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Showing papers on "Fast Fourier transform published in 1985"


Journal ArticleDOI
TL;DR: A new method for quantitative analysis of time-domain signals that is insensitive to truncation at the beginning and/or the end of the signal, and is capable to accurately reconstruct the missing part, and achieves higher resolution than fast Fourier transformation.

487 citations


Book
30 Nov 1985
TL;DR: This book discusses Discrete-Time Signals, or Sequences, and Filter and Systems Examples, and its applications in Speech Synthesis, Oscillators and Synthesizers, and Digital Filter Implementation.
Abstract: 1 Introduction: Terminology and Motivation.- 2 Discrete-Time Signals and Systems.- 2.0 Introduction.- 2.1 Discrete-Time Signals, or Sequences.- 2.2 Discrete-Time Systems and Filters.- 2.3 Stability and Causality.- Problems.- 3 The z Transform.- 3.0 Introduction.- 3.1 Definition of the z Transform.- 3.2 Inverse z Transform.- 3.3 Inverse z Transform for Causal Sequences.- 3.4 Properties of the z Transform.- Problems.- 4 Input/Output Relationships.- 4.0 Introduction.- 4.1 System Function and Frequency Response.- 4.2 Difference Equations.- 4.3 Geometric Evaluations of H(z) and H'(?).- 4.4 State Variables.- Problems.- 5 Discrete-Time Networks.- 5.0 Introduction.- 5.1 Flow Graph Properties.- 5.2 Network Structures.- 5.3 Properties of Network Coefficients.- 5.4 Special Discrete-Time Networks.- Problems.- 6 Sampling Continuous-Time Signals.- 6.0 Introduction.- 6.1 Fourier Transform Relationships.- 6.2 Discrete-Time Fourier Transform.- 6.3 Laplace Transform Relationships.- 6.4 Prefilters, Postfilters and D/A Converters.- Problems.- 7 Discrete Fourier Transform.- 7.0 Introduction.- 7.1 Derivation and Properties of the DFT.- 7.2 Zero Padding.- 7.3 Windows in Spectrum Analysis.- 7.4 FFT Algorithms.- 7.5 Prime-Factor FFT's.- 7.6 Periodogram.- Problems.- 8 IIR Filter Design by Transformation.- 8.0 Introduction.- 8.1 Classical Filter Designs.- 8.2 Impulse-Invariant Transformation.- 8.3 Bilinear Transformation.- 8.4 Spectral Transformation.- Problems.- 9 FIR Filter Design Techniques.- 9.0 Introduction.- 9.1 Window-Function Technique.- 9.2 Frequency-Sampling Technique.- 9.3 Equiripple Designs.- Problems.- 10 Filter Design by Modeling.- 10.0 Introduction.- 10.1 Autoregressive (all-pole) Filters.- 10.2 Moving-Average (all-zero) Filters.- 10.3 ARMA (pole/zero) Filters.- 10.4 Lattice Structures.- 10.5 Spectrum Analysis by Modeling.- Problems.- 11 Quantization Effects.- 11.0 Introduction.- 11.1 Coefficient Quantization.- 11.2 Signal Quantization.- 11.3 Dynamic Range and Scaling.- 11.4 Parallel and Cascade Forms.- 11.5 Limit-Cycle Oscillations.- 11.6 State-Space Structures.- Problems.- 12 Digital Filter Implementation.- 12.0 Introduction.- 12.1 Bit-Serial Arithmetic and VLSI.- 12.2 Distributed Arithmetic.- 12.3 Block IIR Implementations.- Problems.- 13 Filter and Systems Examples.- 13.0 Introduction.- 13.1 Interpolation and Decimation.- 13.2 Hilbert Transformation.- 13.3 Digital Oscillators and Synthesizers.- 13.4 Speech Synthesis.- 13.5 Cepstrum.- Problems.- Answers to Selected Problems.- References.

