Two-dimensional Fast Fourier Transform Research Articles

Aanalytical calculation of rotor losses in high-speed permanent magnet synchronous motor at different load conditions

In this paper, the rotor losses in the high-speed permanent magnet (PM) synchronous motor are discussed. In particular, the influence of different load conditions is highlighted in developed PM synchronous motor. On the basis of analytical field analysis, two-dimensional fast Fourier transformation, and the Poynting theorem, the flux harmonics and rotor losses are predicted and validated by finite element method. Moreover, the difference of rotor losses between the motor with rated- and overload conditions is made quantitatively clear in this work.

Anisotropy in structure and mechanical properties of perpendicular-laid nonwovens

This study addresses the three-dimensional structure and mechanical properties of perpendicular-laid nonwovens produced from PET and PET/PE bicomponent fibers. Two different web-forming methods, air folding and mechanical folding systems, have been employed to produce the perpendicular-laid nonwovens. It is proved that both systems can produce well-developed perpendicular-laid structures. A comparison has been made between mechanical properties and fiber orientation distribution function (ODF). ODFs at three faces of nonwovens were analyzed by image analysis techniques using the two-dimensional Fast Fourier Transform (2D FFT). Further, mechanical measurements were performed at various azimuthal directions to investigate the related mechanical responses in three-dimensions.

Non-Gaussian Random Wave Simulation by Two-Dimensional Fourier Transform and Linear Oscillator Response to Morison Force

The one-dimensional fast Fourier transform (FFT) has been applied extensively to simulate Gaussian random wave elevations and water particle kinematics. The actual sea elevations/kinematics exhibit non-Gaussian characteristics that can be represented mathematically by a second-order random wave theory. The elevations/kinematics formulations contain frequency sum and difference terms that usually lead to expensive time-domain dynamic analyses of offshore structural responses. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency-difference terms, inverse FFT and forward FFT are implemented, respectively, across the two dimensions of the wave interaction matrix. Given specified wave conditions, the statistics of simulated elevations/kinematics compare well with not only the empirical fits but also the analytical solutions based on a modified eigenvalue/eigenvector approach, while the computational effort of simulation is very economical. In addition, the stochastic analyses in both time domain and frequency domain show that, attributable to the second-order nonlinear wave effects, the near-surface Morison force and induced linear oscillator response are more non-Gaussian than those subjected to Gaussian random waves.

A Coarse-Grain Hierarchical Technique for 2-Dimensional FFT on Configurable Parallel Computers

FPGAs (Field-Programmable Gate Arrays) have been widely used as coprocessors to boost the performance of data-intensive applications [1], [2]. However, there are several challenges to further boost FPGA performance: the communication overhead between the host workstation and the FPGAs can be substantial; large-scale applications cannot fit in a single FPGA because of its limited capacity; mapping an application algorithm to FPGAs still remains a daunting job in configurable system design. To circumvent these problems, we propose in this paper the FPGA-based Hierarchical-SIMD (H-SIMD) machine with its codesign of the Pyramidal Instruction Set Architecture (PISA). PISA comprises high-level instructions implemented as FPGA functions of coarse-grain SIMD (Single-Instruction, Multiple-Data) tasks to facilitate ease of program development, code portability across different H-SIMD implementations and high performance. We assume a multi-FPGA board where each FPGA is configured as a separate SIMD machine. Multiple FPGA chips can work in unison at a higher SIMD level, if needed, controlled by the host. Additionally, by using a memory switching scheme and the high-level PISA to partition applications into coarse-grain tasks, host-FPGA communication overheads can be hidden. We enlist the two-dimensional Fast Fourier Transform (2D FFT) to test the effectiveness of H-SIMD. The test results show sustained high performance for this problem. The H-SIMD machine even outperforms a Xeon processor for this problem.

