Showing papers on "Fast Fourier transform published in 1994"

Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods

Abstract: Two-dimensional (2D) phase unwrapping continues to find applications in a wide variety of scientific and engineering areas including optical and microwave interferometry, adaptive optics, compensated imaging, and synthetic-aperture-radar phase correction, and image processing. We have developed a robust method (not based on any path-following scheme) for unwrapping 2D phase principal values (in a least-squares sense) by using fast cosine transforms. If the 2D phase values are associated with a 2D weighting, the fast transforms can still be used in iterative methods for solving the weighted unwrapping problem. Weighted unwrapping can be used to isolate inconsistent regions (i.e., phase shear) in an elegant fashion.

Simulation of Stationary Gaussian Processes in [0, 1] d

Abstract: A method for simulating a stationary Gaussian process on a fine rectangular grid in [0, 1]d ⊂ℝd is described It is assumed that the process is stationary with respect to translations of ℝd, but the method does not require the process to be isotropic As with some other approaches to this simulation problem, our procedure uses discrete Fourier methods and exploits the efficiency of the fast Fourier transform However, the introduction of a novel feature leads to a procedure that is exact in principle when it can be applied It is established that sufficient conditions for it to be possible to apply the procedure are (1) the covariance function is summable on ℝd, and (2) a certain spectral density on the d-dimensional torus, which is determined by the covariance function on ℝd, is strictly positive The procedure can cope with more than 50,000 grid points in many cases, even on a relatively modest computer An approximate procedure is also proposed to cover cases where it is not feasible to apply

Parallel Computing: Theory and Practice

Abstract: PRAM algorithms processor arrays, multiprocessors and multicomputers parallel programming languages mapping and scheduling elementary parallel algorithms matrix multiplication the fast Fourier transform solving linear systems sorting dictionary operations graph algorithms combinational search. Appendices: graph theoretic terminology review of complex numbers parallel algorithm design strategies.

Least-squares two-dimensional phase unwrapping using FFT's

Abstract: A solution of the least-squares two-dimensional phase-unwrapping problem is presented that is simpler to understand and implement than previously published solutions. It extends the phase function to a periodic function using a mirror reflection, and the resulting equation is solved using the Fourier transform. >

Radon transformation of time-frequency distributions for analysis of multicomponent signals

Abstract: The Radon transform of a time-frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals. The Radon-Wigner transform can be efficiently implemented with dechirping in the time domain, however, only half of the possible projections through the time-frequency plane can be realized because of aliasing. We show here that the frequency dual to dechirping exists, so that all of the time-frequency plane projections can be calculated efficiently. Both time and frequency dechirping are shown to warp the time-frequency plane rather rotating it, producing an angle dependent dilation of the Radon-Wigner projection axis. We derive the discrete-time equations for both time and frequency dechirping, and highlight some practical implementation issues. Discrete dechirping is shown to correspond to line integration through the extended-discrete, rather than the discrete, Wigner-Ville distribution. Computationally, dechirping is O(2N log 2N) instead of O(N/sup 3/) for direct projection, and the computation is dominated by the fast Fourier transform calculation. The noise and cross-term suppression of the Radon-Wigner transform are demonstrated by several examples using dechirping and using direct Radon-Wigner transformation. >

Sensorless speed measurement using current harmonic spectral estimation in induction machine drives

Abstract: This paper proposes a sensorless speed measurement scheme which improves the performance of transducerless induction machine drives, especially for low frequency operation. Speed-related harmonics which arise from rotor slotting and eccentricity are analyzed using digital signal processing. These current harmonics exist at any nonzero speed and are independent of time-varying parameters such as stator winding resistance. A spectral estimation technique combines multiple current harmonics to determine the rotor speed with more accuracy and less sensitivity to noise than analog filtering methods or the fast Fourier transform. An on-line initialization routine determines machine-specific parameters required for slot harmonic calculations. This speed detector, which has been verified at frequencies as low as 1 Hz, can provide robust, parameter-independent information for parameter tuning or as an input to a sensorless flux observer for a field-oriented drive. The performance of the algorithm is demonstrated over a wide range of inverter frequencies and load conditions. >

Computations of the complex error function

Abstract: Rational expansions for computing the complex error function $w(z) = e^{ - z^2 } {\text{erfc}}( - iz)$ are presented. These expansions have the following attractive properties: (1) they can be evaluated using a polynomial evaluation routine such as Homer’s method, (2) the polynomial coefficients can be computed once and for all by a single Fast Fourier Transform (FFT), and (3) high accuracy is achieved uniformly in the complex plane with only a small number of terms. Comparisons reveal that in some parts of the complex plane certain competitors may be more efficient. However, the difference in efficiency is never great, and the new algorithms are simpler than existing ones: a complete program takes eight lines of Matlab code.