452 citations


Journal ArticleDOI
TL;DR: A complete set of fast algorithms for computing the discrete Hartley transform is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms.
Abstract: The discrete Hartley transform (DHT) is a real-valued transform closely related to the DFT of a real-valued sequence. Bracewell has recently demonstrated a radix-2 decimation-in-time fast Hartley transform (FHT) algorithm. In this paper a complete set of fast algorithms for computing the DHT is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms. The philosophies of all common FFT algorithms are shown to be equally applicable to the computation of the DHT, and the FHT algorithms closely resemble their FFT counterparts. The operation counts for the FHT algorithms are determined and compared to the counts for corresponding real-valued FFT algorithms. The FHT algorithms are shown to always require the same number of multiplications, the same storage, and a few more additions than the real-valued FFT algorithms. Even though computation of the FHT takes more operations, in some situations the inherently real-valued nature of the discrete Hartley transform may justify this extra cost.

275 citations


Book
01 Jan 1985
TL;DR: This chapter discusses the theory and application of Sampling Theory for Two-Dimensional Signals, and some of the methods used to achieve this goal.
Abstract: 1. Introduction.- 1 Fundamentals of the Theory of Digital Signal Processing.- 2. Elements of Signal Theory.- 2.1 Signals as Mathematical Functions.- 2.2 Signal Space.- 2.3 The Most Common Systems of Basis Functions.- 2.3.1 Impulse Basis Functions.- 2.3.2 Harmonic Functions.- 2.3.3 Walsh Functions.- 2.3.4 Haar Functions.- 2.3.5 Sampling Functions.- 2.4 Continuous Representations of Signals.- 2.5 Description of Signal Transformations.- 2.5.1 Linear Transformations.- 2.5.2 Nonlinear Element-by-Element Transforms.- 2.6 Representation of Linear Transformations with Respect to Discrete Bases.- 2.6.1 Representation Using Vector Responses.- 2.6.2 Matrix Representations.- 2.6.3 Representation of Operators by Means of Their Eigenfunctions and Eigenvalues.- 2.7 Representing Operator with Respect to Continuous Bases.- 2.7.1 Operator Kernel.- 2.7.2 Description in Terms of Impulse Responses.- 2.7.3 Description Using Frequency Transfer Functions.- 2.7.4 Description with Input and Output Signals Referred to Different Bases.- 2.7.5 Description Using Eigenfunctions.- 2.8 Examples of Linear Operators.- 2.8.1 Shift-Invariant Filters.- 2.8.2 The Identity Operator.- 2.8.3 Shi ft Operator.- 2.8.4 Sampling Oparator.- 2.8.5 Gating Operator (Multiplier).- 3. Discretization and Quantization of Signals.- 3.1 Generalized Quantization.- 3.2 Concepts of Discretization and Element-by-Element Quantization.- 3.2.1 Discretization.- 3.2.2 Element-by-Element Quantization.- 3.3 The Sampling Theorem.- 3.4 Sampling Theory for Two-Dimensional Signals.- 3.5 Errors of Discretization and Restoration of Signals in Sampling Theory.- 3.6 Other Approaches to Discretization.- 3.7 Optimal Discrete Representation and Dimensionality of Signals.- 3.8 Element-by-Element Quantization.- 3.9 Examples of Optimum Quantization.- 3.9.1 Example: The Threshold Metric.- 3.9.2 Example: Power Criteria for the Absolute Value of the Quantization Error.- 3.9.3 Example: Power Criteria for the Relative Quantization Error.- 3.10 Quantization in the Presence of Noise. Quantization and Representation of Numbers in Digital Processors.- 3.11 Review of Picture-Coding Methods.- 4. Discrete Representations of Linear Transforms.- 4.1 Problem Formulation and General Approach.