Pattern Recognition for Classification and Matching of Car Tires

Abstract Commercial databases containing images of tire tread patterns are currently used by product designers, forensic specialists and product application personnel to identify whether a given tread pattern matches an existing tire. Currently, this pattern matching process is almost entirely manual, requiring visual searches of extensive libraries of tire tread patterns. Our work explores a first step toward automating this pattern matching process by building on feature analysis techniques from computer vision and image processing to develop a new method for extracting and classifying features from tire tread patterns and automatically locating candidate matches from a database of existing tread pattern images. Our method begins with a selection of tire tread images obtained from multiple sources (including manufacturers' literature, Web site images, and Tire Guides, Inc.), which are preprocessed and normalized using Two-Dimensional Fast Fourier Transforms (2D-FFT). The results of this preprocessing are feature-rich images that are further analyzed using feature extraction algorithms drawn from research in computer vision. A new, feature extraction algorithm is developed based on the geometry of the 2D-FFT images of the tire. The resulting FFT-based analysis allows independent classification of the tire images along two dimensions, specifically by separating “rib” and “lug” features of the tread pattern. Dimensionality of (0,0) indicates a smooth treaded tire with no pattern; dimensionality of (1,0) and (0,1) are purely rib and lug tires; and dimensionality of (1,1) is an all-season pattern. This analysis technique allows a candidate tire to be classified according to the features of its tread pattern, and other tires with similar features and tread pattern classifications can be automatically retrieved from the database.

Fast FFT based GPS satellite acquisition methods

A Global Positioning System (GPS) receiver uses satellite signals to determine position, velocity, and timing information. Measurements are obtained by synchronising the locally generated signal in the receiver with the signals received. A synchronisation procedure called acquisition adjusts the code phases of the incoming signal and the locally generated pseudo-random replica sequence of the corresponding satellite to a small timing offset and finds the residual frequency modulation after carrier wipe-off. New fast techniques for acquiring signals indoors in conditions that require a significant number of computations are presented. In this work many arithmetic operations are shared when exploring different search options by using fast Fourier transform (FFT) and a technique based on the frequency domain replica shifting. It is shown that FFT can be used for the joint processing of multiple (code-phase/frequency) search options in both dimensions at once. With a slight degradation in performance, the algorithm has a modified version that implements the technique using two-dimensional FFT. Several possible processing schemes are presented. Moreover, the presented shifting replica approach in the frequency domain can significantly reduce computational complexity by jointly acquiring different satellites.

Analysis of Shielded Coplanar Structures Type Transmission Lines Using Iterative Method: Application to Cpw and Finline Step Discontinuity

An efficient iterative method based on the concept of waves is presented to determine the characteristics of coplanar waveguide (CPW) and the finline step discontinuity. A two-dimensional fast Fourier transformation algorithm is introduced to simplify calculations and accelerate the convergence with reduced central processing unit time. The general formulation and implementation procedure of the method are described. The numerical results are compared with the published data obtained by other methods. This comparison shows a good agreement.

Nanofractal Analysis of Material Surfaces Using Atomic Force Microscopy

The surface structures of four materials (a pure aluminum sheet, an aluminum alloy sash, a thickness gauge and a magnetic tape) are observed on the nanometer scale by atomic force microscopy (AFM) and analyzed by one-dimensional fractal analyses. It is confirmed for all the surfaces that they have a self-affined fractal property under a resolution of 1 nm. The two-dimensional fast Fourier transformation (2D-FFT) analysis is also applied to these surfaces and their characteristics are clarified. The power spectrum model for surface simulation is proposed and its validity is confirmed by experimental results. A method for simulating the surface structure of any materials is presented, and its validity is shown on some materials whether in-plane isotropic or anisotropic. A computer-aided engineering (CAE) system composed of 2D-FFT and inverse FFT (IFFT) for quantitative estimation of surface nanostructures is advanced and applied to various surface problems. It enables the mass data of a material surface to compress into only three parameters. This compressed information includes all surface waviness, complexity, irregularity, roughness and in-plane anisotropic properties.

Efficient Analysis of Via Hole Grounds by Using the Iterative Method

The via hole ground has many applications in the synthesis of microstrip microwave circuits. Indeed, it can be used for the realization of stub, the parallel insertion of lumped element and the photonic gap structures. This paper presents an extension of the iterative method based on the concept of waves combined with the two-dimensional Fast Fourier Transformation algorithm (F.M.T: Fast Modal Transformation) to analyze microstrip microwave distributed circuits including via hole grounds. The results provided by this method are in good agreement with the data determined by MDS's approach.

