Standard FFT Research Articles

A Brand-New, Area - Efficient Architecture for the FFT Algorithm Designed for Implementation of FPGAs

Elliptic curve cryptography, which is more commonly referred to by its acronym ECC, is widely regarded as one of the most effective new forms of cryptography developed in recent times. This is primarily due to the fact that elliptic curve cryptography utilises excellent performance across a wide range of hardware configurations in addition to having shorter key lengths. A High Throughput Multiplier design was described for Elliptic Cryptographic applications that are dependent on concurrent computations. A Proposed (Carry-Select) Division Architecture is explained and proposed throughout the whole of this work. Because of the carry-select architecture that was discussed in this article, the functionality of the divider has been significantly enhanced. The adder carry chain is reduced in length by this design by a factor of two, however this comes at the expense of additional adders and control. When it comes to designs for high throughput FFT, the total number of butterfly units that are implemented is what determines the amount of space that is needed by an FFT processor. In addition to blocks that may either add or subtract numbers, each butterfly unit also features blocks that can multiply numbers. The size of the region that is covered by these dual mathematical blocks is decided by the bit resolution of the models. When the bit resolution is increased, the area will also increase. The standard FFT approach requires that each stage contain times as many butterfly units as the stage before it. This requirement must be met before moving on to the next stage.

Generalized Gauss-FFT 3D forward gravity modeling for irregular topographic mass having any 3D variable density contrast

A fully numerical forward model for estimating gravity anomalies in the Fourier domain is presented for irregular topographic mass distributions. Modified Parker’s formula using the Gauss-FFT method is utilized for getting better accuracy than the standard FFT algorithm. Existing frequency domain forward modeling for topographic surfaces uses common analytically derivable density functions for evaluating gravity anomalies. But in the real scenario, subsurface mass distributions can take any functional form of depth. Our presented algorithm provides a generalized approach for evaluating forward gravity anomalies due to any horizontal and vertical variation of density distributions. The computational cost depends on the irregularities of the topographic surfaces and the complexity of the functional form of density distributions. The presented algorithm is compared with analytical solutions and space domain prismatic model approximation. A complex, analytically non-integrable density distribution was also considered and compared with the space domain model. The presented algorithm accurately estimates gravity anomalies in all cases, and the results are close to the space domain prismatic model. Finally, an observed gravity anomaly of the real sedimentary basin and its corresponding inverted basement depth for parabolic density variation is considered to evaluate forward anomalies using our presented algorithm. The estimated gravity anomalies provide close approximations to observed gravity anomalies, revealing the proposed algorithm’s reliability for any 3D topographic forward modeling.

What a single electroencephalographic (EEG) channel can tell us about patients with dementia due to Alzheimer's disease

Abnormalities in cortical sources of resting-state eyes-closed electroencephalographic (rsEEG) rhythms recorded by hospital settings (10–20 electrode montage) with 19 scalp electrodes provide useful markers of neurophysiological dysfunctions in the vigilance regulation in patients with Alzheimer's disease dementia (ADD). Here we tested whether these markers may be effective from a few scalp electrodes towards the use of low-cost recording devices.Clinical and rsEEG data acquired in hospital settings (10–20 electrode montage) from 88 ADD participants and 68 age-, education-, and sex-matched normal elderly controls (Nold) were available in an international Eurasian database. Standard spectral FFT analysis of rsEEG data for individual delta, theta, and alpha frequency bands was from C3-P3, C4-P4, P3-O1, and P4-O2 bipolar channels.As compared to the Nold group, the ADD group showed increased delta, theta, low-frequency alpha power density and decreased high-frequency alpha power density at all those bipolar channels. The highest classification accuracy between the ADD and Nold individuals reached 90 % (area under the receiver operating characteristic curve) using Alpha2/Theta power density computed at the C3-P3 bipolar channel.Standard rsEEG power density computed from a few posterior bipolar channels successfully classified Nold and ADD individuals, thus encouraging a massive prescreening of neurophysiological mechanisms underpinning the vigilance dysregulation in underserved old seniors.