- 4.2 Discrete Representation of Shift-Invariant Filters for Band-Limited Signals.- 4.3 Digital Filters.- 4.4 Transfer Functions and Impulse Responses of Digital Filters.- 4.5 Boundary Effects in Digital Filtering.- 4.6 The Discrete Fourier Transform (DFT).- 4.7 Shifted, Odd and Even DFTs.- 4.8 Using Discrete Fourier Transforms.- 4.8.1 Calculating Convolutions.- 4.8.2 Signal Interpolation.- 4.9 Walsh and Similar Transforms.- 4.10 The Haar Tansform. Addition Elements of Matrix Calculus.- 4.11 Other Orthogonal Tansforms. General Representations. Review of Applications.- 5. Linear Transform Algorithms.- 5.1 Fast Algorithms of Discrete Orthogonal Transforms.- 5.2 Fast Haar Transform (FHT) Algorithms.- 5.3 Fast Walsh Transform (FWT) Algorithms.- 5.4 Fast Discrete Fourier Transform (FFT) Algorithms.- 5.5 Review of Other Fast Algorithms. Features of Two-Dimensional Transforms.- 5.5.1 Truncated FFT and FWT Algorithms.- 5.5.2 Transition Matrices Between Various Transforms.- 5.5.3 Calculation of Two-Dimensional Transforms.- 5.6 Combined DFT Algorithms.- 5.6.1 Combined DFT Algorithms of Real Sequences.- 5.6.2 Combined SDFT (1/2, 0) Algorithms of Even and Real Even Sequences.- 5.7 Recursive DFT Algorithms.- 5.8 Fast Algorithms for Calculating the DFT and Signal Convolution with Decreased Multiplication.- 6. Digital Statistical Methods.- 6.1 Principles of the Statistical Description of Pictures.- 6.2 Measuring the Grey-Level Distribution.- 6.2.1 Step Smoothing.- 6.2.2 Smoothing by Sliding Summation.- 6.2.3 Smoothing with Orthogonal Transforms.- 6.3 The Estimation of Correlation Functions and Spectra.- 6.3.1 Averaging Local Spectra.- 6.3.2 Masking (Windowing) the Process by Smooth Functions.- 6.3.3 Direct Smoothing of Spectra.- 6.4 Generating Pseudorandom Numbers.- 6.5 Measuring Picture Noise.- 6.5.1 The Prediction Method.- 6.5.2 The Voting Method.- 6.5.3 Measuring the Variance and the Auto-Correlation Function of Additive Wideband Noise.- 6.5.4 Evaluation of the Intensity and Frequency of the Harmonic Components of Periodic Interference and Other Types of Interference with Narrow Spectra.- 6.5.5 Evaluation of the Parameters of Pulse Noise, Quantization Noise and Strip-Like Noise.- 2 Picture Processing.- 7. Correcting Imaging Systems.- 7.1 Problem Formulation.- 7.2 Suppression of Additive Noise by Linear Filtering.- 7.3 Filtering of Pulse Interference.- 7.4 Correction of Linear Distortion.- 7.5 Correction of Amplitude Characteristics.- 8. Picture Enhancement and Preparation.- 8.1 Preparation Problems and Visual Analysis of Pictures.- 8.1.1 Feature Processing.- 8.1.2 Geometric Transformations.- 8.2 Adaptive Quantization of Modes.- 8.3 Preparation by Nonlinear Transformation of the Video Signal Scale.- 8.4 Linear Preparation Methods.- 8.5 Methods of Constructing Graphical Representation: Computer Graphics.- 8.6 Geometric Picture Transformation.- 8.6.1 Bilinear Interpolation.- 8.6.2 Interpolation Using DFT and SDFT.- 9. Measuring the Coordinates of Objects in Pictures.- 9.1 Problem Formulation.- 9.2 Localizing a Precisely Known Object in a Spatially Homogeneous Picture.- 9.3 Uncertainty in the Object and Picture Inhomogeneity. Localization in "Blurred" Pictures.- 9.3.1 "Exhaustive" Estimator.- 9.3.2 Estimator Seeking an Averaged Object.- 9.3.3 Adjustable Estimator with Fragment-by Fraament Optimal Fi1tering.- 9.3.4 Non-Adjustable Estimator.- 9.3.5 Localization in Blurred and Noisy Pictures.- 9.4 Optimal Localization and Picture Contours. Choice of Reference Objects.- 9.5 Algorithm for the Automatic Detection and Extraction of Bench-Marks in Aerial and Space Photographs.- 10-Conclusion.- References.

