Fast Fourier Transform Results Research Articles

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency) amplitude and phase while suppressing spectral leakage.

Improved design and analysis for electromagnetic performance of magnetic geared permanent magnet machine according to winding pattern and segmentation of permanent magnet

This paper presents an analysis of the operating principle of magnetic geared permanent magnet machines (MGPMMs), electromagnetic analysis results according to the winding pattern, and a method for improving power factor and loss characteristics. To improve electromagnetic performance, the air gap magnetic flux density was calculated using the finite element method, and the harmonics of the inner and outer air gap magnetic flux densities was analyzed using the fast Fourier transform (FFT). From the FFT results, harmonic orders that affect electromagnetic performance were presented, and the electromagnetic analysis results were compared to derive correlations with torque ripple and losses. In addition, a design method for improving electromagnetic performance and operating characteristics was proposed by comparing power factors according to winding pattern. In particular, to improve the robust design and efficiency of MGPMM, a method of reducing eddy current loss by segmenting permanent magnets was addressed. The proposed analysis and design method can be widely used in the design and characteristic analysis of MGPMM.

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies, amplitudes and phases; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase while suppressing spectral leakage.

Data quality evaluation for bridge structural health monitoring based on deep learning and frequency-domain information

Abnormal data recognition is of great importance in structural health monitoring. Most of the existing studies focused on detecting obvious abnormal data, which has obvious abnormal time-domain waveform. Pseudo normal data, which is normally looking in time domain but chaotic in frequency domain, did not receive enough attention and were likely to be misclassified as normal data. As a result, structural performance may be incorrectly evaluated because pseudo normal data are not recognized and eliminated from the monitoring data. This study developed a novel quality evaluation framework for monitoring data of bridge dynamic response. The main novelty of the proposed framework is that the frequency-domain information is used to characterize the quality of the monitoring data so that the normal data, obvious abnormal data, and pseudo normal data can be accurately distinguished. In the framework, the frequency-domain information was obtained by fast Fourier transform (FFT), and the Gramian angular field images converted from FFT results were used to train a designed convolutional neural network (CNN). The cable acceleration data of the Waitan cable-stayed bridge were taken as an example to verify the accuracy of the proposed framework. Compared with the CNN models based on time-domain images and time-frequency stacked images, this framework can better recognize pseudo normal data from the monitoring data. In large-scale testing, the classification accuracy of all channels was more than 96%. Finally, two cable acceleration sensors of another cable-stayed bridge were used to demonstrate the feasibility of the framework in cross-object application. The results show that the framework has good accuracy and robustness in large-scale monitoring data quality evaluation and cross-object application.

An ultra-precise fast fourier transform

<h2>Abstract</h2> The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, is often used to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy' from spectral peaks may ‘leak' into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT, like many other DSP algorithms, is a discrete time approximation of continuous time mathematics. This paper describes a new FFT calculation which uses two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained from each windowing function applied to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase. This technique addresses FFT limitations as follows: (1) spectral peak parameters are calculated directly, unrestricted by FFT frequency step discretization; (2) the windowing functions have narrowband characteristics which attenuate and localize spectral leakage; (3) the windowing functions incorporate a Romberg Integration mechanism to overcome the discrete/continuous time approximation.

Implementation of Brain Computer Interface (BCI) as a Smart Wheelchair Motion Commands

A wheelchair is a tool used to assist people with physical limitations in their legs. The most widely used are standard wheelchairs with a manual operating system by being pushed by hand. However, people with disabilities who have paralysis or suffer from neuromuscular and neurological conditions cannot use this wheelchair. Because of this, in this study focuses on implementing the Brain Computer Interface system to generate five commands to move a wheelchair. There are five important stages in the BCI system, that is signal acquisition, pre-processing, feature extraction, classification, and applications interface. Fast Fourier Transform (FFT) method used to extract brainwave features. The results of FFT are alpha (8-12Hz) and beta (12-30 Hz) waves in the frequency domain. For classifying brain waves into six classes as input commands to drive a DC motor used Support Vector Machine (SVM) method. Based on the test results, the average accuracy of the classification for the whole class reached 93,1%, the accuracy of class 0 (77,3%), class 1 (95,7%), class 2 (97,8%), class 3 (98,0%), and class 4 (97,5%).