A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods for Calculating Electrostatic Interactions in Periodic Molecular Systems

Abstract: We compare the Particle-Particle Particle-Mesh (PPPM) and Ewald methods for calculating electrostatic interactions in periodic molecular systems. A brief comparison of the theories shows that the methods are very similar differing mainly in the technique which is used to perform the “k-space” or mesh calculation. Because the PPPM utilizes the highly efficient numerical Fast Fourier Transform (FFT) method it requires significantly less computational effort than the Ewald method and scales almost linearly with system size.

Noninvasive method and apparatus for determining resonance information for rotating machinery components and for anticipating component failure from changes therein

Abstract: A method and apparatus is described for determining resonant frequencies of vibration of turbine (20) and (22) and fan shafts (16) and blades, and other rotating machines (12) in which a rotating element of the machine (12) has oscillatory vibrations that modulate the fundamental frequency of rotation of the rotating machine (12). A sensor (30) monitors the machine (12), providing a train of sensor pulses or other signal representative of angular rotation of the machine (12). The signal is processed to provide a signal representative of the modulation of the fundamental frequency of rotation of the rotating machine (12), which signal is processed to provide a frequency spectrum representative of instantaneous-frequency components present. The signal spectrum is electronically processed to provide resonance-information, spectral signals representative of frequency or amplitude characteristics, or both, for the resonant vibrations. Signal-processing methods (36) include use of Fast Fourier Transform and Discrete Fourier Transform.

Atomic-level accuracy in simulations of large protein crystals

Abstract: Proper treatment of long-range Coulombic forces presents a major obstacle to providing realistic molecular dynamics simulations of macromolecules. Traditional approximations made to lessen computational cost ultimately lead to unrealistic behavior. The particle mesh Ewald method accommodates long-range Coulombic forces accurately and efficiently by use of fast Fourier transform techniques. We report a 1-ns simulation of bovine pancreatic trypsin inhibitor in a crystal unit cell using the particle mesh Ewald methodology. We find an rms backbone deviation from the x-ray structure (0.33 A) that is lower than that observed between bovine pancreatic trypsin inhibitor in different crystal forms and much lower than those of previous simulations. These results bridge the gap between structures obtained from molecular simulation and those from experiment.

A fast method for the numerical evaluation of continuous Fourier and Laplace transforms

Abstract: The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.

A fast spectral estimation algorithm based on the FFT

Abstract: A simple FFT-based algorithm for spectrum estimation is presented. The major difference between this and spectrum estimation using a single pass through the FFT is that the proposed algorithm is iterative and the FFT is used many times in a systematic may to search for individual spectral lines. Using simulated data, the proposed algorithm is able to detect mulitple sinusoids in additive noise. The algorithm is certainly better than the single pass FFT in separating closely spaced sinusoids. Finally the algorithm is applied to some experimental measurements to illustrate its properties. >

Biomedical signal processing

Abstract: Digital signals and systems z-transforms digital filter design discrete and fast Fourier transform algorithms periodogram and Blackman-Tukey CEPSTRUM adaptive noise cancelling adaptive line enhancer adaptive zero tracking methods autoregressive (AR) method autoregressive moving average (ARMA) method Prony's method.

A projection access order for speedy convergence of ART (algebraic reconstruction technique): a multilevel scheme for computed tomography

Abstract: The practical performance of algebraic reconstruction techniques (ART) for computed tomography (CT) depends heavily on the order in which the projections are considered. Complete orthogonalization, notwithstanding its theoretical justification, is not feasible because the computational time is prohibitive. The authors report here a scheme that yields the most efficient reconstruction without orthogonalization: projections are organized and accessed in a nominally multilevel fashion. Each level makes the best use of the image information reconstructed in the preceding levels. If the number of projections is a power of two. Then the access orders are exactly that for the 1D FFT. The authors' scheme can be easily implemented. Using it, one iteration of ART yields a high-quality image. Experimental results of this algorithm are demonstrated and compared with the results from the conventional sequential method and also random ordering. Comparisons show that this scheme is superior. ART is better in image quality than the Fourier back-projection algorithm, at least for a smaller number of projections. Since the authors have made it much more efficient in computational speed, ART could now find widespread use in medical imaging.