218 citations


Journal ArticleDOI
TL;DR: A three-dimensional photon beam calculation is described which models the primary, first- scatter, and multiple-scatter dose components from first principles and uses the finite fast Fourier transform to perform the required convolutions.
Abstract: A three-dimensional photon beam calculation is described which models the primary, first-scatter, and multiple-scatter dose components from first principles Three key features of the model are (1) a multiple-scatter calculation based on diffusion theory, (2) the demonstration of the modulation transfer function of the radiation dose transport process, and (3) the use of the finite fast Fourier transform to perform the required convolutions The results of calculations for cobalt-60 in a homogeneous phantom are used to verify the accuracy of the model

179 citations


Journal ArticleDOI
TL;DR: It is shown how the effort can be reduced for nonlinear convolution equations for Volterra integral equations with the use of Fast Fourier Transform techniques.
Abstract: Numerical methods for general Volterra integral equations of the second kind need $O(n^2 )$ kernel evaluations and $O(n^2 )$ additions and multiplications. Here it is shown how the effort can be reduced for nonlinear convolution equations. Exploiting the convolution structure, most numerical methods need only $O(n)$ kernel evaluations. With the use of Fast Fourier Transform techniques only $O(n(\log n)^2 )$ additions and multiplications are necessary. The paper closes with numerical examples and comparisons.

178 citations


Proceedings ArticleDOI
26 Apr 1985
TL;DR: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented and a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.
Abstract: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented. First, the mapping into a 2-D discrete Fourier transform (DFT) of a real signal is improved. Then an usual polynomial transform approach is used in order to map the 2-D DFT into a reduced size 2-D DFT and one dimensional odd DFT's. Finally, optimized odd DFT algorithms for real signals are developped. All together, a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.

117 citations


Proceedings ArticleDOI
26 Apr 1985
TL;DR: This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one) and can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.
Abstract: A new algorithm is presented for the fast computation of the Discrete Fourier Transform. This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one). Moreover, this algorithm has the advantage of being performed "in-place", by repetitive use of a "butterfly"- type structure, without any data reordering inside the algorithm. Furthermore, it can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.

109 citations


Journal ArticleDOI
TL;DR: In this paper, the surface response of an infinite, homogeneous elastic plate to an internal dislocation across an infinitestimal area is investigated by means of a classical integral transform in the frequency domain and the spectral response of the plate is expressed in terms of the modal contributions due to the real, imaginary and complex roots of the Rayleigh-Lamb equation.
Abstract: The surface response of an infinite, homogeneous elastic plate to an internal dislocation across an infinitestimal area is investigated. As a companion problem, the normal displacement of the plate surface due to a time-dependent surface load is also calculated. The first problem is relevant for the detection of crack initiation in structural materials through the analysis of high-frequency elastic waves generated by the event. The solution to the second problem is needed for the calibration of test equipment used in the detection of the waves. The problems are formulated by means of a classical integral transform in the frequency domain and the spectral response of the plate is expressed in terms of the modal contributions due to the real, imaginary, and complex roots of the Rayleigh-Lamb equation. Time histories of the response are obtained through the inversion of the spectra by a Fast Fourier Transform (FFT) routine.

104 citations


Patent
19 Nov 1985
TL;DR: In this article, a monolithic high performance processor for computing digital signal processing algorithms based on the Fast Fourier Transform (FFT) is presented. But the processor uses local asynchronous control and simple interfacing with the host computer.
Abstract: A monolithic high performance processor for computing digital signal processing algorithms based on the Fast Fourier Transform. The monolithic processor employs an array of bit-serial multipliers which cooperate with bit-serial adder/substractors to produce fast results with great precision, with reduced printed-circuit board space, and with low power requirements. The processor uses local asynchronous control and simple interfacing with the host computer. The processor, which is applicable to a broad spectrum of digital signal processing, including digital audio, radar/sonar, seismic and speech processing, operates in a variety of modes which allow the device to perform Fast Fourier Transforms, Inverse Fast Fourier Transforms, windowing, multiplication, Finite Impulse Response filtering, convolution and correlation.