Parallel Fast Multipole Method accelerated FFT on HPC clusters

With increasing sizes of distributed systems, there comes an increased risk of communication bottlenecks. In the past decade there has been a growing interest in communication-avoiding algorithms. The distributed memory Fast Fourier Transform is an important algorithm which suffers from major communication bottlenecks. In this work, we take a look at an existing communication-avoiding algorithm FMM-FFT, an alternative to FFT which utilizes the Fast Multipole Method (FMM) to reduce communications to a single all-to-all communication. We present a detailed implementation of FMM-FFT relying on modern libraries and demonstrate it on two distinct distributed memory architectures notably a traditional Intel Xeon based HPC cluster and then a Beowulf cluster. We show that while the FMM-FFT is significantly slower than FFT on the traditional HPC cluster, on the Beowulf cluster it outperforms standard FFT, consistently getting speedups of 1.5x or more against FFTW. We then proceed to show how the communication to computation cost metric is important and useful in explaining the performance results of FMM-FFT against standard FFT. The source code pertaining to this work is being made publicly available under a permissive open source licence at Github.

High Efficient Real-time Calculation Method of here Large FFT with High Overlapping Rate

In order to meet the needs of large number of overlapping samples in sequential fine feature extraction, this work proposes a frame by frame (segment) iterative algorithm based on the “sparse” feature of incremental data to achieve efficient real-time calculation of large FFT, which breaks through the hardware bottleneck of real-time computing platform such as DSP platform in high-resolution spectral analysis. The proposed algorithm makes use of the sparseness of incremental data to make the computation burden of segment iteration lighter than that of standard FFT, and has the potential of parallel computation. The simulation results show that the new algorithm is more efficient than the standard FFT when the number of segments is large.

Band Structure of Phononic Crystal Consist of Hollow Aluminum Cylinders in Different Media; Finite Element Analysis

In this study, we investigated band structure of a 2D Phononic Crystal (PnC) which was consist of hollow aluminum cylinders in different media. To validate the finite element predictions, we made a square lattice PnC which has lattice constant a = 14mm, outer radius r1 = 5mm and inner radius r2 = 4mm of cylinders. In our experimental measurement, by using a signal generator software, we sent 100 Hz-20kHz sine signal for 5 seconds duration from speaker to the PnC where placed 1m away from. With the help of a microphone, we recorded the sound in front of the PnC (Pin ) and backside the PnC (Pout ). Then we were converted our recording into frequency domain by standard FFT algorithm, we calculated the Transmission Loss value according to the formula TL = 20*log10 (Pout / Pin ) and obtained the experimental Transmission Loss. After experimental validation, we conducted band structure analysis of different combination of the 2D PnC by finite element method.

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable 3D numerical modeling method for gravity anomalies in space-wavenumber mixed domain. By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. This method preserves the vertical component in the space domain, which is beneficial when modeling complex topography. The finite element method was used to solve the transformed differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

ProPOSE: Direct Exhaustive Protein-Protein Docking with Side Chain Flexibility.

Despite decades of development, protein-protein docking remains a largely unsolved problem. The main difficulties are the immense space spanned by the translational and rotational degrees of freedom and the prediction of the conformational changes of proteins upon binding. FFT is generally the preferred method to exhaustively explore the translation-rotation space at a fine grid resolution, albeit with the trade-off of approximating force fields with correlation functions. This work presents a direct search alternative that samples the states in Cartesian space at the same resolution and computational cost as standard FFT methods. Operating in real space allows the use of standard force field functional forms used in typical non-FFT methods as well as the implementation of strategies for focused exploration of conformational flexibility. Currently, a few misplaced side chains can cause docking programs to fail. This work specifically addresses the problem of side chain rearrangements upon complex formation. Based on the observation that most side chains retain their unbound conformation upon binding, each rigidly docked pose is initially scored ignoring up to a limited number of side chain overlaps which are resolved in subsequent repacking and minimization steps. On test systems where side chains are altered and backbones held in their bound state, this implementation provides significantly better native pose recovery and higher quality (lower RMSD) predictions when compared with five of the most popular docking programs. The method is implemented in the software program ProPOSE (Protein Pose Optimization by Systematic Enumeration).

Nonlinear System Identification Based on Convolutional Neural Networks for Multiple Drug Interactions.

In heart failure patients, hemodynamics can be regulated by therapeutic drugs. Although the cardiovascular responses to these drugs usually include nonlinearity and drug interactions, it is difficult to identify the characteristics of the dynamics under such conditions. This study, therefore, was aimed at evaluating the technique used for nonlinear system identification based on convolutional neural networks (CNN). As an image i.e., pixel values corresponding to time-course data), CNN can be used to treat the complicated relation between previous inputs (i.e., drug infusions) and outputs i.e., hemodynamics). To compare the accuracy of CNN, traditional methods based on the standard neural networks (NN) and fast Fourier transformation FFT were applied to nonlinear system identification with drug interactions. The cardiac output and arterial blood pressure under heart failure were modulated by the drug infusions of an inotropic agent and a vasodilator. CNN accurately predicted the dynamic system responses regardless of the inclusion of nonlinearity and drug interactions. Based on the findings of this study, CNN to carry out nonlinear system identification could clarify complicated pharmacodynamics, and thus could be useful for in appropriate cardiac treatment with multiple therapeutic agents.