The fast Fourier Poisson method for calculating Ewald sums

Abstract: The conventional Ewald expression for the electrostatic energy and forces is recast in a form that can be evaluated to high accuracy in order N log(N) steps using fast Fourier transforms. The fast Fourier Poisson method does not rely on interpolation approaches or Taylor/multipole expansions, and can be easily integrated with conventional molecular dynamics algorithms.

Kinoform design with an optimal-rotation-angle method

Abstract: Kinoforms (i.e., computer-generated phase holograms) are designed with a new algorithm, the optimalrotation- angle method, in the paraxial domain. This is a direct Fourier method (i.e., no inverse transform is performed) in which the height of the kinoform relief in each discrete point is chosen so that the diffraction efficiency is increased. The optimal-rotation-angle algorithm has a straightforward geometrical interpretation. It yields excellent results close to, or better than, those obtained with other state-of-the-art methods. The optimal-rotation-angle algorithm can easily be modified to take different restraints into account; as an example, phase-swing-restricted kinoforms, which distribute the light into a number of equally bright spots (so called fan-outs), were designed. The phase-swing restriction lowers the efficiency, but the uniformity can still be made almost perfect.

Transceiver apparatus employing wideband FFT channelizer with output sample timing adjustment and inverse FFT combiner for multichannel communication network

Abstract: A physically compact, multichannel wireless communication transceiver architecture employs overlap and add or polyphase signal processing functionality, for wideband signal processing, together with a sample rate. A receiver section receives a plurality of multiple frequency communication channels and outputs digital signals representative of the contents of the plurality of multiple frequency communication channels. The receiver section contains an FFT-based channelizer that processes the digital signals output by a wideband digital receiver and couples respective channel outputs to a first plurality of digital signal processor units, which process (e.g. demodulate) respective ones of the digital channel signals and supply processed ones of the digital channel signals at respective output ports for distribution to an attendant voice/data network. On the transmit side, a transmit section contains a plurality of digital signal processors, respectively associated with respective ones of a plurality of incoming (voice/data) communication signals to be transmitted over respectively different frequency channels. Their processed (modulated, encoded) outputs are supplied to an inverse FFT combiner. The FFT combiner supplies a combined multichannel signal to a wideband transmitter which transmits a multiple frequency communication channel signal. Each of the channelizer and combiner may be implemented using overlap and add or polyphase filtering.

Algorithm-based fault tolerance for FFT networks

Abstract: Algorithm-based fault tolerance (ABFT) is a low-overhead system-level fault tolerance technique. Many ABFT schemes have been proposed in the past for fast Fourier transform (FFT) networks. In this paper, a new ABFT scheme for FFT networks is proposed. We show that the new approach maintains the high throughput of previous schemes, yet needs lower hardware overhead and achieves higher fault converge than previous schemes by J.Y. Jou et al. (1988) and D.I. Tao et al. (1990). >

A precorrected-FFT method for capacitance extraction of complicated 3-D structures

Abstract: In this paper we present a new approach to three-dimensional capacitance extraction based on a precorrected FFT scheme. The approach is compared to the now commonly used multipole-accelerated algorithms for a variety of structures, and the new method is shown to have substantial performance and memory advantages.

Minimum entropy deconvolution with frequency-domain constraints

Abstract: A method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented. The algorithm (FMED) described is compared with the classical minimum entropy deconvolution (MED) as well as with the linear programming (LP) and autoregressive (AR) approaches. The MED is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace. By comparison, the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum. This procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band-limited data, avoiding the inherent limitations of linear operators. The proposed method is illustrated under a variety of synthetic examples. Field data are also used to test the algorithm. The results show that the proposed method is an effective way to process band-limited data. The FMED and the LP arise from similar conceptions. Both methods seek an extremum of a particular norm subjected to frequency constraints. In the LP approach, the linear programming problem is solved using an adaptation of the simplex method, which is a very expensive procedure. The FMED uses only two fast Fourier transforms (FFTs) per iteration; hence, the computational cost of the inversion is reduced.

