy intensity maps by extracting one- or two-dimensional angular frequency spectra from single or concatenated circular cuts in either spatially fixed or scanning mode. The method also enables the evaluation of the quality of beam shaping and optical transmission. Results of proof-of-principle experiments are presented, resolution limits are discussed, and the potential for applications is addressed. [ABSTRACT FROM AUTHOR]

This paper proposes a new method for calculating the quaternion discrete Fourier transform for one-dimensional data. Although the computational complexity of the proposed method still belongs to the O (N log 2 N) class, it allows us to reduce the total number of arithmetic operations required to perform it compared to other known methods for computing this transform. Moreover, compared to the method using symplectic decomposition, the presented method does not require changing the basis in the subspace of pure quaternions and, consequently, calculating the new basis vectors and change-of-basis matrix. [ABSTRACT FROM AUTHOR]

Structures for the evaluation of fast Fourier transforms are important components in several signal-processing applications and communication systems. Their capabilities play a key role in the performance enhancement of the whole system in which they are embedded. In this paper, a novel implementation of the discrete Fourier transform is proposed, based on a bit-slice approach and on the exploitation of the input sequence finite word length. Input samples of the sequence to be transformed are split into binary sequences and each one is Fourier transformed using only complex sums. An FPGA-based solution characterized by low latency and low power consumption is designed. Simulations have been carried out, first in the Matlab environment, then emulated in Quartus IDE with Intel. The hardware implementation of the conceived system and the test for the functional accuracy verification have been performed, adopting the DE2-115 development board from Terasic, which is equipped with the Cyclone IV EP4CE115F29C7 FPGA by Intel. [ABSTRACT FROM AUTHOR]

Competition on the local and global market forces enterprises to implement modern solutions and adapt to technological changes. Applying modern solutions allows an increase in the quality of the product and reduces production costs. The acoustic sensor, as a relatively cheap solution, allows signals to be obtained which, after appropriate processing, can be used to develop an automatic control of the longwall shearer, together with the recognition of the type of shale. This paper presents an introductory research, the goal of which has been to check whether acoustic signals carry useful information on what kind of material–shale or coal–is being cut by the cutting head of a longwall shearer. For this purpose, the fast Fourier transform and short-time Fourier transform functions implemented in MatLab were used. The results of the analysis are presented in the form of three-dimensional graphs and spectrograms. To sum up, the research carried out so far justifies the need for continuation in the form of systematic experiments, the results of which could be incorporated into the control system of an unmanned combine. [ABSTRACT FROM AUTHOR]

Driving wheel operation is characterized by force interactions with the ground, manifested in the form of vibrations. Signals generated by driving wheels can be analyzed in the frequency spectrum of tractor drawbar pull. The paper presents the analysis of a drawbar pull signal generated by a tractor equipped with two types of special driving wheels and standard tires. Beside the evaluation of special driving wheels' properties according to drawbar power, the frequency spectra of measured signals were analyzed using a fast Fourier transformation. The model spectrum intervals for the standard tires, spike tires, and blade wheels were calculated according to the number of rubber lugs, blades, or spikes and compared with the experimental results. The results showed that the specific frequencies typical for blades and spikes were identified in model spectrum intervals. In the case of standard tires, the spectrum components typical for rubber lugs of the tire tread pattern were not identified. The highest amplitude of the typical frequency component was detected in the case of blades wheels, which showed the highest difference in drawbar power in comparison with the standard tires. Smaller dimensions of spikes resulted in lower amplitude and lower difference in drawbar power in comparison with the standard tires. [ABSTRACT FROM AUTHOR]

This paper introduces the Fourier spectral method combined with the strongly stable exponential time difference method as an attractive and easy-to-implement alternative for the integration of the multi-dimensional Allen–Cahn equation with no-flux boundary conditions. The main advantages of the proposed method are that it utilizes the discrete fast Fourier transform, which ensures efficiency, allows an extension to two and three spatial dimensions in a similar fashion as one-dimensional problems, and deals with various boundary conditions. Several numerical experiments are carried out on multi-dimensional Allen–Cahn equations including a two-dimensional Allen–Cahn equation with a radially symmetric circular interface initial condition to demonstrate the fourth-order temporal accuracy and stability of the method. The numerical results show that the proposed method is fourth-order accurate in the time direction and is able to satisfy the discrete energy law. [ABSTRACT FROM AUTHOR]

