Fourier Transform Algorithm Research Articles

Design and Simulation of 1xN Optical Switch Based on LCoS SLM by Using Iterative Fourier Transform Algorithm with the Optimization Method

Proceedings of the International Display Workshops Volume 28 (IDW '21),Design and Simulation of 1xN Optical Switch Based on LCoS SLM by Using Iterative Fourier Transform Algorithm with the Optimization Method

High-performance computation of pricing two-asset American options under the Merton jump-diffusion model on a GPU

This paper is concerned with fast, parallel and numerically accurate pricing of two-asset American options under the Merton jump-diffusion model, which gives rise to a two-dimensional partial integro-differential complementarity problem (PIDCP) with a nonlocal two-dimensional integral term. Following method-of-lines approach, the solution to the PIDCP can be computed quite accurately by a robust numerical technique that combines Ikonen–Toivanen splitting with an alternating direction implicit scheme. However, we observed that computing the numerical solution with this technique becomes extremely time consuming, mainly due to the handling of the integral term. In this paper we parallelize this technique by applying a parallel fast Fourier transformation algorithm to all matrix-vector multiplications involving the huge and dense integral approximation matrix by exploiting its block Toeplitz with Toeplitz block structure. We also parallelize other computationally intensive steps of this technique by applying a recently developed parallel cyclic reduction algorithm for pentadiagonal systems. Our solutions computed on a graphics processing unit (GPU) using CUDA® platform are compared for accuracy with those available in the literature. It is observed that by solving the PIDCP parallelly we could bring down the computational times from several hours to a few seconds in certain cases in our experiments.

Mathematical modeling of signals, linear links and responses of telecommunications and radioelectronics systems in time domain

A single mathematical model of time characteristics of signals, links and responses of telecommunications and radioelectronics systems is suggested. It embodies Dirac- and Heaviside responses of all types of linear links, as well as their responses to the input in the form of periodic signals, no periodic finite and no periodic eternal signals. On the basis of the suggested model the algorithm for calculation of time characteristics was developed, which allows creation of effective automated simulations procedure of signals, links and responses in time-domain. The comparative quantitative analysis of accuracy of the suggested algorithm and discrete Fourier transformation (DFT) algorithm was carried out.

Performance Analysis of Associate Radix-2, Radix- 4 and Radix-8 based FFT using Folding Technique

Abstract : In recent years, as a result of advancing VLSI technology, Orthogonal Frequency Division Multiplexing (OFDM) has received a great deal of attention and has been adopted in many new generation wideband data communication systems such as IEEE 802.11a, IEEE 802.16e, HiPerLAN/2, Digital Audio/Video Broadcasting (DAB/DVB), and for 4G Radio mobile communications. This is because of its high bandwidth efficiency as the use of orthogonal waveforms with overlapping spectra. The immunity to multipath fading channel and the capability for parallel signal processing make it a promising candidate for the next generation mobile communication systems. The modulation and demodulation of OFDM based communication systems can be efficiently implemented with an FFT and IFFT, which has made the FFT valuable for those communication systems. The complexity of an OFDM system highly depends upon the computation of Fast Fourier Transform (FFT) algorithm. With the advent of new technology in the fields of VLSI and communication, there is also an ever growing demand for high speed processing and low area design. It is also a well-known fact that the multiplier unit forms an integral part of processor design. Due to this regard, high speed multiplier architectures become the need of the day.

Circadian Rhythm Analysis Using Wearable Device Data: Novel Penalized Machine Learning Approach.