Thermo-mechanical properties prediction of Ni-reinforced Al2O3 composites using micro-mechanics based representative volume elements

For effective cutting tool inserts that absorb thermal shock at varying temperature gradients, improved thermal conductivity and toughness are required. In addition, parameters such as the coefficient of thermal expansion must be kept within a reasonable range. This work presents a novel material design framework based on a multi-scale modeling approach that proposes nickel (Ni)-reinforced alumina (Al2O3) composites to tailor the mechanical and thermal properties required for ceramic cutting tools by considering numerous composite parameters. The representative volume elements (RVEs) are generated using the DREAM.3D software program and the output is imported into a commercial finite element software ABAQUS. The RVEs which contain multiple Ni particles with varying porosity and volume fractions are used to predict the effective thermal and mechanical properties using the computational homogenization methods under appropriate boundary conditions (BCs). The RVE framework is validated by the sintering of Al2O3-Ni composites in various compositions. The predicted numerical results agree well with the measured thermal and structural properties. The properties predicted by the numerical model are comparable with those obtained using the rules of mixtures and SwiftComp, as well as the Fast Fourier Transform (FFT) based computational homogenization method. The results show that the ABAQUS, SwiftComp and FFT results are fairly close to each other. The effects of porosity and Ni volume fraction on the mechanical and thermal properties are also investigated. It is observed that the mechanical properties and thermal conductivities decrease with the porosity, while the thermal expansion remains unaffected. The proposed integrated modeling and empirical approach could facilitate the development of unique Al2O3-metal composites with the desired thermal and mechanical properties for ceramic cutting inserts.

Graph theoretical analysis of EEG after audiovisual stimulation in different anxiety states

AbstractIn this study, a brain network was created using graph theoretical analysis based on electroencephalography (EEG) data. The purpose of the study was to investigate the functional connectivity of the brain in different states of anxiety. Seventeen adults with anxiety (A‐G), and 13 adults without anxiety (AF‐G) were examined. They were given three different stimulations: resting, pleasant, and unpleasant. EEG was measured immediately after the stimulation. The EEG was analyzed by Fast Fourier Transform (FFT), coherence analysis, and graph theory. The results of FFT and coherence analysis showed that the anxiety group (A‐G) had higher power spectra and coherence values than those for the anxiety‐free group (AF‐G) in all sessions. The results of graph theory analysis showed that the clustering coefficient and small‐worldness in A‐G were lower than those in AF‐G, although the characteristic path length in A‐G was higher than that in AF‐G. This study shows that the brain of A‐G has smaller clusters and longer paths to compare with those of AF‐G. These events suggest that the brain of A‐G would have an inefficient network structure to transmit emotional information.

The Role of 2D Fast Fourier Transform and High Pass Filter in Regional and Residual Anomaly Separation in Gravity

Regional and residual Separation anomaly is one thing that must do in gravity processing data. It is important before calculating the depth of anomaly by power spectrum. There are several ways to do this, one of them is using 2D Fast Fourier Transform (FFT). 2D FFT will calculate the two-dimensional power of the gravity map (Bouger anomaly) to change the spatial domain into the wavenumber domain. 2D FFT result has no unit because it works in the wavenumber domain. Power spectrum do in wavenumber domain map. Besides that, to make the wavenumber map in the frequency domain, it should be convolved with some filter (high–pass filter) and then inverse to separate the regional and the residual map. The design of the filter matrix depends on the number of the data and the location of anomalies will be enhanced. It will influence the separation result. The best result gets from the trial and error process. 2D FFT is act like Upward Continuation or Polynomial Fitting in the gravity method with the simple process. In this paper, the process fully done in Python. Python is an effective and simple language programming because it has many modules to support the processing and covering the big data. It also gives the flexibility to the researcher to determine the specific location that will be enhanced

FPGA Implementation of an Efficient FFT Processor for FMCW Radar Signal Processing

This paper presents the design and implementation results of an efficient fast Fourier transform (FFT) processor for frequency-modulated continuous wave (FMCW) radar signal processing. The proposed FFT processor is designed with a memory-based FFT architecture and supports variable lengths from 64 to 4096. Moreover, it is designed with a floating-point operator to prevent the performance degradation of fixed-point operators. FMCW radar signal processing requires windowing operations to increase the target detection rate by reducing clutter side lobes, magnitude calculation operations based on the FFT results to detect the target, and accumulation operations to improve the detection performance of the target. In addition, in some applications such as the measurement of vital signs, the phase of the FFT result has to be calculated. In general, only the FFT is implemented in the hardware, and the other FMCW radar signal processing is performed in the software. The proposed FFT processor implements not only the FFT, but also windowing, accumulation, and magnitude/phase calculations in the hardware. Therefore, compared with a processor implementing only the FFT, the proposed FFT processor uses 1.69 times the hardware resources but achieves an execution time 7.32 times shorter.