A multiharmonic method for non‐linear vibration analysis

Abstract: A multiharmonic method for analysis of non-linear dynamic systems submitted to periodic loading conditions is presented. The approach is based on a systematic use of the fast Fourier transform. The exact linearization of the resulting equations in the frequency domain allows to obtain full quadratic convergence rate

Detection of a multi-sequence spread spectrum signal

Abstract: A detector of a multiple-sequence spread spectrum signal uses a Hadamard transform (106) to simultaneously correlate a received signal comprising two sequences (64) with a plurality of candidate sequences The received signal is stripped of the first sequence (65, 66), and the signal is permuted (via a table lookup) (104) A Hadamard transform is performed on the permuted data and the candidate sequences (106) After transformation, the data is permuted again (112 ) to determine the symbol (sequence) transmitted Alternatively, Fast Fourier Transforms (FFTs) (FIG 3), Winograd Fourier Transform Algorithms (WFTA), or other cyclic correlation algorithms (FIG 5) may be used to compute the transformation In a preferred embodiment, a "pilot" signal is transmitted in quadrature (90 degrees phase offset) with an information-bearing signal And, a block error correcting code (150) (eg, a modified Reed-Solomon code) is transmitted with the information-bearing signal a(t) The block length of the block error correcting code (150) is equal to an integral multiple of the period of the pilot signal The period of the pilot signal is an integral multiple of the information bearing signal Thus, carrier recovery, sequence synchronization, and block code synchronization are all achieved simultaneously by correlating (synchronizing) the received signal with a baseband version of the pilot signal

Performance of fast multipole methods for calculating electrostatic interactions in biomacromolecular simulations

Abstract: The fast multipole method proposed by Greengard and Rokhlin (GR) is applied to large biomacromolecular systems. In this method, the system is divided into a hierarchy of cells, and electric field exerted on a particle is decomposed into two parts. The first part is a rapidly varying field due to nearby cells, so that it needs rigorous pairwise calculations. The second part is a slowly varying local field due to distant cells; hence, it allows rapid calculations through a multipole expansion technique. In this work, two additional possibilities for improving the performance are numerically examined. The first is an improvement of the convergence of the expansion by increasing the number of nearby cells, without including higher-order multipole moments. The second is an acceleration of the calculations by the particle–particle and particle–mesh/multipole expansion (PPPM/MPE) method, which uses fast Fourier transform instead of the hierarchy. For this purpose, the PPPM/MPE method originally developed by the authors for a periodic system is extended to a nonperiodic isolated system. The advantages and disadvantages of the GR and PPPM/MPE methods are discussed for both periodic and isolated systems. It is numerically shown that these methods with reasonable costs can reduce the error in potential felt by each particle to 0.1–1 kcal/mol, much smaller than the 30-kcal/mol error involved in conventional simple truncations. © 1994 by John Wiley & Sons, Inc.

Feedback detector and suppressor

Abstract: An A/D converter converts an analog signal to a digital signal. A plurality of cascade-connected notch filters include a first notch filter which is connected to the output of the A/D converter. A D/A converter is connected to the output of the last stage notch filter for converting a digital signal to an analog signal. The output of the last stage notch filter is connected to the input of a fast Fourier transform unit for analyzing the frequency. Analysis results of the fast Fourier transform unit are supplied to a detector. A coefficient having the same center frequency as that of a peak frequency outputted from the detector is selected from a coefficient memory and it is transferred to a second coefficient memory. Thus, the frequencies of the notch filters are set to eliminate howling.

Generalized sliding FFT and its application to implementation of block LMS adaptive filters

Abstract: This paper has two contributions. First, the concept of the generalized sliding fast Fourier transform (GSFFT) as an efficient implementation of the hopping FFT is introduced. Application of the GSFFT is broad and not limited to what has been considered in this paper. The frequency domain block LMS (FBLMS) adaptive filters are then revised, and their implementations for block lengths less than the length of the adaptive filter are studied. The GSFFT and the available pruned FFTs are used to give an efficient implementation of these filters. In the particular case of the block length equal to one, where the FBLMS algorithm reduces to the frequency domain LMS (FLMS) algorithm, it is shown that the latter can be implemented with the order of M complexity, where M is the length of the adaptive filter. >