A new precise Co-geoid determined by spherical FFT for the Malaysian peninsula

A new gravimetric Co-geoid is produced for the Malaysian peninsula making it one of the most recent contributions to Co-geoid modelling in the region. Several data sources are included for the computations; these include 7447 terrestrial free-air gravity anomalies, 10243 altimeter derived gravity anomalies and 692881 mean digital elevation heights. The EGM96 global geopotential model to degree 40 is used in order to determine the long wavelength effect of the Co-geoid surface. Co-geoid undulations are determined through implementation of the remove-restore technique by combining the above-mentioned data sets with the geopotential model in a specific manner. The computations have been done using a two-dimensional spherical Fast Fourier Transform (FFT) with 100% zero padding. Terrain corrections are also computed using the FFT method and applied in the remove-restore technique. The absolute accuracy estimates are given for the Co-geoid undulations using 95 GPS control stations co-located with third order levelling. The comparisons show that using the Wong and Gore (1969) modification of Stoke’s function for the long wave length effect using EGM96 up to degree/order 360 removed, and the modified Stoke’s function with L= 40 and a spherical cap radius of 1.6°, with data padding for areas of no gravity data produces a Co-geoid which gives a bias of 0.378 meters and a standard deviation of ±0.277 meters respectively. Where no data padding is used a Co-geoid is produced which gives a bias of 0.439 meters and a standard deviation of ±0.284 meters respectively, thus showing the improvement of the Co-geoid solution through the data padding.

Single Mode Extraction from Multiple Modes of Lamb Wave and Its Application to Defect Detection

Lamb waves generally consist of many dispersive modes, which makes mode identification difficult. This study describes the extraction of a single mode from multiple modes. The single mode extraction is based on two-dimensional Fast Fourier Transform (2D FFT) in time and space, signal filtering, and 2D inverse FFT. An air-coupled ultrasonic technique was adopted for non-contact fast measurements. Using this technique, the A0 and S0 mode were clearly detected in preliminary tests of intact plates. Furthermore, multiple reflections of the A0 mode, which were shown only in the computer simulation, were experimentally confirmed in reflection tests of plates with a rectangular notch. In the reflection tests, two reflected waves were extracted in the intervals corresponding to notch widths.

Spontaneous Formation of Regular Defect Array in Water-in-Cholesteric Liquid Crystal Emulsions

We have investigated the spontaneous formation of the regular quadrilateral defect array in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. We observe nucleation of numerous point defects, in the cholesteric planar texture immediately after termination of shear to the emulsion, which leads to the formation of the regular defect array. We examined the temporal changes in density, size, and the positional correlation of point defects through the formation process of the defect array by means of two-dimensional fast Fourier transformation (2D FFT) image analysis. Two distinct stages were identified in the formation process; the early stage is the nucleation and growth process of point defects, and the late stage is the rearrangement process of point defects to the regular defect array. Water droplets destabilize the arrangement of cholesteric helix, which induces the transition from the shear-induced planar alignment to the homeotropic orientation.

Fast Fourier Transform and Filtered Image Analyses of Fiber Orientation in OSB

The objective of this paper is to investigate the relationship between resolution of images and measurement of fiber orientation in oriented strand board with the ultimate aim of optimising the fiber orientation and quality of the manufactured product. An important consideration has been the capture of images from a distance of 2 meters corresponding to conditions on an OSB production line. In this paper, Filtered Image Analysis (FIA) was used to measure fiber orientation at different resolutions, and results were compared with those for strand grid models. These grid models were adopted to investigate how the FIA technique measures orientation. A two-dimensional Fast Fourier Transform (FFT) analysis was also investigated as a comparative method for measuring fiber orientation. The following conclusions can be drawn: the FFT analysis measures the periodicity of lines and indicates the orientation of lines. The FIA measures the orientation of zones surrounded by lines and shows the orientation of the zones. Hence, the FFT analysis and the FIA analysis measure orientation differently. Both methods are able to measure the fiber orientation of the OSB from a high resolution image. In addition the FIA technique could also measure the fiber orientation from low-resolution images and from a distance of 2 meters. In conclusion, whilst the FFT method is able to analyse high resolution images successfully, the FIA method is superior for analysing low resolution images and the orientation of OSB strands under production condition.

DETERMINATION OF CRYSTALLINE LAMELLAR THICKNESS IN POLY(ETHYLENE TEREPHTHALATE) USING SMALL-ANGLE X-RAY SCATTERING AND TRANSMISSION ELECTRON MICROSCOPY1*

The crystalline lamellar thickness of semicrystalline poly(ethylene terephthalate) (PET) was evaluated using small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) techniques. Both SAXS onedimensional (1D) correlation function and interface distribution function analyses were utilized to determine the crystalline lamellar thickness. The two-dimensional fast Fourier transformation (2D-FFT) of the TEM image and the Gaussian-like lamellar thickness distribution determined from the TEM image were also performed. Results indicate that the larger value of the two correlation lengths calculated from the SAXS analysis should be assigned to the crystalline lamellar thickness in PET. Discussions and comparison among different methods for characterizing the lamellar thickness of semicrystalline polymers are made. *Dedicated to Prof. Francisco J. Baltá Calleja on the occasion of his 65th birthday.