Fourier Transform and Autoregressive HRV Features in Prediction and Classification of Breast Cancer

ABSTRACT The decision making in diagnosis of breast cancer (BC) at the earliest is the necessity to decrease the mortality rate. The 5-minute electrocardiogram of 114 BC subjects and 13 age-matched healthy controls were recorded and spectral features of heart rate variability (HRV) were calculated. Fast Fourier transform (FFT) and autoregressive (AR) spectral methods were compared to analyse the frequency domain of HRV. Lavenberg–Marquardt algorithm-based artificial neural network (ANN) and support vector machine (SVM) classified all the spectral measures with maximum accuracy of 54.2% and 100%, respectively. ANOVA with Tukey’s HSD Posthoc test has also been employed to evaluate the significant variations in different parameters due to BC with respect to control subjects with the help of statistical analysis. The FFT and AR results were found almost similar. Clinicians can achieve an insight of the severity of the disease as per the findings of spectral measures as per Eastern Cooperative Oncology Group Performance Status and improvise the quality of their patients.

Analysis of rainfall patterns in Kalimantan using fast fourier transform (FFT) and empirical orthogonal function (EOF)

Rainfall patterns in Kalimantan are generally divided into 2 types, namely monsoonal and equatorial. The pattern can be determined by analyzing the 6-month frequency of rainfall signal. This analysis has been carried out on general data in Indonesia, but no one has yet examined it in detail in Kalimantan. Therefore, this study will analyze the 6-month frequency signal and rainfall patterns spatially and temporally in Kalimantan using TRMM 3B42RT as the main data. The Fast Fourier Transform (FFT) method is applied to analyze the 6-month frequency of rainfall signal, while the Empirical Orthogonal Function (EOF) method is applied to reduce data and obtain the main pattern of rainfall in Kalimantan. The results of FFT analysis in 15 cities of Kalimantan show that the rainfall pattern in Samarinda, Sendawar, Tarakan, Tanjungselor, Malinau, Pangkalanbun, Pontianak, Ketapang, and Sintang are an equatorial type, while a monsoonal type appear in Balikpapan, Palangkaraya, Purukcahu, Banjarmasin, Kotabaru and Barabai. Moreover, based on the results of FFT and EOF analysis, most areas in West, East and North Kalimantan have an equatorial rainfall pattern. Meanwhile, most areas in Central and South Kalimantan have a monsoonal rainfall pattern.

The Implementation of Fast Fourier Transform and Coherence Function to Detect the Millimetric Hole on Strip Iron Plate

In this study, Fast Fourier Transform (FFT) was used in order to detect bore hole in a structure. FFT is a common method in digital signal processing (DSP) to characterize the frequency emitted by some structure. This method is widely used because of its simplicity. Computational time needed for FFT is relatively lower than another method. The use of FFT to analyze defect in structure is not commonly used since FFT has some weakness for example spatial frequency cannot be extracted to point out the defect location. In this paper, defect was designated as a hole in a strip iron plate with 20 mm in diameter. The strip iron plate was 1 meter long, 38 mm wide and 3 mm thick. This strip iron plate was clamped at one of its ends while the other side is left free. In order to produce vibration signal, impact hammer Bruel Kjaer Type 8202 was used with plastic tip to limit the vibration frequency in to the range of 0 - 1000 Hz. The trigger point was 30 mm from its free end. Three accelerometers were placed series in one line with the trigger point with 300 mm distance of each accelerometer. The position of the hole was varied in three different position. The first position was between trigger point and first accelerometer, between first and second accelerometer and between the second and third accelerometer. The raw signal obtained from the accelerometer was processed by using FFT to understand the mode shape changes in the strip iron plate due to the bore hole. Furthermore, the FFT result was analyzed as function of receiver position to determine the position of hole. The result shows that the frequency characters were different in each case and further analysis by using magnitude-squared coherence function need to be used in order to quantitatively find the difference between FFT result.

Higher Sensitivity and Reproducibility of Wavelet-Based Amplitude of Resting-State fMRI.