The Partial Fast Fourier Transform

An efficient algorithm for computing the one-dimensional partial fast Fourier transform $$f_j=\sum _{k=0}^{c(j)}e^{2\pi ijk/N} F_k$$ is presented. Naive computation of the partial fast Fourier transform requires $${\mathcal O}(N^2)$$ arithmetic operations for input data of length N. Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on the space variable j; this prevents one from directly applying standard FFT algorithms. It is shown that the space–frequency domain can be partitioned into rectangular and trapezoidal subdomains over which efficient algorithms can be developed. As in the previous work of Ying and Fomel (Multiscale Model Simul 8(1):110–124, 2009), the contribution from rectangular regions can be reduced to a series of fractional-phase Fourier transforms over squares, each of which can be reduced to a convolution. In this work, we demonstrate that the partial Fourier transform over trapezoidal domains can also be reduced to a convolution. Since the computational complexity of a dealiased convolution of N inputs is $${\mathcal O}(N\log N)$$ , a fast algorithm for the partial Fourier transform is achieved, with a lower overall coefficient than obtained by Ying and Fomel.

High-accuracy 3D Fourier forward modeling of gravity field based on the Gauss-FFT technique

The 3D Fourier forward modeling of 3D density sources is capable of providing 3D gravity anomalies coincided with the meshed density distribution within the whole source region. This paper firstly derives a set of analytical expressions through employing 3D Fourier transforms for calculating the gravity anomalies of a 3D density source approximated by right rectangular prisms. To reduce the errors due to aliasing and imposed periodicity as well as edge effects in the Fourier domain modeling, we develop the 3D Gauss-FFT technique to the 3D gravity anomalies forward modeling. The capability and adaptability of this scheme are tested by simple synthetic models. The results show that the accuracy of the Fourier forward methods using the Gauss-FFT with 4 Gaussian-nodes (or more) is comparable to that of the spatial modeling. In addition, the “ghost” source effects in the 3D Fourier forward gravity field due to imposed periodicity of the standard FFT algorithm are remarkably depressed by the application of the 3D Gauss-FFT algorithm. More importantly, the execution times of the 4 nodes Gauss-FFT modeling are reduced by two orders of magnitude compared with the spatial forward method. It demonstrates that the improved Fourier method is an efficient and accurate forward modeling tool for the gravity field.

Elastic Image Registration Based on Domain Decomposition with Mesh Adaptation

Medical images are increasingly used within healthcare for diagnosis, planning treatment, and monitoring disease progression. The images acquired at different times, with different imaging modalities, from different subjects etc. often provide an additional clinical information that is not revealed in the separate images. The spatial relation between the images has to be found and this process is called image registration. In our contribution, we use elastic registration which assumes that the images are two different observations of an elastic body which is discretized by the finite element method. We are especially interested in the problems where the requirements on the registration prevent the application of standard FFT based solvers to the solution of auxiliary linear problems, which is the case when the part of the two observations can be related by a rigid body motion. Because the medical images usually contain a large area of background and a small area of changes, a regular discretization results in waste of computational resources due to the fine refinement of the space outside the region of interest (especially in 3D). To avoid this, we use coarser grid with local refinement that takes into account specific features of the images and their differences. The related elasticity problems are solved by TFETI, which is a variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method for massively parallel numerical solution of elliptic Partial Differential Equations (PDE) with optimal complexity.

A novel nonlocal potential solver based on nonuniform FFT for efficient simulation of the Davey−Stewartson equations

We propose an efficient and accurate solver for the nonlocal potential in the Davey−Stewartson equations using nonuniform FFT (NUFFT). A discontinuity in the Fourier transform of the nonlocal potential causes accuracy locking if the potential is solved by standard FFT with periodic boundary conditions on a truncated domain. Using the fact that the discontinuity disappears in polar coordinates, we reformulate the potential integral and split it into high and low frequency parts. The high frequency part can be approximated by the standard FFT method, while the low frequency part is evaluated with a high order Gauss quadrature accelerated by nonuniform FFT. The NUFFT solver has O(N log N) complexity, where N is the total number of discretization points, and achieves higher accuracy than standard FFT solver, which makes its use in simulations very attractive. Extensive numerical results show the efficiency and accuracy of the proposed new method.