Spatial alignment evolution of self-assembled In 0.4Ga 0.6As island arrays grown on GaAs (3 1 1)B surface by atomic hydrogen-assisted molecular beam epitaxy

Self-assembled In 0.4Ga 0.6As island arrays have been grown on (3 1 1)B GaAs substrates by using atomic hydrogen-assisted molecular beam epitaxy (H-MBE). The evolution process of surface morphology with deposition has been analyzed by atomic force microscopy (AFM) and the development of lateral ordering has been highlighted by two-dimensional fast Fourier transformation (2DFFT) analysis of the AFM images. It is revealed that the InGaAs islands are arranged in nearly perfect two-dimensional (2D) square-like lattice with two sides parallel to [0 1 −1] and [−2 3 3] azimuths. Such an alignment of islands is coincident with the anisotropy of bulk elastic modulus of the GaAs (3 1 1)B substrate.

Time-dependent oscillations of tunneling current on partially oxidized Si (111) surfaces

Clean and partially oxidized Si (111) surfaces were investigated by scanning tunneling microscopy and spectroscopy (STM/STS). In contrast to STS spectra measured on clean Si surfaces, time-dependent periodic oscillations of tunneling current were detected on partially oxidized Si surfaces. The STM current images of the clean Si surface with atomic resolution and the partially oxidized Si surfaces were analyzed by two-dimensional fast Fourier transformation (2D-FFT). The oscillation frequencies determined by STS and Fourier analysis are roughly multiples of a basic frequency of 30 Hz. The oscillations disappear at small tip–sample distance.

Indian Ocean Rossby waves observed in TOPEX/POSEIDON altimeter data and in model simulations

Analysis of 3 years of TOPEX/POSEIDON (T/P) altimeter data in the Indian Ocean revealed discrepancies between observed and theoretical Rossby wave phase speeds. Rossby waves were observed at all latitudes using Hovmoller diagrams or longitude/time plots; their phase speeds were computed using twodimensional Fast Fourier Transforms (FFTs). Complex Principal Component Analysis (CPCA) was applied to detect travelling waves. A simple wind-driven layer model was implemented for this region and forced with the ERS-1 scatterometer winds, sampled over the same period as the T/P data, to demonstrate that these winds account for much of the observed Rossby wave activity.

Analysis of a microstrip antenna with fractal multilayer substrate using iterative method

A microstrip antenna with fractal multilayer substrates is studied by using an iterative method based on the concept of waves. A two-dimensional fast Fourier transformation algorithm is introduced to simplify calculations and accelerate the convergence with reduced central processing unit time. Good agreements are obtained with already published results on fractal antenna. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 212–218, 2001.

Real-time image reconstruction for spiral MRI using fixed-point calculation.

Because spiral magnetic resonance imaging (MRI) is more robust to motion artifacts than echo planar imaging (EPI), spiral imaging method is more suitable in real-time imaging applications where dynamic processes are to be observed. The major hurdle to use spiral imaging method in real-time applications is its slow reconstruction speed. Since spiral trajectories do not sample data on rectilinear grids, raw data must be regridded before inverse fast Fourier transform (FFT). At present, the computational cost for the spiral reconstruction algorithm is still too high and it is not fast enough to achieve the minimum speed requirement of 20 frames/s for real-time imaging applications. In this paper, we propose to replace floating-point calculations with fixed-point calculations in the reconstruction algorithm to remove the computational bottlenecks. To overcome the quantization and round-off errors introduced by fixed-point calculations, we devise a method to find the optimal precision for the fixed-point representation. Adding with a highly efficient vector-radix two-dimensional (2-D) FFT algorithm and modifications to speed up the gridding convolution, we have cut the reconstruction time by 42% and achieved real-time reconstruction at 30 frames/s for 128 x 128 matrices on low-cost PC's.

Objective Evaluation of Wrinkle Recovery

A device for wrinkle recovery measurements involves the installation of a laser sensor. The shapes of fabric wrinkles are described by magnitude and sharpness using power spectra obtained from two-dimensional fast Fourier transformation and the distribution of fabric surface angles obtained from spline interpolation and vector operation. For the objective evaluation of wrinkle recovery, artificial neural networks are used rather than the AATCC subjective evaluation method. Five kinds of input patterns are categorized from the characterizations of wrinkle shape, and these are supplied to the neural networks for evaluation. Objective results from the neural networks are compared with subjective ones from human experts. The relationship is good with a correction coefficient of 0.95, but wrinkle rank depends somewhat on the color or pattern of the fabric.