BackgroundWearable devices have been widely used in clinical studies to study daily activity patterns, but the analysis remains a major obstacle for researchers.ObjectiveThis study proposes a novel method to characterize sleep-activity rhythms using actigraphy and further use it to describe early childhood daily rhythm formation and examine its association with physical development.MethodsWe developed a machine learning–based Penalized Multiband Learning (PML) algorithm to sequentially infer dominant periodicities based on the Fast Fourier Transform (FFT) algorithm and further characterize daily rhythms. We implemented and applied the algorithm to Actiwatch data collected from a cohort of 262 healthy infants at ages 6, 12, 18, and 24 months, with 159, 101, 111, and 141 participants at each time point, respectively. Autocorrelation analysis and Fisher test in harmonic analysis with Bonferroni correction were applied for comparison with the PML. The association between activity rhythm features and early childhood motor development, assessed using the Peabody Developmental Motor Scales-Second Edition (PDMS-2), was studied through linear regression analysis.ResultsThe PML results showed that 1-day periodicity was most dominant at 6 and 12 months, whereas one-day, one-third–day, and half-day periodicities were most dominant at 18 and 24 months. These periodicities were all significant in the Fisher test, with one-fourth–day periodicity also significant at 12 months. Autocorrelation effectively detected 1-day periodicity but not the other periodicities. At 6 months, PDMS-2 was associated with the assessment seasons. At 12 months, PDMS-2 was associated with the assessment seasons and FFT signals at one-third–day periodicity (P<.001) and half-day periodicity (P=.04), respectively. In particular, the subcategories of stationary, locomotion, and gross motor were associated with the FFT signals at one-third–day periodicity (P<.001).ConclusionsThe proposed PML algorithm can effectively conduct circadian rhythm analysis using time-series wearable device data. The application of the method effectively characterized sleep-wake rhythm development and identified the association between daily rhythm formation and motor development during early childhood.

Hand character gesture recognition based on a single millimetre‐wave radar chip

In this work, a new method for hand character gesture recognition based on a single millimetre-wave radar chip is proposed. Most current radar-based gesture recognition approaches use Doppler spectrograms or the feature extraction of Doppler spectrograms. In contrast, the authors propose using the trajectory points of gesture movements. Compared with the previous methods, the variations in the gesture movement speed, distance and direction during data acquisition have relatively little impact on the generated trajectories. The character trajectories drawn by gestures in the air output a fixed shape, and this fixed output facilitates the classification of gestures at a later stage. In this work, a single millimetre-wave radar is used to collect data and a three-dimensional fast Fourier Transform (3D-FFT) algorithm is used to obtain the gesture trajectories. For the trajectory points, a trajectory conversion image method is proposed and finally the improved Xception network proposed in this work is used for image recognition. Compared with traditional methods, the proposed method does not require large-scale data acquisition to facilitate different users. This work is concluded by recognising hand character gestures and comparing them with other commonly used classification methods to verify the gesture recognition accuracy of the proposed method.

Evaluating FFT-based algorithms for strided convolutions on ARMv8 architectures

Convolutional Neural Networks (CNNs) have been widely adopted in many kinds of artificial intelligence applications. Most of the computational overhead of CNNs is spent on convolutions. An effective approach to reducing the overhead is transforming convolutions in the time domain into multiplications in the frequency domain by means of Fast Fourier Transform (FFT) algorithms, known as FFT-based fast algorithms for convolutions. However, current FFT-based fast implementations only work for unit-strided convolutions with stride as 1, and cannot be directly applied to strided convolutions with stride size greater than 1, which are usually used as the first layer of CNNs and as an effective alternative to the pooling layers for downsampling.In this paper, we first introduce rearrangement- and sampling-based methods for applying FFT-based fast algorithms to strided convolutions, and the arithmetic complexities of these two methods and the direct method are compared in detail. Then, the highly optimized parallel implementations of the two methods on ARMv8-based many-core CPU are presented. Lastly, we benchmark these implementations against two GEMM-based implementations on this ARMv8 CPU. Our experimental results with convolutions of different kernels, feature maps, and batch sizes show that the rearrangement-based method generally exceeds the sampling-based one under the same optimizations in most cases, and these two methods can get much better performance than GEMM-based ones when the kernels, feature maps and batch sizes are large. The experimental results on the convolutional layers in popular CNNs further demonstrate the conclusions above.

Feature selection to classify lameness using a smartphone-based inertial measurement unit.

Background and objectivesGait can be severely affected by pain, muscle weakness, and aging resulting in lameness. Despite the high incidence of lameness, there are no studies on the features that are useful for classifying lameness patterns. Therefore, we aimed to identify features of high importance for classifying population differences in lameness patterns using an inertial measurement unit mounted above the sacral region.MethodsFeatures computed exhaustively for multidimensional time series consisting of three-axis angular velocities and three-axis acceleration were carefully selected using the Benjamini–Yekutieli procedure, and multiclass classification was performed using LightGBM (Microsoft Corp., Redmond, WA, USA). We calculated the relative importance of the features that contributed to the classification task in machine learning.ResultsThe most important feature was found to be the absolute value of the Fourier coefficients of the second frequency calculated by the one-dimensional discrete Fourier transform for real input. This was determined by the fast Fourier transformation algorithm using data of a single gait cycle of the yaw angular velocity of the pelvic region.ConclusionsUsing an inertial measurement unit worn over the sacral region, we determined a set of features of high importance for classifying differences in lameness patterns based on different factors. This completely new set of indicators can be used to advance the understanding of lameness.