The fast Fourier transform (FFT) is a widely used algorithm used to depict the amplitude of low-frequency fluctuation (ALFF) of resting-state functional magnetic resonance imaging (RS-fMRI). Wavelet transform (WT) is more effective in representing the complex waveform due to its adaptivity to non-stationary or local features of data and many varieties of wavelet functions with different shapes being available. However, there is a paucity of RS-fMRI studies that systematically compare between the results of FFT versus WT. The present study employed five cohorts of datasets and compared the sensitivity and reproducibility of FFT-ALFF with those of Wavelet-ALFF based on five mother wavelets (namely, db2, bior4.4, morl, meyr, and sym3). In addition to the conventional frequency band of 0.0117–0.0781 Hz, a comparison was performed in sub-bands, namely, Slow-6 (0–0.0117 Hz), Slow-5 (0.0117–0.0273 Hz), Slow-4 (0.0273–0.0742 Hz), Slow-3 (0.0742–0.1992 Hz), and Slow-2 (0.1992–0.25 Hz). The results indicated that the Wavelet-ALFF of all five mother wavelets was generally more sensitive and reproducible than FFT-ALFF in all frequency bands. Specifically, in the higher frequency band Slow-2 (0.1992–0.25 Hz), the mean sensitivity of db2-ALFF results was 1.54 times that of FFT-ALFF, and the reproducibility of db2-ALFF results was 2.95 times that of FFT-ALFF. The findings suggest that wavelet-ALFF can replace FFT-ALFF, especially in the higher frequency band. Future studies should test more mother wavelets on other RS-fMRI metrics and multiple datasets.

Characteristics of counter-current gas-liquid two-phase flow and its limitations in vertical annuli

This paper aims to characterise the complex flow behaviour of counter-current gas-liquid flows in concentric vertical annuli over a wide range of gas and liquid flowrates. The experiments were performed with air and water in two different annulus sizes: (a) a 100 mm hydraulic diameter annulus with a 170 mm diameter outer pipe and a 70 mm diameter inner pipe; and (b) a 19 mm hydraulic diameter annulus between 44 mm and 25 mm pipes, to investigate the effect of flow geometry on flow structure. Flow regimes were identified quantitatively by applying fast Fourier transform (FFT) on the associated pressure fluctuation signals, collected at 10 Hz and 100 Hz frequency. Video images captured at 4,000 fps with a high-speed camera were used in a visual analysis of the flow regimes to verify the FFT results. Furthermore, flow regime transitions and their underlying mechanisms were determined by their associated pressure gradient and void fractions, as well as analysis of temporal pressure signals. The commonly described slug flow regime, consisting of stable Taylor bubbles traversing the length of the channel, was not observed in the larger annulus. However, the FFT of the pressure signals indicate that unstable Taylor bubbles form as a result of bubble coalescence but collapse due to instability at the gas-liquid interface, known as Rayleigh-Taylor instability. Therefore, the apparent slug-churn flow regime was classified as a highly turbulent heterogeneous flow, developing at superficial gas velocities from 0.265 to 3.968 m/s and superficial liquid velocities from 0.004 to 0.147 m/s. Interestingly, annular flow regime did not develop in either of the tested small and large annuli. The onsets of counter-current flow limitations, or flooding, were identified in the 100 mm hydraulic diameter annulus with gas flooding due to very high gas flow rates and liquid flooding due to very high liquid flow rates. The mechanism that initiates gas flooding was observed to be the formation of large waves flowing upward near the water inlet point, with counter-current flow observed below the water inlet point at the onset of gas flooding. Clarity was also provided on the concepts of flooding and zero liquid penetration for the cases of flow in a water filled channel and a falling film, and a new empirical correlation for the onset of flooding was developed.

Real-Time Monitoring of Micro-Electricity Generation Through the Voltage Across a Storage Capacitor Charged by a Simple Microbial Fuel Cell Reactor with Fast Fourier Transform

The pattern of micro-electricity production of simple two-chamber microbial fuel cells (MFC) was monitored in this study. Piggery wastewater and anaerobic sludge served as fuel and inocula for the MFC, respectively. The output power, including voltage and current generation, of triplicate MFCs was measured using an on-line monitoring system. The maximum voltage obtained among the triplicates was 0.663 V. We also found that removal efficiency of chemical oxygen demand (COD) and biochemical oxygen demand (BOD) in the piggery wastewater was 94.99 and 98.63%, respectively. Moreover, analytical results of Fast Fourier Transform (FFT) demonstrated that the output current comprised alternating current (AC) and direct current (DC) components, ranging from mA to μA.