Fast convolution with free-space Green's functions

We introduce a fast algorithm for computing volume potentials – that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Green's function by cutting off the interaction in physical space beyond the domain of interest. This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data. Moreover, the method can be interpreted as employing a Nystrom discretization of the corresponding integral operator, with matrix entries which can be obtained explicitly and rapidly. This is of use in the design of preconditioners or fast direct solvers for a variety of volume integral equations. The method proposed permits the computation of any derivative of the potential, at the cost of an additional FFT.

F2DPR: a fast and robust cross-correlation technique for volumetric PIV

The current state-of-the-art in cross-correlation based time-resolved particle image velocimetry (PIV) techniques are the fluid trajectory correlation, FTC (Lynch and Scarano 2013) and the fluid trajectory evaluation based on an ensemble-averaged cross-correlation, FTEE (Jeon et al 2014a). These techniques compute the velocity vector as a polynomial trajectory in space and time, enabling the extraction of beneficial quantities such as material acceleration whilst significantly increasing the accuracy of the particle displacement prediction achieved by standard two-frame PIV. In the context of time-resolved volumetric PIV, the drawback of trajectory computation is the computational expense of the three-dimensional (3D) cross-correlation, exacerbated by the requirement to perform N − 1 cross-correlations, where N (for typically ) is the number of sequential particle volumes, for each velocity field. Therefore, the acceleration of this calculation is highly desirable. This paper re-examines the application of two-dimensional (2D) cross-correlation methods to three-dimensional (3D) datasets by Bilsky et al () and the binning techniques of Discetti and Astarita (). A new and robust version of the 2D methods is proposed and described, called fast 2D projection—re-projection (f2dpr). Performance tests based on computational time and accuracy for both two-frame and multi-frame PIV are carried out on synthetically generated data. The cases presented herein include uniaxial uniform linear displacements and shear, and simulated turbulence data. The proposed algorithm is shown to be in the order of 10 times faster than a standard 3D FFT without loss of precision for a wide range of synthetic test cases, while combining with the binning technique can yield 50 times faster computation. The algorithm is also applied to reconstructed synthetic turbulent particle fields to investigate reconstruction noise on its performance and no significant loss of precision is observed.

Pseudo-Polar Fourier Transform-Based Compressed Sensing MRI

The use of radial k-space trajectories has drawn strong interest from researchers for their potential in developing fast imaging methods in magnetic resonance imaging (MRI). Compared with conventional Cartesian trajectories, radial sampling collects more data from the central k-space region and the radially sampled data are more incoherent. These properties are very suitable for compressed sensing (CS)-based fast imaging. When reconstructing under-sampled radial data with CS, regridding and inverse-regridding are needed to transfer data between the image and frequency domains. In each CS iteration, two-dimensional interpolations are implemented twice in the regridding and inverse-regridding, introducing errors and undermining reconstruction quality. To overcome these problems, a radial-like pseudo-polar (PP) trajectory is proposed for the CS MRI applications. The PP trajectory preserves all the essential features of radial trajectory and allows an image reconstruction with PP fast Fourier transform (PPFFT) instead of interpolations. This paper attempts to investigate the performance of PP trajectory-based CS-MRI. In CS-based image reconstruction, the transformation of PP-sampled k-space data into the image domain is realized through PPFFT, which is based on the standard one-dimensional FFT and the fractional Fourier transform. To evaluate the effectiveness of the proposed methods, both numerical and experimental data are used to compare the new methods with conventional approaches. The proposed method provided high-quality reconstruction of the MR images with over 2-dB gain in peak signal-to-noise ratio while keeping structural similarity over 0.88 in different situations. Compared with the conventional radial sampling-based CS MRI methods, the proposed method achieves a more accurate reconstruction with respect to image detail/edge preservation and artifact suppression. The successful implementation of the PP subsampling-based CS scheme provides a practical and accurate CS-based rapid imaging method for clinical applications.

