Showing papers on "Fast Fourier transform published in 2001"

Advances in sensitivity encoding with arbitrary k-space trajectories.

Abstract: New, efficient reconstruction procedures are proposed for sensitivity encoding (SENSE) with arbitrary k-space trajectories. The presented methods combine gridding principles with so-called conjugate-gradient iteration. In this fashion, the bulk of the work of reconstruction can be performed by fast Fourier transform (FFT), reducing the complexity of data processing to the same order of magnitude as in conventional gridding reconstruction. Using the proposed method, SENSE becomes practical with nonstandard k-space trajectories, enabling considerable scan time reduction with respect to mere gradient encoding. This is illustrated by imaging simulations with spiral, radial, and random k-space patterns. Simulations were also used for investigating the convergence behavior of the proposed algorithm and its dependence on the factor by which gradient encoding is reduced. The in vivo feasibility of non-Cartesian SENSE imaging with iterative reconstruction is demonstrated by examples of brain and cardiac imaging using spiral trajectories. In brain imaging with six receiver coils, the number of spiral interleaves was reduced by factors ranging from 2 to 6. In cardiac real-time imaging with four coils, spiral SENSE permitted reducing the scan time per image from 112 ms to 56 ms, thus doubling the frame-rate. Magn Reson Med 46:638–651, 2001. © 2001 Wiley-Liss, Inc.

A computational scheme for linear and non-linear composites with arbitrary phase contrast

Abstract: A numerical method making use of fast Fourier transforms has been proposed in Moulinec and Suquet (1994, 1998) to investigate the effective properties of linear and non-linear composites. This method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases. Composites with high contrast (typically above 104) or infinite contrast (those containing voids or rigid inclusions or highly non-linear materials) cannot be handled by the method. This paper presents two modified schemes. The first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in Eyre and Milton (1999). Its rate of convergence varies as the square root of the contrast. The second scheme, adequate for composites with infinite contrast, is based on an augmented Lagrangian method. The resulting saddle-point problem involves three steps. The first step consists of solving a linear elastic problem, using the fast Fourier transform method. In the second step, a non-linear problem is solved at each individual point in the volume element. The third step consists of updating the Lagrange multiplier. Applications of this scheme to rigidly reinforced and to voided composites are shown. Copyright © 2001 John Wiley & Sons, Ltd.

Structured Matrices and Polynomials: Unified Superfast Algorithms

Abstract: Structure matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms.

Wavelet Analysis and Envelope Detection For Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities

Abstract: The components which often fail in a rolling element bearing are the outer-race, the inner-race, the rollers, and the cage. Such failures generate a series of impact vibrations in short time intervals, which occur at Bearing Characteristic Frequencies (BCF). Since BCF contain very little energy, and are usually overwhelmed by noise and higher levels of macro-structural vibrations, they are difficult to find in their frequency spectra when using the common technique of Fast Fourier Transforms (FFT). Therefore, Envelope Detection (ED) is always used with FFT to identify faults occurring at the BCF. However, the computation of ED is complicated, and requires expensive equipment and experienced operators to process. This, coupled with the incapacity of FFT to detect nonstationary signals, makes wavelet analysis a popular alternative for machine fault diagnosis. Wavelet analysis provides multi-resolution in time-frequency distribution for easier detection of abnormal vibration signals. From the results of extensive experiments performed in a series of motor-pump driven systems, the methods of wavelet analysis and FFT with ED are proven to be efficient in detecting some types of bearing faults. Since wavelet analysis can detect both periodic and nonperiodic signals, it allows the machine operator to more easily detect the remaining types of bearing faults which are impossible by the method of FFT with ED. Hence, wavelet analysis is a better fault diagnostic tool for the practice in maintenance.

Fast Fourier transforms for nonequispaced data: a tutorial

Abstract: In this chapter we consider approximativemethods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particularwe are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFTiaalgorithms with respect to roundoff errors and applyNDFTalgorithms for the fast computation of Besseltransforms.

The algorithm of interpolating windowed FFT for harmonic analysis of electric power system

Abstract: The fast Fourier transform (FFT) cannot be directly used in the harmonic analysis of an electric power system because of its higher errors, especially the phase error. This paper discusses the leakage phenomenon of FFT and presents a new amending algorithm, poly-item cosine window interpolation, which is based on the interpolating algorithm proposed by V. Jain and T Grandke. This new algorithm improves the accuracy of the FFT, so it can be applied to the precision analysis for electrical harmonics. The simulation result shows that applying different windows has different effects on the accuracy, and the Blackman-Harris window has the highest accuracy.

Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT

Abstract: The concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. We develop efficient algorithms for QFT, QCV, and quaternion correlation. The conventional complex two-dimensional (2-D) Fourier transform (FT) is used to implement these quaternion operations very efficiently. With these algorithms, we only need two complex 2-D FTs to implement a QFT, six complex 2-D FTs to implement a one-side QCV or a quaternion correlation and 12 complex 2-D FTs to implement a two-side QCV, and the efficiency of these quaternion operations is much improved. Meanwhile, we also discuss two additional topics. The first one is about how to use QFT and QCV for quaternion linear time-invariant (QLTI) system analysis. This topic is important for quaternion filter design and color image processing. Besides, we also develop the spectrum-product QCV. It is an improvement of the conventional form of QCV. For any arbitrary input functions, it always corresponds to the product operation in the frequency domain. It is very useful for quaternion filter design.

Theory of synthetic aperture radar imaging of a moving target

Abstract: Two novel image processing techniques have been developed to refocus a moving target image from its smeared response in the synthetic aperture radar (SAR) image which is focused on the stationary ground. Both approaches may be implemented with efficient fast Fourier transform (FFT) routines to process the Fourier spatial spectrum of the image data. The first approach utilizes a matched target filter that is derived from the signal history along the range-Doppler migration path mapped onto the SAR image from the moving target trajectory in real space. The coherent spatial filter is specified by the apparent target range in the image and the magnitude of the relative target-to-radar velocity. The second approach eliminates the range-dependence by reconstructing the moving target image from a spectral function that is obtained from the SAR image data spectrum via a spatial frequency coordinate transformation.

Analysis of low-complexity windowed DFT-based MMSE channel estimator for OFDM systems

Abstract: Low-complexity windowed discrete Fourier transform (DFT)-based minimum mean square error (MMSE) channel estimators are proposed and analyzed for both the interpolation and noninterpolation cases for orthogonal frequency-division multiplexing (OFDM) mobile communications systems. In the proposed method, the frequency domain data windowing is used to reduce the aliasing errors for the interpolation case and get better noise filtering performance for the noninterpolation case. The time domain MMSE weighting is also used to suppress the channel noise for both cases. Moreover, the optimal generalized Hanning window shape is searched to minimize the channel estimation mean square error (MSE). Analysis and simulation results show that the proposed method performance is close to the optimal MMSE estimator and is much better than the direct DFT-based estimator for both cases. Compared with the optimal MMSE estimator, however, the computation load of the proposed method can be significantly reduced because the IDFT/DFT transforms can be implemented with the fast algorithms IFFT/FFT.

A multicarrier system based on the fractional Fourier transform for time-frequency-selective channels

Abstract: Traditional multicarrier techniques perform a frequency-domain decomposition of a channel characterized by frequency-selective distortion in a plurality of subchannels that are affected by frequency flat distortion. The distortion in each independent subchannel can then be easily compensated by simple gain and phase adjustments. Typically, digital Fourier transform schemes make the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is time-frequency-selective, as it usually happens in the rapidly fading wireless channel, this traditional methodology fails. Since the channel frequency response is rapidly time-varying, the optimal transmission/reception methodology should be able to process nonstationary signals. In other words, the subchannel carrier frequencies should be time-varying and ideally decompose the frequency distortion of the channel perfectly at any instant in time. However, this ideally optimal approach presents significant challenges both in terms of conceptual and computational complexity. The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of nonstationary signals. We propose in fact the use of a multicarrier system that employs orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis. The significance of the methodology relies on the important practical consideration that analysis/synthesis methods of the fractional Fourier type can be implemented with a complexity that is equivalent to the traditional fast Fourier transform.

