Showing papers on "Fast Fourier transform published in 1995"

Convolution-based interpolation for fast, high-quality rotation of images

Abstract: This paper focuses on the design of fast algorithms for rotating images and preserving high quality. The basis for the approach is a decomposition of a rotation into a sequence of one-dimensional translations. As the accuracy of these operations is critical, we introduce a general theoretical framework that addresses their design and performance. We also investigate the issue of optimality and present an improved least-square formulation of the problem. This approach leads to a separable three-pass implementation of a rotation using one-dimensional convolutions only. We provide explicit filter formulas for several continuous signal models including spline and bandlimited representations. Finally, we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm. Our results indicate that the present algorithm in its higher-order versions outperforms all standard high-accuracy methods of which we are aware, both in terms of speed and quality. Its computational complexity increases linearly with the order of accuracy. The best-quality results are obtained with the sine-based algorithm, which can be implemented using simple one-dimensional FFTs. >

Fluorescence Rejection in Raman Spectroscopy by Shifted-Spectra, Edge Detection, and FFT Filtering Techniques

Abstract: The use of shifted-spectra, first-derivative spectroscopy (or edge detection), and fast Fourier transform filtering techniques for fluorescence rejection in Raman spectra is demonstrated. These techniques take advantage of the fact that Raman signals are very narrow in comparison to fluorescence bands in order to discriminate between the two. None of these techniques require modification of existing instrumentation. Fast Fourier transform filtering and deconvolution techniques also provide a means of improving spectral resolution and the signal-to-noise ratio.

Efficient Convolution without Input/Output Delay

Abstract: A block FFT implementation of convolution is vastly more efficient than the direct-form FIR filter. Unfortunately block processing incurs significant input-output delay, which is undesirable for real-time applications. A hybrid convolution method is proposed, which combines direct-form and block FFT processing. The result is a zero-delay convolver that performs significantly better than direct-form methods

A fast single-chip implementation of 8192 complex point FFT

Abstract: Large-scale single-frequency networks are now being considered in Europe as very promising network topologies to achieve drastic savings in spectrum usage for digital terrestrial television transmission. Such networks are possible using the COFDM system, with large guard intervals (more than 200 /spl mu/s) to absorb long echoes. In order to limit the spectral efficiency loss to about 20%, very long size fast Fourier transforms (up to 8 K complex points) have to be performed in real time for the demodulation of every COFDM symbol (every 1 ms). This paper presents the first VLSI single chip dedicated to the computation of direct or inverse fast Fourier transforms of up to 8192 complex points. Due to its pipelined architecture, it can perform an 8 K FFT every 400 /spl mu/s and a 1 K FFT every 50 /spl mu/s. All the storage is onchip, so that no external memories are required. A new internal result scaling technique, called convergent block floating point, has been introduced in order to minimize the required storage for a given quantization noise, The chip, 1 cm/sup 2/ large with 1.5 million transistors, has been designed in a 3.3 V-0.5 /spl mu/m triple-level metal CMOS process and is fully functional. The 8 K complex FFT function could therefore be introduced in the coming years in digital terrestrial TV receivers at low cost. >

A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems

Abstract: In this paper, an algorithm for computation of the scattered fields from three dimensional inhomogeneous dielectric scatterers is presented. In this method, the Galerkin's testing formulation of an integral equation for 3D electromagnetic (EM) fields is represented by a multi-input and multi-output linear system with known kernels. On a regular grid with rooftop basis functions, the kernels are discretized and accurately evaluated. Furthermore they are represented by Toeplitz matrices which dramatically reduces the storage and computational complexity in solving for the scattered fields. Also, the kernels are independent of the scattering configuration and the incident waves. For a given frequency, they can be evaluated once and for all. The biconjugate gradient (BCG) algorithm combined with fast Fourier transform (FFT) is applied to solve the discrete linear system iteratively. The memory required for this algorithm is of order N, and the computational complexity of the BCG process costs order N log N op...

Fast approximation of self-similar network traffic

Abstract: Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle`s estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.