Hw/Sw Co-Design technique for 2D fast fourier transform algorithm on Zynq SoC

The Two-Dimensional Fast Fourier Transform (2D-FFT) algorithm is used for the study of many modern systems applied for security and biometrics. The adoption of this algorithm, which is a compute intensive task, is limited due to its hardware design complexity. The first objective of this paper is to underline the effect of the hardware/software co-design (Hw/Sw co-design) for the reduction of the processing time and power consumption. Secondly, we propose an innovative architecture for the 2D-FFT algorithm tested on Zynq Soc, which requires less processing time and memory compared to the traditional algorithm. Three implementations (one software and two Hw/Sw co-designs) of the 2D-FFT algorithm using the Zynq SoC are presented in this paper. The first is based on ARM processor. A speedup of 29x is obtained compared to the original implementation thanks to many optimizations. The second is a Hw/Sw co-design solution of the traditional 2D-FFT algorithm introduced on a hybrid platform combining an ARM Cortex-A9 processor with an FPGA. The third is also a Hw/Sw co-design solution using our optimized 2D-FFT algorithm to reach the real-time contraints for high-resolution images (1920 × 1080). It provides a speedup of 1.13x, 3.31x and 96.21x faster than the Hw/Sw co-design implementation of the traditional RC algorithm, the pure software implementations with and without optimizations, respectively.

Viscoelastic Love numbers and long-period geophysical effects

SUMMARY Long term deformations strongly depend on the earth model and its rheological parameters, and in particular its viscosity. We give the general theory and the numerical scheme to compute them for any spherically non-rotating isotropic earth model with linear rheology, either elastic or viscoelastic. Although the Laplace transform (LT) is classically used to compute viscoelastic deformation, we choose here instead, to implement the integration with the Fourier transform (FT) in order to take advantage of the fast FT algorithm and avoid some of the LT mathematical difficulties. We describe the methodology to calculate deformations induced by several geophysical signals regardless of whether they are periodic or not, especially by choosing an adapted time sampling for the FT. As examples, we investigate the sensitivity of the displacements due to long period solid Earth tides, glacial isostatic adjustment and present-day ice melting, to anelastic parameters of the mantle. We find that the effects of anelasticity are important for long period deformation and relatively low values of viscosities for both Maxwell and Burgers models. We show that slight modifications in the rheological models could significantly change the amplitude of deformation but also affect the spatial and temporal pattern of the signal to a lesser extent. Especially, we highlight the importance of the mantle anelasticity in the low degrees deformation due to present-day ice melting and encourage its inclusion in future models.

Ultrahigh-aspect-ratio beam generation with super-resolution spot

Focusing to a small spot along a large depth of focus (DOF) beyond the limits imposed by diffraction has attracted extensive theoretical as well as practical interest. The aspect ratio, defined as the DOF divided by the diameter of spot, has been extended by several schemes with reasonable success, but there is no report that enables one to modulate the aspect ratio as long as possible with sidelobe suppression. In this Letter, we propose a method to generate ultrahigh-aspect-ratio beams (UARBs) by introducing an analytic procedure using Zernike polynomials in the modified iterative Fourier-transform algorithm, and a super-resolution spot is also realized to further extend the aspect ratio. We design the diffractive optical elements that generate UARBs with sidelobe suppression and further experimentally demonstrate a stretched 1602:1 aspect ratio of UARBs with a lateral super-resolution spot, suggesting potential applications for further super-resolution imaging or precision fabrication.