Block Acquisition of Weak GPS Signals in a Software Receiver

Abstract: Block algorithms have been developed to acquire very weak Global Positioning System (GPS) coarse/acquisition (C/A) signals in a software receiver. These algorithms are being developed in order to enable the use of weak GPS signals in applications such as geostationary orbit determination. The algorithms average signals over multiple GPS data bits after a squaring operation that removes the bits’ signs. Methods have been developed to ensure that the pre-squaring summation intervals do not contain data bit transitions. The algorithms make judicious use of Fast Fourier Transform (FFT) and inverse FFT (IFFT) techniques in order to speed up operations. Signals have been successfully acquired from 4 seconds worth of bitgrabbed data with signal-to-noise ratios (SNRs) as low as 21 dB Hz.

A deterministic least-squares approach to space-time adaptive processing (STAP)

Abstract: A direct data domain (D/sup 3/) least-squares space-time adaptive processing (STAP) approach is presented for adaptively enhancing signals in a nonhomogeneous environment. The nonhomogeneous environment may consist of nonstationary clutter and could include blinking jammers. The D/sup 3/ approach is applied to data collected by an antenna array utilizing space and in time (Doppler) diversity. Conventional STAP generally utilizes statistical methodologies based on estimating a covariance matrix of the interference using data from secondary range cells. As the results are derived from ensemble averages, one filter (optimum in a probabilistic sense) is obtained for the operational environment, assumed to be wide sense stationary. However for highly transient and inhomogeneous environments the conventional statistical methodology is difficult to apply. Hence, the D/sup 3/ method is presented as it analyzes the data in space and time over each range cell separately. The D/sup 3/ method is deterministic in approach. From an operational standpoint, an optimum method could be a combination of these two diverse methodologies. This paper represents several new D/sup 3/ approaches. One is based on the computation of a generalized eigenvalue for the signal strength and the others are based on the solution of a set of block Hankel matrix equations. Since the matrix of the system of equations to be solved has a block Hankel structure, the conjugate gradient method and the fast Fourier transform (FFT) can be utilized for efficient solution of the adaptive problem. Illustrative examples presented in this paper use measured data from the multichannel airborne radar measurements (MCARM) database to detect a Sabreliner in the presence of urban, land, and sea clutter. An added advantage for the D/sup 3/ method in solving real-life problems is that simultaneously many realizations can be obtained for the same solution for the signal of interest (SOI). The degree of variability amongst the different results can provide a confidence level of the processed results. The D/sup 3/ method may also be used for mobile communications.

Spectral subtraction using reduced delay convolution and adaptive averaging

Abstract: In hands-free speech communication, the signal-to-noise ratio (SNR) is often poor, which makes it difficult to have a relaxed conversation. By using noise suppression, the conversation quality can be improved. This paper describes a noise suppression algorithm based on spectral subtraction. The method employs a noise and speech-dependent gain function for each frequency component. Proper measures have been taken to obtain a corresponding causal filter and also to ensure that the circular convolution originating from fast Fourier transform (FFT) filtering yields a truly linear filtering. A novel method that uses spectrum-dependent adaptive averaging to decrease the variance of the gain function is also presented. The results show a 10-dB background noise reduction for all input SNR situations tested in the range -6 to 16 dB, as well as improvement in speech quality and reduction of noise artifacts as compared with conventional spectral subtraction methods.

Comparative study of joint-detection techniques for TD-CDMA based mobile radio systems

Abstract: Third-generation mobile radio systems use time division-code division multiple access (TD-CDMA) in their time division duplex (TDD) mode. Due to the time division multiple access (TDMA) component of TD-CDMA, joint (or multi-user) detection techniques can be implemented with a reasonable complexity. Therefore, joint-detection will already be implemented in the first phase of the system deployment to eliminate the intracell interference. In a TD-CDMA mobile radio system, joint-detection is performed by solving a least squares problem, where the system matrix has a block-Sylvester structure. We present and compare several techniques that reduce the computational complexity of the joint-detection task even further by exploiting this block-Sylvester structure and by incorporating different approximations. These techniques are based on the Cholesky factorization, the Levinson algorithm, the Schur algorithm, and on Fourier techniques, respectively. The focus of this paper is on Fourier techniques since they have the smallest computational complexity and achieve the same performance as the joint-detection algorithm that does not use any approximations. Similar to the well-known implementation of fast convolutions, the resulting Fourier-based joint-detection scheme also uses a sequence of fast Fourier transforms (FFTs) and overlapping. It is well suited for the implementation on parallel hardware architectures.

Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method

Abstract: An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm.