Lorentzian sparsity based spectroscopic reconstruction for fast high-dimensional magnetic resonance spectroscopy

Two-dimensional magnetic resonance spectroscopy (2D MRS) is challenging, even with state-of-art compressive sensing methods, such as L1-sparsity method. In this work, using the prior that the 2D MRS can be regarded as a series of Lorentzian functions, we aim to develop a robust Lorentzian-sparsity based spectroscopy reconstruction method for high-dimensional MRS.The proposed method sparsifies 2D MRS in Lorentzian functions. Instead of thousands of pixel-wise variables, this Lorentzian-sparsity method significantly reduces the number of unknowns to several geometric variables, such as the center, magnitude and shape parameters for each Lorentzian function. The spectroscopy reconstruction is formulated as a nonlinear and nonconvex optimization problem, and the simulated annealing algorithm is developed to solve the problem.The proposed method was compared with inverse FFT method and L1-sparsity method, under various undersampling factors. While FFT and L1 results contained severe artifacts, the Lorentzian-sparsity results provided significantly improved spectroscopy.A new 2D MRS reconstruction method is proposed using the Lorentzian sparsity, with significantly improved MRS reconstruction quality, in comparison with standard inverse FFT method or state-of-art L1-sparsity method.

An Efficiency Multiplexing Scheme and Improved Sampling Method for Multichannel Data Acquisition System

The paper proposes an efficient multiplexing scheme that is easy to realize synchronous sampling in a multichannel acquisition system with the large number of analogue inputs and different sampling rates. And then, a simple improved sampling control method is also employed to improve the performance. All the technology of implementing the method is by using a low-cost field programmable gate array (FPGA). A sampling lookup table is built by the rule-based synchronous sampling frame structure for the input analogue multiplexers and stored into the internal block RAM resource in the FPGA to reduce the internal wiring resources and optimize the utilization. The improved sampling method obtains several samples in a sampling period and gets the average value as the final output for the sampling channel. In addition, the standard sine wave FFT test method is implemented to test the dynamic parameters of the acquisition channels. The experiment results show that the dynamic performance of the acquisition system is significantly improved. The proposed multiplexing scheme and sampling method can easily be reconfigured for other applications.

High Frequency Acceleration Envelope Power Spectrum for Fault Diagnosis on Journal Bearing using DEWESOFT

The aim of study is to apply the condition monitoring technique in the journal bearing to detect the faults at an early stage and to prevent the occurrence of catastrophic failures. This study presents fault diagnosis on journal bearing through the experimental investigation at high rotational speed. Journal bearings are widely used to support the shaft of industrial machinery with heavy loads, such as compressors, turbines and centrifugal pumps. The major problem in journal bearing is catastrophic failure due to corrosion and erosion, results in economic loss and creates high safety risks. So, it is necessary to provide condition monitoring technique to detect and diagnose failures, to achieve cost benefits to industry. High frequency acceleration enveloping facilitates the extraction of low amplitude, high frequency signals associated with repetitive impacts in journal bearings, providing a key tool for early detection in the onset of bearing damage and similar machinery health problems when coupled with standard FFT analysis. The DEWESOFT software-based methods for implementing and interpreting high frequency acceleration enveloping are presented and compared. In this study the application of STFT (Short Time Fourier Transform) and Autocorrelation through FFT are used for processing vibration signal to detect faults in journal bearing is presented. A bearing testing apparatus is used for experimental studies to obtain vibration signal from a healthy bearing and fault bearing.

Application of High Frequency Acceleration Envelope Power Spectrum and ANN for Fault Diagnosis on Journal Bearing Under Various Loading Conditions

Journal bearings are widely used to support the shaft of industrial machinery with heavy loads, such as compressors, turbines and centrifugal pumps. The major problem in journal bearing is catastrophic failure due to corrosion and erosion, results in economic loss and creates high safety risks. So, it is necessary to provide condition monitoring technique to detect and diagnose failures, to achieve cost benefits to industry. High frequency acceleration enveloping facilitates the extraction of low amplitude, high frequency signals associated with repetitive impacts in journal bearings, providing a key tool for early detection in the onset of bearing damage and similar machinery health problems when coupled with standard FFT analysis. The DEWESOFT software-based methods for implementing and interpreting high frequency acceleration enveloping are presented and compared. In this paper the application of STFT (Short Time Fourier Transform) and Autocorrelation through FFT are used for processing vibration signal to detect faults in journal bearing is presented. A bearing testing apparatus is used for experimental studies to obtain vibration signal from a healthy bearing and fault bearing. Further application of ANN for extracting features like RMS, mean, kurtosis, shape factor, crest factor and impulse factor is investigated as a model for automated fault diagnosis is presented.