Fast Analysis of Broadband Electromagnetic Scattering Characteristics of Electrically Large Targets using Precorrected Fast Fourier Transform Algorithm based on Near Field Matrix Interpolation Method

In this paper, a new method is proposed to analyze the broadband electromagnetic characteristics of electrically large targets by combining the precorrected-FFT algorithm (P-FFT) with the near-field matrix interpolation technique. The proposed method uses the precorrected-FFT algorithm to reduce the storage and accelerate the matrix vector product of the far field. In order to make the precorrected-FFT algorithm can calculate the broadband characteristics of electrically large targets more quickly, the matrix interpolation method is used to interpolate the near-field matrix of the precorrected-FFT algorithm to improve the efficiency of calculation. The numerical results obtained validate the proposed method and its implementation in terms of accuracy and runtime performance.

Mobile image processing system based on the Raspberry Pi 4 platform

The article presents an image processing system based on the Raspberry Pi (RPi) platform. At the beginning of the article, the basic assumptions and purpose of the system are discussed. The following section presents the structure and operation of the system. The window application managing the system and allowing to perform contextual and spectral transformations on images as well as the measurement of parameters such as image processing time and mean square error (MSE) was discussed. The transformations performed were based both on ready formulas contained in the OpenCV library and the author's implementations, including the function implementing the Fast Fourier Transform algorithm radix-2. Examples of transformations were presented along with their usefulness. In the end, the development potential of the created system is presented and its application in specific solutions is proposed.

Fabry Perot Cavity Length Demodulation Method Based on Continuous Thinning Algorithm of Fast Fourier Transform Spectrum

Optical fiber Fabry Perot sensors are widely used in industrial production and life. It is of great significance to improve the performance of sensor demodulation algorithm. Based on the analysis of the principle and error source of the cavity length demodulated by the Fast Fourier Transform (FFT) algorithm, the FFT-FT algorithm with continuous refinement of FFT spectrum is introduced. By using the feature that FFT-FT algorithm can refine at the peak of discrete spectrum, the length of F-P cavity demodulated by FFT algorithm is optimized to improve the accuracy of the demodulation. Through simulation experiments, the F-P cavity length of FFT demodulation algorithm and FFT-FT demodulation algorithm under the same light source signal are compared and analyzed, and the goodness of fit of the fitting curve of continuous demodulation is analyzed. The simulation results show that the error of FFT demodulation algorithm is more than 100 times that of FFT-FT algorithm when it is refined 100 times near the peak value of FFT discrete spectrum. The goodness of fit of the demodulation fitting curve calculated by FFT-FT algorithm is more than 2 times that of FFT algorithm, which proves that the improved algorithm demodulation F-P cavity length value has better consistency with the real value.

Accurate frequency estimation of multiple complex and real sinusoids based on iterative interpolation

Frequency estimation of multiple complex and real sinusoids in noise has attracted wide attention in many fields. In this paper, two frequency domain parametric methods are proposed to estimate the frequencies of multiple complex and real sinusoids accurately. The first method for complex sinusoids adopts Discrete Fourier Transform (DFT) and interpolation algorithm to obtain the coarsely estimated frequencies, and then the interpolation is used iteratively to refine the estimated frequencies. In each step, the estimated frequency components are subtracted to reduce spectrum leakage. The second method for multiple real sinusoids, which is modified based on the first one, focuses on reducing the spectrum leakage caused by negative frequencies and then employs iterative interpolation to refine the estimated frequencies. Simulation results show that two proposed methods have lower mean square error (MSE) and signal-to-noise ratio (SNR) breakdown threshold than other frequency domain parametric methods, and are capable of achieving the Cramér-Rao lower bound (CRLB) for both multiple complex and real signals under a wide range of SNR.

Differential-geometry-based surface normal vector calculation method using a time-of-flight camera.

A surface normal vector of an object is often needed to detect an orientation of the object. A simple calculation method of the surface normal vector by means of a time-of-flight (ToF) camera is thus proposed here, using a coordinate transformation of three-dimensional irregular points acquired by the ToF camera to regular grid representation. Each point of the regular grid representation has a depth (distance from the camera) defined on the regular grid. The surface normal vector on the regular grid can be derived based on differential geometry with partial derivatives of the depth, and can then be in the form of the discretized Fourier transformation to which the fast Fourier transformation algorithm is applicable. The method of the surface normal vector calculation is thus theoretically derived. Validation of the method is also experimentally performed.