On the use of fast Fourier transform for optical layer thickness determination

Thin film thickness determination with a reflectometer is a fast and pretty cheap method that can be applied on many thin and thick films that are transparent or semitransparent in the considered spectral range. For evaluation of the reflectance spectrum either nonlinear regression analysis is used for very thin films or fast Fourier transform (FFT) for films thicker than approximately 1 µm. Using FFT for layer thickness determination there are some special facts to consider in contrast to the common use of FFT in signal processing. First of all, the sampling points are in general not equidistant as the wavelengths of the used spectrometer are not equidistant. Next the number of sampling points may be different from a power of 2. The reason is that the measured spectral range may be restricted by the user. And finally the analogues in layer thickness determination to the independent parameters “time” and “frequency” in signal processing are not independent of each other. The reason is the dispersion of the refractive index of the layer material that causes unwanted Moire effects in the reflectance spectrum. All these deviations lead to additional sources for errors in the thickness determination beyond those error sources that are well-known from common FFT applications in signal processing. In this paper we discuss how these deviations affect the thickness determination and present a solution for the main problem caused by the dispersion of the refractive index. Further improvements of the FFT result in combination with a grid search algorithm and a nonlinear regression are presented and discussed. Finally we present with structured samples and highly doped semiconductors two specific applications of FFT on layer thickness determination.

Low-Complexity Joint Extrapolation-MUSIC-Based 2-D Parameter Estimator for Vital FMCW Radar

In this paper, a low-complexity joint extrapolation-multiple signal classification (MUSIC)-based 2-D parameter estimator is proposed for vital frequency-modulated continuous-wave (FMCW) radar. Recently, an FMCW radar, which can detect the distance and vital Doppler information, has been considered for vital non-contact radar. In the conventional FMCW radar system, fast Fourier transform (FFT)-based algorithms with low complexity are used to extract multiple parameters. However, the resolution and accuracy of an FFT-based parameter estimator are considerably low. Thus, 2-D high-resolution algorithms, such as the 2-D estimation of signal parameters via rotational invariance techniques and 2-D MUSIC, have been suggested as an alternative method. However, a large computation power is required compared with the FFT-based methods. Therefore, this paper proposes a 2-D parameter estimator that combines extrapolated FFT and MUSIC to reduce the computational load for vital detection. The proposed method uses an extrapolated FFT to overcome the disadvantages of the low-resolution FFT for the distance information, and then, the 1-D MUSIC algorithm is applied to the Doppler domain direction only for the extracted magnitude and phase information of the target’s extrapolated FFT results. Hence, the proposed algorithm combines the advantages of FFT and MUSIC. The performance of the proposed estimation is compared with that of other algorithms using Monte Carlo simulation results. The root-mean-square error of the proposed method is compared with that of 2-D MUSIC with various parameters. To verify the performance of the proposed combination method, the FMCW radar was used, and its performance was verified in an indoor environment.

Vibration fatigue dynamic stress simulation under multi-load input condition: Application to metro lifeguard

The formula for calculating the time history of structure dynamic stress under multi-load input condition was deduced based on structural dynamics theory, and fatigue life prediction of weld toe was performed by notch stress approach. In the dynamic stress time history simulation method, firstly, we calculate the frequency response function (FRF) of each external load at concerned point, which including the phase information. Then, the method was based on fast Fourier transform (FFT) to get the frequency domain with real and imaginary part of each external load rather than power spectrum density (PSD) calculation, avoiding loss of the phase information by PSD method. Finally, the dynamic stress frequency domain data could be calculated by FFT results and FRFs, based on above, the dynamic stress time history could be acquired by Inverse FFT (IFFT) of frequency domain data. Compared with the conventional stress PSD calculation method, the method in this paper can retain the phase information of the each external load, and the formula for calculating the dynamic stress under multi-load input condition was verified effective by a metro lifeguard line test data. The line test stress results show that the damage error between the numerical stress and the experimental stress is 4.1%, which is acceptable in project. At last, the method was used to guide the lifeguard structure optimization.

Harmonic Spectrum of Output Voltage for Space Vector-Modulated Matrix Converter Based on Triple Fourier Series

The output voltage of matrix converter (MC) is related to the frequency of input, output, and carrier signals, and these three frequencies are independent of each other. This makes it difficult to give a precise description of the harmonic spectrum with the commonly used methods such as fast Fourier transform (FFT) and the double Fourier analysis. Based on triple Fourier series, this paper proposes an analytical method to determine harmonic components of MC under space vector modulation (SVM). First, combined with the SVM strategy of MC, the expressions of output voltage harmonics are derived. Then the analytical solutions are obtained on the basis of the calculated expressions. From the analytical solutions, the harmonic amplitudes can be determined precisely, and the values of index variables k, p and q of harmonic frequency kf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ± pf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out</sub> ± qf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> are confirmed. According to the results, the harmonic distribution characteristics as well as main harmonic components are analyzed. Finally, the feasibility and accuracy of the proposed analysis method is verified by comparative analysis against the FFT results of measured output voltage waveform.