The CG-FFT method : application of signal processing techniques to electromagnetics

Abstract: Part 1 Introduction to the conjugate gradient fast Fourier transform (CG-FFT) method: brief survey of electromagnetic computational methods CG methods Toeplitz symmetries and the CG-FFT method. Part 2 Fourier transforms: discrete Fourier transform (DFT) continuous Fourier transform (CFT). Part 3 Static problems: formulating a one-dimensional continuous convolutional problem for individual structures discretization of the continuous EPP discretization of periodic problems spectral domain discretization of problems involving individual structures. Part 4 Conjugate gradient algorithms: integral equation formulation of electromagnetic problems the method of moments solution of the integral equation iterative solutions of the integral equation conjugate gradient methods the generalized biconjugate gradient method examples of convergence rates. Part 5 Arbitrary flat conducting plates: formulation of the problem discretization process discretization of the integral equation results for induced current applications to radiation and scattering problems. Part 6 Three-dimensional bodies: discretization process discretization of the integral equation, resolution of the operator, and final results results for induced equivalent currents application to radiation and scattering problems. Part 7 Problems formulated in terms of systems of integral equations: formulation of the continuous SIE discretization of the SIE. Part 8 Metallic surfaces that conform to bodies of revolution: integral equation surfaces that conform to cylinders surfaces that conform to arbitrary BORs. Part 9 Flat periodic structures: direct and reciprocal lattices Floquet's Theorem MPIE formulation for periodic structures discretization process completing the discretization in the spectral domain operational form of the MPIE reflection and transmission coefficients. Part 10 Flat periodic structures in multilayer media: integral equation in the spectral domain discretization process some numerical results and applications. Part 11 Finite-sized conducting patches in multilayer media: formulation of the problem formulation of the equivalent continuous operator equation computation of the windowed Green's function some results for induced currents application to scattering problems application to S-parameter analysis of open microstrip structures. Part 12 Volumetric analysis of 3D bodies that are periodic in one direction: formulation of the continuous operator equation for a VODIPEB formulation of the discrete operator equation computation of convolutional integrals using FFT results.

Random Networks in Configuration Space for Fast Path Planning

Abstract: In the main part of this dissertation we present a new path planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles. This method proceeds according to two phases: a preprocessing phase and a query phase. In the preprocessing phase, a probabilistic network is constructed and stored as a graph whose nodes correspond to collision-free configurations and edges to feasible paths between these configurations. These paths are computed using a fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the network; the network is then searched for a path joining these two nodes. The method is general and easy to implement. Increased efficiency can be achieved by tailoring some of its components (e.g. the local planner) to the considered robots. We apply the method to articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation ($\approx$150 MIPS), after relatively short preprocessing times (a few dozen to a few hundred seconds). In the second part of this dissertation, we present a new method for computing the obstacle map used in motion planning algorithms. The method computes a convolution of the workspace and the robot using the Fast Fourier Transform (FFT). It is particularly promising for workspaces with many and/or complicated obstacles. Furthermore, it is an inherently parallel method that can significantly benefit from existing experience and hardware on the FFT. In the third part of this dissertation, we consider a problem from assembly planning. In assembly planning we are interested in generating feasible sequences of motions that construct a mechanical product from its individual parts. The problem addressed is the following: given a planar assembly of polygons, decide if there is a proper subcollection of them that can be removed as a rigid body without colliding with or disturbing the other parts of the assembly. We prove that this problem is NP-complete. The result extends to several interesting variants of the problem.

A comparison of spectrum estimation techniques for sensorless speed detection in induction machines

Abstract: This paper compares digital spectrum estimation techniques which can be used to extract speed information from rotor slot and eccentricity harmonics contained in the stator current. In previous work, speed-related current harmonics have been shown to improve the performance of existing back-EMF-based sensorless schemes, since these harmonics are parameter independent and exist at virtually any nonzero speed. Digital filtering, however, requires a minimum data sampling time in order to achieve the desired resolution. The contribution of this paper is to determine the optimal method for accurately extracting the speed-related harmonics in the least amount of time. Several digital signal processing algorithms are investigated, including the fast Fourier transform and other traditional methods, as well as parametric techniques which can provide improved spectrum estimation for short data records. Each approach is evaluated on the criteria of accuracy, robustness, and computation time given a short data record.

Extending the Hong-Kung Model to Memory Hierarchies

Abstract: The speed of CPUs is accelerating rapidly, outstripping that of peripheral storage devices and making it increasingly difficult to keep CPUs busy. Consequently multi-level memory hierarchies, scaled to simulate single-level memories, are increasing in importance. In this paper we introduce the Memory Hierarchy Game, a multi-level pebble game that simulates data movement in memory hierarchies in terms of which we study space-time tradeoffs.