This article presents the effectiveness of bispectrum analysis for the detection of the rotor unbalance of an induction motor supplied by the mains and a frequency converter. Two diagnostic signals were analyzed, as well as the stator current and mechanical vibrations of the tested motors. The experimental tests were realized for two low-power induction motors, with one and two pole pairs, respectively. The unbalance was modeled using a test mass mounted on a specially prepared disc and directly on the rotor and the influence of this unbalance location was tested and discussed. The results of the bispectrum analysis are compared with results of Fourier transform and the effectiveness of unbalance detection are discussed and compared. The influence of the registration time of the analyzed signal on the quality of fault symptom analyses using both transforms was also tested. It is shown that the bispectrum analysis provides an increased number of fault symptoms in comparison with the classical spectral analysis as well as it is not sensitive to a shorter registration time of the diagnostic signals. [ABSTRACT FROM AUTHOR]

In recent years, the number of outer rotor permanent magnet brushless direct current (PM BLDC) motor drives has been intensively growing. Due to the specifics of drive operation, bearing faults are especially common, which results in motor stoppage. In a number of these types of motor applications, the monitoring and diagnostics of bearing conditions is relatively rare. This article presents the results of research aimed at searching for simple and simultaneously effective methods for assessing the condition of bearings that can be built into the drive control system. In the experimental research, four vibration signal processing methods were analysed with regards to the identification accuracy of fault symptoms in the geometric elements of bearings (characteristic frequencies). The results are presented for three cases of bearing faults and compared with a new bearing, they were obtained based on a vibration signal analysis using the classical fast Fourier transform (FFT), Fourier transform of signal absolute values, Fourier transform of an envelope signal obtained using the Hilbert transform, and the Fourier transform of a signal filtered with the Teager–Kaiser energy operator (TKEO). [ABSTRACT FROM AUTHOR]

Discrete Fourier transform (DFT) is a common analysis tool in digital signal processing. This transform is well studied and its shortcomings are known as well. Various window functions (e.g., Hanning, Blackman, Kaiser) are often used to reduce sidelobes and to spread the spectrum. In this paper, we introduce a transformation that allows removing the sidelobes of the Fourier transform and increasing the resolution of the DFT without changing the time sample. The proposed method is based on signal phase analysis. We give the comparison of the proposed approach with known methods based on window functions. The advantages and disadvantages of the proposed technique are explicitly shown. We also give a set of examples illustrating the application of our technique in some practical applications, including engine vibration analysis and a short-range radar system. [ABSTRACT FROM AUTHOR]

It is significant for biological cells to predict self-interacting proteins (SIPs) in the field of bioinformatics. SIPs mean that two or more identical proteins can interact with each other by one gene expression. This plays a major role in the evolution of protein‒protein interactions (PPIs) and cellular functions. Owing to the limitation of the experimental identification of self-interacting proteins, it is more and more significant to develop a useful biological tool for the prediction of SIPs from protein sequence information. Therefore, we propose a novel prediction model called RP-FFT that merges the Random Projection (RP) model and Fast Fourier Transform (FFT) for detecting SIPs. First, each protein sequence was transformed into a Position Specific Scoring Matrix (PSSM) using the Position Specific Iterated BLAST (PSI-BLAST). Second, the features of protein sequences were extracted by the FFT method on PSSM. Lastly, we evaluated the performance of RP-FFT and compared the RP classifier with the state-of-the-art support vector machine (SVM) classifier and other existing methods on the human and yeast datasets; after the five-fold cross-validation, the RP-FFT model can obtain high average accuracies of 96.28% and 91.87% on the human and yeast datasets, respectively. The experimental results demonstrated that our RP-FFT prediction model is reasonable and robust. [ABSTRACT FROM AUTHOR]