СПОСІБ РОЗРОБКИ ІЗОЕФЕКТИВНОЇ ГЕТЕРОГЕННОЇ СИСТЕМИ НА ОСНОВІ МАШИННОГО НАВЧАННЯ ДЛЯ ЗАДАЧІ ДИСКРЕТНОГО ПЕРЕТВОРЕННЯ ФУР’Є

In this paper, the isoefficiency of MPP systems and heterogeneous CPU-GPU systems on the problem of discrete Fourier transform is considered. The development of parallel applications as its goal can not only reduce execution time, but also provide opportunities to solve problems of a larger dimension. The peculiarity of algorithm parallelization includes the efficient use of hardware while increasing the dimension of the problem is an important characteristic of parallel computing. However, currently heterogeneous systems have not been researched extensively to determine isoefficiency characteristics and build application-specific systems around said method, although there are articles that show potential using isoefficiency to design the system and using heterogeneous approach to accelerate performance of different tasks. Discrete Fourier Transform algorithm lets build systems that discretize analogue and digital signals and it can serve as a benchmark to test different systems. Algorithms suited for MPP systems can use analytical approach to find out issoefficiency function and to determine how scaling the system or changing the size of the task will change its performance metrics. One of the most popular approaches to linking up processing units in MPP systems is using hypercube topology. MPP system that is connected using this topology will be analyzed. CPU-GPU heterogeneous system will be analyzed using an approach based on polynomial regression. Due to the nature of heterogeneous systems, analytic approach used in MPP system is impossible. Predictive model based on polynomial regression will use modelling results from using CPU and GPU separately to estimate how much time it will take for heterogeneous system to finish the task. To ensure accuracy of the experiment, several systems will be used to model the task. Using this approach, resulting issoefficient heterogeneous system will be analyzed using performance metrics s

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

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

Experimental and theoretical analysis of carbon driven detonation waves in a heterogeneously premixed Rotating Detonation Engine

Coal dust explosions can be hazardous; however, they can also generate a significant rise in stagnation pressure if adequately harnessed. Rotating detonation combustors seek to take advantage of the stagnation pressure rise phenomenon in a more sustained and controlled manner via confinement to a physical annulus, leading to increased overall thermodynamic efficiency. This investigation presents an analysis of detonations fueled by Carbon Black, a solid particulate consisting of virtually pure carbon molecules and lean Hydrogen-Air mixtures. It is realized that with the addition of Carbon Black, an increase of lean mixture detonability and detonation velocities extending the operating limit over that of a pure hydrogen-air mixture is experienced. For all testing conditions, the total equivalence ratio is held at φ = 1, while the fuel mixture's carbon mass fraction is increased from 0 to 0.7 while the hydrogen is decreased. Detonation wave velocities are extracted from high-speed imaging through applying a Discrete Fourier Transform algorithm to determine changes to the wave speed as Carbon Black particles are introduced. As a result, due to the addition of Carbon Black as an auxiliary fuel source, detonations were formed instead of deflagrations in operating conditions where one would expect deflagrations at the same hydrogen-air equivalence ratios without Carbon Black addition. The detonation formation provides evidence that the coal particles are reacting within the detonation wave in a large enough capacity to support a detonation wave within the annulus. Furthermore, the wave speed is shown to increase with the additional of carbon particles. At a constant global equivalence ratio, the detonation wave velocities were found to decrease with hydrogen's incremental replacement with coal particles. Whereby, through a theoretical comparison of the heat of combustion as computed from the experimentally derived detonation wave velocities, a linear relationship of the two was shown to exist. Therefore, the heat of combustion has the potential to describe an operational limit to sustaining a detonation wave.

On The Vibration Spectrum Analysis of Planar Mechanisms.(Dept.M)

The paper presents a method for the determination of the vibration Spectra of planar mechanisms with arbitrary number of links, which are paired by arbitrary kinds of joints including clearanced turning joints. The mechanism frames may be supported with an arbitrary number of springs and dashpots having arbitrary locations. The equations of motion of the mechanism frame are formulated and solved numerically together with the equations of motion of the links using Runge-Kutta-Jill method. In doing so, and with the aid of Fast Fourier Transform Algorithm, the frequency spectra of the frame in horizontal, vertical, and angular directions are obtained. The mathematical model presented may be considered as a basis to construct a computer program which can provide the vibration spectra of any planar mechanism with arbitrary number and locations of clearanced joints just by feeding its mechanism matrix with its data into the computer program.