A fast integral-equation solver for electromagnetic scattering problems

Abstract: We describe a new fast integral-equation solver applicable to large-scale electromagnetic scattering problems. In our approach, the field generated by a given current distribution M decomposed into near and far field components. The near field is computed using the conventional method of moments technique with the Galerkin discretization. The far field is calculated by approximating the original current distribution by an equivalent current distribution on a regular Cartesian grid, such that the two currents have identical multipole moments up to a required order m. As the result of this discretization, the original full impedance matrix is decomposed into a sum of a sparse matrix (corresponding to the near field component) and a product of sparse and Toeplitz matrices (corresponding to the far field component). Because of the convolution nature of the Toeplitz kernel, the field generated by the equivalent current distribution can be then obtained by means of discrete fast Fourier transforms. The single computational domain solver based on our formulation requires both memory and computation time of order O(N log N) (in volume problems) or O(N/sup 3/2/) (in surface problems), where N is the number of unknown current elements. In the domain-decomposed parallelized version of the solver, with the number P of processors equal to the number of domains, the total memory required in surface problems is reduced to O(N/sup 3/2//P/sup 1/2/). The corresponding speedup factor is equal to the number of processors P. During the talk, applications of the solver to 2- and 3-dimensional electromagnetic volumetric and boundary-value problems will be presented. >

A rotating and warping projector/backprojector for fan-beam and cone-beam iterative algorithm

Abstract: A rotating-and-warping projector/backprojector is proposed for iterative algorithms used to reconstruct fan-beam and cone-beam single photon emission computed tomography (SPECT) data. The development of a new projector/backprojector for implementing attenuation, geometric point response, and scatter models is motivated by the need to reduce the computation time yet to preserve the fidelity of the corrected reconstruction. At each projection angle, the projector/backprojector first rotates the image volume so that the pixelized cube remains parallel to the detector, and then warps the image volume so that the fan-beam and cone-beam rays are converted into parallel rays. In the authors' implementation, these two steps are combined so that the interpolation of voxel values are performed only once. The projection operation is achieved by a simple weighted summation, and the backprojection operation is achieved by copying weighted projection array values to the image volume. An advantage of this projector/backprojector is that the system point response function can be deconvolved via the Fast Fourier Transform using the shift-invariant property of the point response when the voxel-to-detector distance is constant. The fan-beam and cone-beam rotating-and-warping projector/backprojector is applied to SPECT data showing improved resolution. >

Quasi-synchronous sampling algorithm and its applications

Abstract: Synchronous sampling is a commonly used method with good performance. However, when perfect synchronization is impossible, or when the signal contains interharmonics, undesirable asynchronous deviations between the sampling and some components of the signal may exist. Consequently, possibly large leakage or truncation errors may occur. Consisting of a quasi-synchronous window to reduce the long-range leakage, and a compensation algorithm to reduce the short-range leakage after normal FFT, the method described in this paper will give much more accurate measurement of many electrical quantities, e.g., spectral content of signal and phase difference between two periodic signals in power networks, than the traditional one. >

Quadrature-to-directional format conversion of Doppler signals using digital methods

Abstract: Four possible quadrature-to-directional format conversion methods using digital techniques are described. These are the phasing-filter technique, the extended Weaver receiver technique, the Hilbert transform in the frequency domain, and the complex FFT. All methods are implemented to give separated time domain outputs as well as frequency domain outputs. The theoretical descriptions are verified by practical implementations. Each of the methods has been implemented in real-time using a commercially available digital signal processing board.

Wiener filter for filtering noise from a video signal

Abstract: A digital Wiener filtering method is proposed which applies motion compensation by successive approximations of increasing resolution to determine displacement vectors for two successive image frames, a vectors defining a real displacement only being applied to a block of one of the frames when the mean absolute error associated with that vector is not greater than a given fraction of the mean absolute error between that block and the corresponding block of the other frame. The current frame is then filtered block-by-block, with the blocks overlapping. In this filtering, each block is a 3D volume of pixels from the current frame and blocks selected from the preceding and succeeding frames so as to correspond according to the displacement vectors. In one embodiment, the filtering comprises applying a 3D FFT to convert to a power spectrum in the frequency domain, followed by attenuation according to a Wiener filter and conversion from the frequency domain by the inverse FFT.