101 citations


Journal ArticleDOI
TL;DR: One, iterative reweighted least squares (IRLS), is discussed with an eye toward improving its computational efficiency, while the other, residual steepest descent (RSD) is considered in an attempt to improve its convergence properties.
Abstract: This paper discusses two algorithms for l_{p}, 1 \leq p \leq 2 , deconvolution. One, iterative reweighted least squares (IRLS), is discussed with an eye toward improving its computational efficiency, while the other, residual steepest descent (RSD), is considered in an attempt to improve its convergence properties. In the first case, fast Fourier transforms are used to reduce the number of computations. In the second, a new rescaling procedure which enhances RSD convergence is introduced. The lack of stability of l 1 , filters, and its implications are discussed. Simple examples are used to illustrate pertinent concepts.

Journal ArticleDOI
TL;DR: A “prime factor” Fast Fourier Transform algorithm is described which is self-sorting and computes the transform in place and it is obtained that the required indexing is actually simpler than that for a conventional FFT.

Journal ArticleDOI
TL;DR: Different simulation models are investigated with emphasis given to a model based on the vector diffraction analysis of a curved reflector with displaced panels, which is used to reconstruct the location and amount of displacement of the surface panels by employing a fast Fourier transform (FFT)/iterative procedure.
Abstract: The performance of large reflector antennas can be improved by identifying the location and amount of their surface distortions and then by correcting them. Microwave holography techniques are finding considerable applications as viable tools for performing this task. In these techniques, the complex (amplitude and phase) far-field pattern of the antenna is measured, using a reference antenna. Then, the Fourier transform relationship, which exists between the far field and a function related to the induced current, is invoked to result in the identification of the surface distortions. To critically examine the accuracy of the constructed surface profiles, simulation studies are required to incorporate both the effects of systematic and random distortions, particularly the effects of the displaced surface panels. In this paper, different simulation models are investigated with emphasis given to a model based on the vector diffraction analysis of a curved reflector with displaced panels. The simulated far-field patterns are then used to reconstruct the location and amount of displacement of the surface panels by employing a fast Fourier transform (FFT)/iterative procedure. The sensitivity of the microwave holography technique based on the number of far-field sampled points, level of distortions, polarizations, illumination tapers, etc., is also examined. In addition, the relationships between Az-El and u-v spaces are addressed in the Appendix. Most of the data are tailored to the dimensions of the NASA/JPL Deep Space Network (DSN) 64-m reflector antennas for which the result of a recent measurement is also presented.

Journal ArticleDOI
TL;DR: The algorithm is in essence a fast implementation of the Trench algorithm in reverse and involves imbedding of the given matrix in a cyclic matrix and a fast HD (half-divisor) algorithm to compute the first row of the inverse matrix.
Abstract: A fast algorithm for the solution of a Toeplitz system of equations is presented. The algorithm requires order N(\log N)^{2} computations where N is the number of equations. For banded Toeplitz matrices the order of computations is reduced to only N \log N + m(\log m)^{2} where 2m is the maximum number of nonzero principal subdiagonals of the Toeplitz matrix. The algorithm is in essence a fast implementation of the Trench algorithm in reverse. Thus, the algorithm involves imbedding of the given matrix in a cyclic matrix and a fast HD (half-divisor) algorithm to compute the first row of the inverse matrix. The desired solution is then obtained directly from the first row by applying fast Fourier transform techniques in order N \log N computations. Finally, the extension of the algorithm to block Toeplitz matrices is also presented.

Journal ArticleDOI
TL;DR: In this paper, a new method for the calculation of absorption in inhomogeneous, lossy dielectrics is presented by exploiting the convolutional nature of the electric field integral equation.
Abstract: A new method for the calculation of absorption in inhomogeneous, lossy dielectrics is presented. In this method, the convolutional nature of the electric-field integral equation is exploited by use of the FFT algorithms and the conjugate gradient method (CGM). The method is illustrated by solving for the SAR distribution for an anatomical cross transsection through the human eyes at 1 GHz.