Simulation of stochastic wind velocity field on long-span bridges

Abstract: An improved algorithm is introduced in this paper for digital simulation of the stochastic wind velocity field on long-span bridges, when the cross-spectral density matrix of the field is given. The target wind velocity field is assumed to be a one-dimensional, multivariate, homogeneous stochastic process. The basic method of simulation used is the spectral representation method. It is improved by explicitly expressing Cholesky's decomposition of the cross-spectral density matrix in the form of algebraic formulas, then cutting off as many as possible of the cosine terms, so long as the accuracy of results is not affected. The fast Fourier transform technique is used to enhance the efficiency of computation. A numerical example of simulation for buffeting analysis is included in this paper to illustrate the improved method introduced. It is demonstrated that deviations between the simulated correlation functions and the target are sufficiently small and that the simulated power spectra are close to the target.

Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation

Abstract: The finite-difference time domain (FDTD) technique and the Pade approximation with Baker's algorithm are used to calculate the mode frequencies and quality factors of cavities. Comparing with the fast Fourier transformation/Pade method, we find that the Pade approximation and the Baker's algorithm can obtain exact resonant frequencies and quality factors based on a much shorter time record of the FDTD output.

A fast method for fully nonlinear water-wave computations

Abstract: A fast computational method for fully nonlinear non-overturning water waves is derived in two and three dimensions. A corresponding time-stepping scheme is developed in the two-dimensional case. The essential part of the method is a fast converging iterative solution procedure of the Laplace equation. One part of the solution is obtained by fast Fourier transform, while another part is highly nonlinear and consists of integrals with kernels that decay quickly in space. The number of operations required is asymptotically O(N logN), where N is the number of nodes at the free surface. While any accuracy of the computations is achieved by a continued iteration of the equations, one iteration is found to be sucient for practical computations, while maintaining high accuracy. The resulting explicit approximation of the scheme is tested in two versions. Simulations of nonlinear wave elds with wave slope even up to about unity compare very well with reference computations. The numerical scheme is formulated in such a way that aliasing terms are partially or completely avoided.

Fourier-transform method of phase-shift determination

Abstract: A new phase-shifting interferometry analysis technique has been developed to overcome the errors introduced by nonlinear, irregular, or unknown phase-step increments. In the presence of a spatial carrier frequency, by observation of the phase of the first-order maximum in the Fourier domain, the global phase-step positions can be measured, phase-shifting elements can be calibrated, and the accuracy of phase-shifting analysis can be improved. Furthermore, reliance on the calibration accuracy of transducers used in phase-shifting interferometry can be reduced; and phase-retrieval errors (e.g., fringe print-through) introduced by uncalibrated fluctuations in the phase-shifting phase increments can be alleviated. The method operates deterministically and does not rely on iterative global error minimization. Relative to other techniques, the number of recorded interferograms required for analysis can be reduced.

Power system harmonics estimation using linear least squares method and SVD

Abstract: The paper examines singular value decomposition (SVD) for the estimation of harmonics in signals in the presence of high noise. The proposed approach results in a linear least squares method. The methods developed for locating the frequencies as closely spaced sinusoidal signals are appropriate tools for the investigation of power system signals containing harmonics and interharmonics differing significantly in their multiplicity. The SVD approach is a numerical algorithm to calculate the linear least squares solution. The methods can also be applied for frequency estimation of heavy distorted periodical signals. To investigate the methods several experiments have been performed using simulated signals and the waveforms of a frequency converter current. For comparison, similar experiments have been repeated using the FFT with the same number of samples and sampling period. The comparison has proved the superiority of SVD for signals buried in the noise. However, the SVD computation is much more complex than FFT and requires more extensive mathematical manipulations.

Real-time location of multiple time-varying strain disturbances, acting over a 40-km fiber section, using a novel dual-Sagnac interferometer

Abstract: Updated results using a novel sensing architecture based on a Sagnac interferometer are presented and, for the first time, real-time separation and positioning of multiple disturbances has been realized. A 40-km long dual-Sagnac sensor was formed by spectral slicing of light from a single, broad-band erbium-doped-fiber super-luminescent source and wavelength division multiplexed (WDM) routing around the loop to form an inherently low loss system. Independent active phase biasing of each Sagnac was employed, allowing the use of a single optical detector. The effects of residual optical cross talk between the two Sagnacs has been accurately modeled, allowing resulting errors to be corrected. The new system has capability for narrow-band fast Fourier transform (FFT) analysis of detected disturbance signals, and hence their separation in the frequency domain. For audio-frequency excitation, an average positional resolution of 100 m over a 40-km length was achieved with a postdetection signal processing bandwidth of 8 Hz.