Application of autoregressive spectral analysis for ultrasound attenuation estimation: interest in highly attenuating medium

Abstract: The authors deal with the application of parametric spectral analysis for attenuation estimation on the reflected ultrasound signal of biological tissues. A second-order autoregressive (AR2) model, whose parameters are estimated with the Burg algorithm, is used to estimate the center frequency on echo signals and its evolution versus depth. Data simulation of independent A-lines backscattered by a homogeneous medium of scatterers are generated by a computer model with attenuation values ranging from 1 to 5 dB/cmMHz, an ultrasonic frequency of 5 MHz and different pulse durations. The performance of the estimator is evaluated for time windows ranging from 5 to 0.3 /spl mu/s. The comparison is made with the classical short time Fourier analysis using a fast Fourier transform (FFT). It is found that the AR2 model provides a better estimation of attenuation than the Fourier technique: the relative error of attenuation is below 5% for windows between 0.6 to 2.5 /spl mu/s, while the one obtained with the Fourier technique lies between 3 and 16% for the same window sizes. However, the variance of attenuation estimate is the same with the two techniques. These results offer promises for determining attenuation in highly attenuating medium (material or biological tissue) either because of their structure or because high frequencies are used. >

Detection of tool failure in end milling with wavelet transformations and neural networks (WT-NN)

Abstract: Detection of tool failure is very important in automated manufacturing. In this study, tool failure detection was conducted in two steps by using Wavelet Transformations and Neural Networks (WT-NN). In the first step, data were compressed by using wavelet transformations and unnecessary details were eliminated. In the second step, the estimated parameters of the wavelet transformations were classified by using Adaptive Resonance Theory (ART2)-type self-learning neural networks. Wavelet transformations represent transitionary data and complex patterns in a more compact form than time-series methods (frequency and time-domain) by using a family of the most suitable wave forms. Wavelet transformations can also be implemented on parallel processors and require less computations than Fast Fourier Transformation (FFT). The training of ART2-type neural networks is faster than backpropagation-type neural networks and ART2 is capable of updating its experience with the help of an operator while it is monitoring the sensory signals. The proposed approach was tested in over 171 cases and all the presented cases were accurately classified. The proposed system can be easily trained to inspect data during transition and/or any complex cutting conditions. The system will indicate failure instantaneously by creating a new category, thus alerting the operator.

On Cyclic Reduction Applied to a Class of Toeplitz-Like Matrices Arising in Queueing Problems

Abstract: We observe that the cyclic reduction algorithm leaves unchanged the structure of a block Toeplitz matrix in block Hessenberg form. Based on this fact, we devise a fast algorithm for computing the probability invariant vector of stochastic matrices of a wide class of Toeplitz-like matrices arising in queueing problems. We prove that for any block Toeplitz matrix H in block Hessenberg form it is possible to carry out the cyclic reduction algorithm with O(k 3 n + k 2 n log n) arithmetic operations, where k is the size of the blocks and n is the number of blocks in each row and column of H. The probability invariant vector is computed within the same cost. This substantially improves the O(k 3 n 2) arithmetic cost of the known methods based on Gaussian elimination. The algorithm, based on the FFT, is numerically weakly stable. In the case of semi-infinite matrices the cyclic reduction algorithm is rephrased in functional form by means of the concept of generating function and a convergence result is proved.

A FFT-Based Numerical Method for Computing the Mechanical Properties of Composites from Images of their Microstructures

Abstract: The effective properties of composite materials are strongly influenced by the geometry of their microstructures, which can be extremely complex. Most of the numerical simulations known to the authors make use of two- or three-dimensional finite elements analyses which are often time consuming because of the complexity imposed by the requirement of extremely precise description of the reinforcements distribution. A numerical method is presented here that directly uses images of the microstructure - supposed to be periodically repeated - to compute the composite overall properties, as well as the local distribution of stresses and strains, without requiring further geometrical interpretation by the user. The linear elastic problem is examined first. Its analysis is based on the Lippmann-Schwinger’s equation, which is solved iteratively by means of the Green operator of an homogeneous reference medium. Then the method is extended to non-linear problems where the local stress strain relation is given by an incremental relation.

On the fast translation functions for molecular replacement

Abstract: This paper describes the theory and results obtained with the correlation-search technique to solve the translation problem in the molecular-replacement method. The correlation function is expressed in terms of intensities of structure factors and is calculated by fast Fourier transforms.

Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems

Abstract: The integral equations of acoustic and electromagnetic scattering generate large dense systems of linear equations. These systems are efficiently solved with iterative methods where the matrix-vector multiplication is computed using a special fast method, such as the fast Fourier transform or the fast multipole method (FMM). In this paper, the so called diagonal forms of the translation operators for the fast multipole method are derived starting from integral representations of certain special functions. Error analysis of the FMM is given, considering both the truncation error of potential expansions and the errors from the use of numerical integration in the diagonal translation theorem. The implications of the error bounds on the FMM algorithm are discussed.

Application of the fast Fourier transform to broadband beamforming

Abstract: The processing of broadband signals using an array of sensors is normally carried out in a time domain using a tapped delay line filter or in a frequency domain where each frequency channel is weighed by complex weights and no tapped delay line filter is required. The time domain implementation of the broadband structure is important in the area of communication where the frequency domain implementation may not be suitable due to its associated delay. This paper derives relationships between the weights, the array correlation matrices, and the constraints on the weights of the two structures to produce identical results. These relationships are then used to update the weights of the tapped delay line filter structure using narrow‐band techniques. The method has potential for computational saving to estimate weights of the broadband structure, for a large bandwidth signal requiring a long tapped delay line filter.

A digital measurement scheme for time-varying transient harmonics

Abstract: This paper presents an enhanced measurement scheme on the harmonics in power system voltages and currents which is not limited to stationary waveforms, but can also estimate harmonics in waveforms with time-varying amplitudes. The paper starts with a review of the common techniques for harmonics measurement based on the fast Fourier transform (FFT). The major pitfalls in the common FFT application techniques are described and the concepts of a new scheme for reducing the picket-fence effect are introduced. The proposed scheme is based on Parseval's relation and the energy concept which defines a "group harmonic" identification algorithm for the estimation of the energy distribution in the harmonics of time-varying waveforms. The scheme is tested on a portable computer-based harmonic recorder providing on-site harmonic data collection and precise harmonic identification. >

A sparse‐matrix canonical‐grid method for scattering by many scatterers

Abstract: A new efficient algorithm based on the decomposition of strong and weak interactions among scatterers is proposed. The weak interactions, which account for the majority of the required CPU time and memory, are calculated using a canonical grid with a translation addition theorem. This facilitates the use of FFT and results in an N log N-type efficiency for CPU and O(N) for memory.

The use of Fourier descriptors in the classification of particle shape

Abstract: A new quantitative method for characterizing quartz grain shape is presented. The method employs a harmonic analysis based upon Fourier descriptors which is a distinct variation of the traditional and widely used Fourier series. Quartz grain images from a scanning electron microscope were ‘frame grabbed’and converted to a digitized grey-level image. The image processing techniques of enhancement, segmentation and boundary tracking were applied to remove all features except the image boundary. This boundary was sampled at uniform intervals of are length and represented mathematically on the complex plane. In this way problems associated with the location of particle centroid and re-entrant values were avoided. The resulting data was standardized relative to scale, rotation and starting position. Hence the discrete Fourier transform was applied using modern fast Fourier transform techniques and the modulus of the resulting harmonic amplitude used to characterize the grain shape. The technique was applied to a sample of 0–5-m quartz grains from three distinct populations: desert quartz, beach grains (Fire Island, New York) and Brazilian crushed quartz. Whilst plots of average amplitude vs. harmonic number for each population appeared similar, discriminant analysis applied to each grain sample distinguished characteristic grain shape with an excellent degree of success. The problems of location of the centroid and re-entrant values were eliminated. This allowed the technique to be applied to a much wider group of irregularly shaped sedimentary particles such as loess.

Propagation of ultra-wide-band electromagnetic pulses through dispersive media

Abstract: We develop an efficient method for the analysis of ultra-wide-band (UWB) electromagnetic pulses (e.g., double-exponential pulse) propagating through a waveguide or cold plasma (i.e., the ionosphere). First we show that the inverse Fourier-transform representations for the electric and magnetic fields satisfy second order, nonhomogeneous, ordinary, differential equations. These differential equations are solved analytically, thereby yielding closed-form expressions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed using efficient convergent and asymptotic series expansions. We demonstrate the usefulness of the ILHI expressions by comparing them with the fast Fourier-transform technique (FFT). Because of the long tails associated with UWB pulses, a large number of sample points are required in the FFT, to avoid aliasing errors. In contrast, the ILHI expressions provide accurate and efficient numerical results, regardless of the number of points computed. An asymptotic series representation for the ILHIs is also employed, to obtain a relatively simple, late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the waveform over a large portion of its time history. >