Journal ArticleDOI
TL;DR: In this paper, a least squares parameter identification technique for a class of deterministic nonlinear systems modeled by polynomial input-output differential equations is formulated for one-shot and sequential least squares.
Abstract: A least-squares parameter identification technique is formulated for a class of deterministic nonlinear systems modeled by polynomial input-output differential equations. The basis of the technique is Shinbrot's method of moment functionals using trigonometric modulating functions. Given the input-output data over a single finite time interval for a one-shot estimate, or over a sequence of finite time intervals for sequential least squares, the underlying computations utilize a fast fourier transform algorithm on polynomials of the data without the need for estimating unknown initial or boundary conditions at the start of each finite time interval.

Journal ArticleDOI
TL;DR: In this paper, a new method for the solution of the time dependent Schrodinger equation, expressed in polar or spherical coordinates, is presented, where the radial part of the Laplacian operator is computed using Fast Hankel Transform.

01 Jan 1985
TL;DR: In this article, two algorithms for Ip, 1 Q p Q 2, deconvolution are discussed with an eye toward improving its computational efficiency, while the other, residual steepest descent (RSD), is considered in an attempt to improve its convergence properties.
Abstract: Abstracl-This paper discusses two algorithms for Ip, 1 Q p Q 2, deconvolution. One, iterative reweighted least squares(IRLS), isdiscussed with an eye toward improving its computational efficiency, while the other, residual steepest descent (RSD), is considered in an attempt to improve its convergence properties. In the first case, fast Fourier transforms are used to reduce the number of computations. In the second, a new rescaling procedure which enhances RSD convergence is introduced. The lack of stability of I1, filters, and its implications are discussed. Simple examples are used to illustrate pertinent concepts.

Journal ArticleDOI
TL;DR: An ‘objective’ algorithm which takes account of the specificity and the sensitivity of the procedure of maximum frequency detection, based on the statistical characteristics of FFT spectral estimators, and allows thresholds to be set to be used in two-step decision procedures.
Abstract: Real-time spectral analysis is often used to detect the maximum frequency envelope of Doppler signals, and thus the so-called spectral broadening, which is claimed to be a sensitive indicator of arterial stenosis. However, a rational criterion for the estimation of maximum frequencies is lacking. In the paper an ‘objective’ algorithm which takes account of the specificity and the sensitivity of the procedure of maximum frequency detection is proposed. This algorithm is based on the statistical characteristics of FFT spectral estimators, and allows thresholds to be set to be used in two-step decision procedures. The proposed algorithm can be easily implemented on microcomputers and/or commercial spectral analysers. The results obtained are fairly independent of the operator’s subjective judgement and spectral analyser gain.

Journal ArticleDOI
TL;DR: An exact performance analysis of the BLMS algorithm is presented and an optimal choice of this gain is presented resulting in the fastest convergence rate of the algorithm.
Abstract: An exact performance analysis of the BLMS algorithm is presented in this paper. Based on equations describing second statistics behavior, bounds are derived for the adaptation gain guaranteeing convergence of the algorithm. Within these bounds an optimal choice of this gain is presented resulting in the fastest convergence rate of the algorithm.

Journal ArticleDOI
TL;DR: In this article, the conjugate gradient method was applied to the deconvolution problem in the time domain, which is solved by passing the autocorrelation matrix computation, storage required is 5N as opposed to N2.
Abstract: Since it is impossible to generate and propagate an impulse, often a system is excited by a narrow time-domain pulse. The output is recorded and then a numerical deconvolution is often done to extract the impulse response of the object. Classically, the fast Fourier transform (FFT) technique has been applied with much success to the above deconvolution problem. However, when the signal-to-noise ratio becomes small, sometimes one encounters instability with the FFT approach. In this paper, the method of conjugate gradient is applied to the deconvolution problem. The problem is solved entirely in the time domain. The method converges for any initial guess in a finite number of steps. Also, for the application of the conjugate gradient method, the time samples need not be uniform, like FFT. Since, in this case, one is solving the operator equation directly, by passing the autocorrelation matrix computation, storage required is 5N as opposed to N2. Computed impulse response utilizing this technique has been presented for measured incident and scattered fields.