Multicomponent gas mixture analysis using a single tin oxide sensor and dynamic pattern recognition

Abstract: A new method, which is based on the discrete wavelet transform, is presented for extracting important features from the response transients of a micromachined, tin oxide-based gas sensor. It is shown that two components in a mixture can be simultaneously and accurately quantified by processing the response dynamics of a single sensor operated in a temperature-modulated mode. The discrete wavelet transform outperforms the fast Fourier transform (classical approach) because it is more appropriate for the non- linear frequency-time problem encountered here.

Surface scattering in three dimensions: an accelerated high-order solver

Abstract: We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in threedimensional space. This algorithm evaluates scattered fields through fast, highorder, ac...

An extended split-radix FFT algorithm

Abstract: An extended split-radix fast Fourier transform (FFT) algorithm is proposed. The extended split-radix FFT algorithm has the same asymptotic arithmetic complexity as the conventional split-radix FFT algorithm. Moreover, this algorithm has the advantage of fewer loads and stores than either the conventional split-radix FFT algorithm or the radix-4 FFT algorithm.

Radar target identification using one-dimensional scattering centres

Abstract: Identification concerning different types of radar targets can be achieved by using various radar signatures, such as one-dimensional (1-D) range profiles, 2-D radar images, and 1-D or 2-D scattering centres on a target. To solve the target identification problem, the authors utilise 1-D scattering centres, which correspond to the highest peaks in the 1-D range profile. The proposed approach obtains scale and translational-invariant features based on the central moments from the distribution of the 1-D scattering centres on the target; these 1-D scattering centres can be extracted from various techniques such as the inverse fast Fourier transform (IFFT), fast root-multiple signal classification (fast root-MUSIC), total least squares-Prony (TLS-Prony), generalised eigenvalues utilising signal subspace eigenvectors (GEESE), and the matrix-pencil (MP) algorithm. The information redundancy contained in these features, as well as their dimensions, are further reduced via the Karhunen-Loeve transform, followed by adequate scaling of the computed central moments. The resulting small dimensional and redundancy-free feature vectors are classified using the Bayes classifier. Finally, this new strategy for radar target identification is demonstrated with data measured in the compact range facility, and the above five different techniques for 1-D scattering centre extraction are compared and investigated in the context of target identification.

A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns.

Abstract: A new method of estimating the phase-shift between interferograms is introduced. The method is based on a recently introduced two-dimensional Fourier-Hilbert demodulation technique. Three or more interferogram frames in an arbitrary sequence are required. The first stage of the algorithm calculates frame differences to remove the fringe pattern offset; allowing increased fringe modulation. The second stage is spatial demodulation to estimate the analytic image for each frame difference. The third stage robustly estimates the inter-frame phase-shifts and then uses the generalised phase-shifting algorithm of Lai and Yatagai to extract the offset, the modulation and the phase exactly. Initial simulations of the method indicate that high accuracy phase estimates are obtainable even in the presence of closed or discontinuous fringe patterns.

Three‐dimensional weak‐form conjugate‐ and biconjugate‐gradient FFT methods for volume integral equations

Abstract: A large-scale three-dimensional volume integral equation solution for electromagnetic radiation and scattering problems remains a great challenge in spite of many ongoing research efforts. The conventional method of moments, although accurate and flexible, is limited to small-scale problems because of its large requirement of computer memory and computation time. In this paper, we develop two fast methods, the weak-form conjugate- and biconjugate-gradient FFT methods, to solve the Fredholm integral equation of the second kind arising from Maxwell's equations in three dimensions. The weak form is a modified version of the Zwamborn–van den Berg formulation, where the singularity is circumvented by employing the weak-form discretization by rooftop vectorial basis and testing functions. Both weak- form CG–FFT and BCG–FFT methods require O(N log2 N) CPU time, and O(N) computer memory, but the latter converges three–six times faster than the CG–FFT method. We validate the numerical results by comparing them with analytical solutions to multilayer spherical media, and with other published results. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 350–356, 2001.