Implementation of a 2-D Fast Fourier Transform on an FPGA-Based Custom Computing Machine

Abstract: The two dimensional fast Fourier transform (2-D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors This paper presents the implementation and performance figures for the Fourier transform on a FPGA-based custom computer The computation of a 2-D FFT requires O(N2log2N) floating point arithmetic operations for an NxN image By implementing the FFT algorithm on a custom computing machine (CCM) called Splash-2, a computation speed of 180 Mflops and a speed-up of 23 times over a Sparc-10 workstation is achieved

AFC frequency synchronization network

Abstract: A frequency synchronization network is disclosed that is particularly suited for a Eureka-147 system transmitting synchronization symbols and multiple data carriers, wherein the multiple carriers are transmitted simultaneously and separated from each other by a bin quantity. The network comprises a Fast Fourier transform (FFT) network, a complex rotation device, and a power analyzer. The power analyzer determines the peak condition of the FFT bin quantities and routes this information to an interpolation sequence that determines the zero-crossover condition of the peak bin quantity, and which ultimately determines an output as the frequency offset of the AFC frequency symbol. The frequency offset quantity is provided to an automatic frequency control (AFC) network to provide for frequency locking of the transmitting and receiving elements of the Eureka-147 system.

Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions

Abstract: The correlation performance of binary joint transform correlators with unknown input-image light illumination is investigated for different thresholding methods used in the Fourier plane. It is shown that a binary joint transform correlator that uses a spatial frequency dependent threshold function for binarization of the joint power spectrum is invariant to uniform input-image illumination. Computer simulations and optical experimental results are provided.

A fast algorithm for signature prediction and image formation using the shooting and bouncing ray technique

Abstract: We present a fast simulation algorithm for generating the range profiles and inverse synthetic aperture radar (ISAR) images of complex targets using the shooting and bouncing ray (SBR) technique. Starting with the time-domain and image-domain ray-tube integration formulas we derived previously, we cast these formulas into a convolution form. The convolution consists of a nonuniformly sampled signal and a closed-form time-domain or image-domain ray spread function. Using a fast scheme proposed by Sullivan (1990), the nonuniformly sampled function is first interpolated onto a uniform grid before the convolution is performed by the fast Fourier transform (FFT) algorithm. Results for several complex targets are presented to demonstrate the tremendous computation time savings and excellent fidelity of the scheme. Using the fast scheme, a speed gain of a factor of 30 is achieved in performing the ray summation as compared to the direct convolution in range profile computation and a factor of 180 in ISAR image formation for a typical aircraft at S-band. >

Fast Fourier transform techniques for efficient simulation of Z-scan measurements

Abstract: Fast Fourier beam–propagation methods (BPM’s) for simulating the roles of internal refractive effects and external propagation from nonlinear media are introduced. These techniques are applied to model picosecond Z-scan measurements for the induced absorber, the dye Chloro-Aluminum Phthalocyanine, at 532 nm. Within the thin-sample approximation an incident Gaussian beam is taken to experience a change in phase profile on propagation through the medium but remains of Gaussian amplitude profile. Outside this approximation one must determine both the phase and the amplitude profiles at the sample exit face that are due to the influence of nonlinear refraction (and nonlinear absorption) on the beam propagating through the medium. The BPM technique allows this to be achieved efficiently, and the external propagation technique enables a single discrete fast Fourier transform to be used to describe the subsequent external propagation of the non-Gaussian-shaped beams. The analysis is especially useful for such self-enhancing nonlinearities as one would wish to exploit in optical limiting.

Computationally attractive real Gabor transforms

Abstract: We present a Gabor transform for real, discrete signals and present a computationally attractive method for computing the transform. For the critically sampled case, we derive a biorthogonal function which is very localized in the time domain. Therefore, truncation of this biorthogonal function allows us to compute approximate expansion coefficients with significantly reduced computational requirements. Further, truncation does not degrade the numerical stability of the transform. We present a tight upper bound on the reconstruction error incurred due to use of a truncated biorthogonal function and summarize computational savings. For example, the expense of transforming a length 2048 signal using length 16 blocks is reduced by a factor of 26 over similar FFT-based methods with at most 0.04% squared error in the reconstruction. >