18 Nov 1985
TL;DR: A new domain decomposed fast Poisson solver on a rectangle divided into parallel strips or boxes is presented, which is especially suited for parallel implementation, since the independent problems in the subdomains can be solved in parallel, and the communication involves the interface variables only.
Abstract: : This document presents a new domain decomposed fast Poisson solver on a rectangle divided into parallel strips or boxes. The method first performs uncoupled fast solves on each subdomain, and then the interface variables are computed exactly by fast Fourier transform, without computing or inverting the capacitance matrix explicitly. Finally, the solution on the interior of the subdomains can be computed by one more fast solve on each subdomain. This method, as opposed to others, does not involve any iteration in the solution of the system for the interface variables. It is especially suited for parallel implementation, since the independent problems in the subdomains can be solved in parallel, and the communication involves the interface variables only. Keywords: parallel processing. (Author)

Journal ArticleDOI
TL;DR: In this article, an autoregressive model fitting with singular value decomposition is applied to the interferogram data measured by a Fourier transform spectrometer to estimate superresolving spectra.
Abstract: Autoregressive model fitting with singular value decomposition is applied to the interferogram data measured by a Fourier transform spectrometer to estimate superresolving spectra. The interferogram data matrix is decomposed into singular values with eigenvectors and its generalized inverse matrix is used for estimating the coefficients of the autoregressive model. This method suppresses the noise component in the data and avoids the risk of producing spurious peaks, which were the problem inherent in our earlier work using the maximum entropy method [ Appl. Opt.22, 3593 ( 1983)]. The experimental results of superresolving spectral estimation are shown with the data of a visible emission spectrum and infrared absorption spectra.

Journal ArticleDOI
TL;DR: This work sets up a relationship to a general class of linear and nonlinear fast algorithms such as FFT, FWT, and optimal sorting using a slightly modified Viterbi algorithm of an increased basis.
Abstract: The Viterbi algorithm is an efficient technique to estimate the state sequence of a discrete-time finite-state Markov process in the presence of memoryless noise. This work sets up a relationship to a general class of linear and nonlinear fast algorithms such as FFT, FWT, and optimal sorting. The performance of a Viterbi detector is a function of the minimum distance between signals in the observation space of the estimated Markov process. It is shown that this distance may efficiently be calculated with dynamic programming using a slightly modified Viterbi algorithm of an increased basis.

Journal ArticleDOI
TL;DR: This paper presents a method to transform a recursive computation task into a VLSI structure systematically, and presents a constant threshold estimation for hierarchical scene matching.
Abstract: VLSI technology has recently received increasing attention due to its high performance and high reliability. Designing a VLSI structure systematically for a given task becomes a very important problem to many computer engineers. In this paper, we present a method to transform a recursive computation task into a VLSI structure systematically. The main advantages of this approach are its simplicity and completeness. Several examples, such as vector inner product, matrix multiplication, convolution, comparison operations in relational database and fast Fourier transformation (FFT), are given to demonstrate the transformation procedure. Finally, we apply the proposed method to hierarchical scene matching. Scene matching refers to the process of locating or matching a region of an image with a corresponding region of another view of the same image taken from a different viewing angle or at a different time. We first present a constant threshold estimation for hierarchical scene matching. The VLSI implementation of the hierarchical scene matching is then described in detail.

Journal ArticleDOI
TL;DR: The storage allocation requirement and solution speed of the k-space formulation of the scattering problem in the time domain developed by Bojarski as mentioned in this paper were improved by a factor of 2 and 4, respectively, by the replacement of the earlier two temporal propagators by a single more accurate propagator and the utilization of the special case real to complex FFT algorithm.
Abstract: The storage allocation requirement and solution speed of the k‐space formulation of the scattering problem in the time domain developed by this author [N Bojarski, J Acoust Soc Am 72, 570–584 (1982)] were improved by a factor of 2 and 4, respectively, by the replacement of the earlier two temporal propagators by a single more accurate propagator and the utilization of the special case real to complex FFT algorithm It is shown that for problems of the size of about one million spatially discretized cells this method is about five times slower than an ideal solution, and requires about five times as much in core storage allocation as an ideal solution It is shown that for a modern array processor this solution is I/O bound It is pointed out that this method is ideally suited for parallel array processor implementation, resulting in even greater speed

Journal ArticleDOI
C. Stanghan1, B. MacDonald
TL;DR: In this paper, a theoretical model to assess the signal degradation caused by the packaging of new devices is discussed, and its predictions are compared with results from time domain reflectometry (TDR) and network analysis measurements.
Abstract: Advances in silicon bipolar and GaAs FET technology have enabled digital circuits of medium complexity to be fabricated for operation at gigabit rates. However, signal degradation caused by the packaging of these new devices will limit their useful application. A theoretical model to help assess this problem is discussed, and its predictions are compared with results from time domain reflectometry (TDR) and network analysis measurements. Also described is a novel exlension of the TDR technique based on the use of fast Fourier transform (FFT) analysis, including the design of test fixtures and the analysis software which is run on a desktop computer. The results presented demonstrate that both the model and the FFT measurement technique accurately represent the electrical performance of all those packages tested.

Journal ArticleDOI
R. Tolimieri1, S. Winograd1
TL;DR: In the final section, approximation theory is applied directly to the problem of computing the discrete ambiguity function, and the algorithm required to carry out the necessary computations turns out to be the same as on the prevoius approximation method based on a decimating FIR filter.
Abstract: The computation of the discrete ambiguity function is considered. Two straightforward methods are developed depending upon whether we write the discrete ambiguity as a filter or as a discrete Fourier transform. A modification of the transform method produces an approximation to the discrete ambiguity function, but has increased computational efficiency. This method is based on a recent work [1]. In most major applications, we need to compute limited portions of the DFT description of the discrete ambiguity function. To do so, we first pass a long sequence of "data" through a decimated FIR filter, and then use the FFT algorithm on the results. The Remez algorithm is employed to control the resulting aliasing errors. In the final section, approximation theory is applied directly to the problem of computing the discrete ambiguity function. The algorithm required to carry out the necessary computations turns out to be the same as on the prevoius approximation method based on a decimating FIR filter.

Journal ArticleDOI
TL;DR: Computer techniques for implementing the Marr-Hildreth edge detection operator, −∇2G(r) and its space-time extensions are considered and it is shown how this kind of convolution operation may be carried out simply and efficiently by factorizing the mask and performing the multidimensional convolution as a sequence of one-dimensional convolutions.
Abstract: Computational techniques for implementing the Marr-Hildreth edge detection operator, −∇2G(r) and its space-time extensions are considered. It is shown how this kind of convolution operation may be carried out simply and efficiently by factorizing the mask and performing the multidimensional convolution as a sequence of one-dimensional convolutions. For ad-dimensional mask of sizen, the computational effort required in order to carry out the sequence of 1D convolutions varies roughly asd2n compared tond for a multidimensional convolution. Computational examples carried out on a SIMD machine (an ICL Distributed Array Processor—DAP) are described and it is shown that convolution with masks of radius 8 on 64 × 64 images can be carried out in 13 ms in two dimensions (mask support ≈ 200 pixels) and 21 ms in three dimensions (support ≈ 2000 pixels). A brief comparison is made with the FFT technique for performing the convolution.

Journal ArticleDOI
01 Dec 1985
TL;DR: In this paper, it was shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than using a complex Fast Fourier Transform.
Abstract: It is shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than by using a complex Fast Fourier Transform. However, more sophisticated FFT algorithms exist which give the same speedup factor. A simple FHT subroutine is presented to illustrate the similarity of the FHT and FFT butterflies in their simplest forms.