Showing papers on "Discrete Fourier transform published in 1991"

A digital recursive measurement scheme for online tracking of power system harmonics

Abstract: An optimal measurement scheme for tracking the harmonics in power system voltage and current waveforms is presented. The scheme does not require an integer number of samples in an integer number of cycles. It is not limited to stationary signals, but it can track harmonics with time-varying amplitudes. A review is first presented of the common frequency domain techniques for harmonics measurement. The frequency domain techniques are based on the discrete Fourier transform and the fast Fourier transform. Examples of pitfalls in the common techniques are given. The authors then introduce the concepts of the new scheme. This scheme is based on Kalman filtering theory for the optimal estimation of the parameters of time-varying harmonics. The scheme was tested on simulated and actual recorded data sets. It is concluded that the Kalman filtering algorithm is more accurate than the other techniques. >

Classification of rotated and scaled textured images using Gaussian Markov random field models

Abstract: Consideration is given to the problem of classifying a test textured image that is obtained from one of C possible parent texture classes, after possibly applying unknown rotation and scale changes to the parent texture. The training texture images (parent classes) are modeled by Gaussian Markov random fields (GMRFs). To classify a rotated and scaled test texture, the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the GMRF. For the rotated and scaled image, a bona fide likelihood function that shows the explicit dependence of the likelihood function on the GMRF parameters, as well as on the rotation and scale parameters, is derived. Although, in general, the scaled and/or rotated texture does not correspond to a finite-order GMRF, it is possible nonetheless to write down a likelihood function for the image data. The likelihood function of the discrete Fourier transform of the image data corresponds to that of a white nonstationary Gaussian random field, with the variance at each pixel (i,j) being a known function of the rotation, the scale, the GMRF model parameters, and (i,j). The variance is an explicit function of the appropriately sampled power spectral density of the GMRF. The estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete Fourier transform of the image data. Cramer-Rao error bounds on the scale and rotation estimates are easily computed. A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes. The classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album. >

Fast Fourier Transforms

Abstract: Basic aspects of fourier series definition of fourier series examples of fourier series fourier series of real functions pointwise convergence of fourier series further aspects of convergence of fourier series fourier sine series and cosine series convergence of fourier sine and cosine series the discrete fourier transform (DFT) the fast fourier transform (FFT) some applications of fourier series fourier transforms properties of fourier transforms inversion of fourier transforms convolution - an introduction the convolution theorem an application of convolution in quantum mechanics filtering, frequency detection, and removal of noise summation kernals arising from poisson summation fourier optics fresnel diffraction fraunhofer diffraction circular apertures the phase transformation induced by a thin lens imaging with a single lens user's manual for fourier analysis software some computer programmes the schwarz inequality.

DFT/FFT and Convolution Algorithms: Theory and Implementation

Abstract: From the Publisher: This readable handbook provides complete coverage of both the theory and implementation of modern signal processing algorithms for computing the Discrete Fourier transform. Reviews continuous and discrete-time transform analysis of signals and properties of DFT, several ways to compute the DFT at a few frequencies, and the three main approaches to an FFT. Practical, tested FORTRAN and assembly language programs are included with enough theory to adapt them to particular applications. Compares and evaluates various algorithms.

Cosine-modulated analysis-synthesis filterbank with critical sampling and perfect reconstruction

Abstract: The authors present a simple derivation of a parallel filterbank based on cosine-modulated versions of a model low-pass filter. With a nonuniform channel separation an efficient implementation consisting of a DFT (discrete Fourier transform) related transform and subfilters is possible. Using critical sampling of each channel and FIR (finite impulse response) filters, the conditions for perfect reconstruction are given. The computational complexity of the derived FIR filterbank is much lower than for a tree-structured FIR filterbank but cannot compete with the most efficient IIR filterbanks. >

A Parallel Algorithm For Computing Fourier Transforms On the Star Graph.

Abstract: The n-star graph, denoted by S/sub n/, is one of the graph networks that have been recently proposed as attractive alternatives to the n-cube topology for interconnecting processors in parallel computers. We present a parallel algorithm for the computation of the Fourier transform on the star graph. The algorithm requires O(n/sup 2/) multiply-add steps for an input sequence of n! elements, and is hence cost-optimal with respect to the sequential algorithm on which it is based. This is believed to be the first algorithm, and the only one to date, for the computation of the Fourier transform on the star graph. >

An experimental approach to analog fault models

Abstract: A comprehensive approach to model faults in analog circuits and systems based on experimental statistics of manufacturing defects is presented. A case study based on a simple sample-and-hold circuit is discussed with specific results. It is shown that the digital fault models are applicable to analog and mixed-signal circuits but they account only for catastrophic faults. Out-of-specification faults occur as often as catastrophic faults and must be addressed in any DFT (discrete Fourier transform) technique or test generation algorithm. >

Signals, systems, and transforms

Abstract: (NOTE: Each chapter begins with an Introduction and ends with a Summary and Problems). 1. Overview of Signals and Systems. Signals. Systems. 2. Continuous-Time and Discrete-Time Signals. PART A Continuous-Time Signals. Basic Continuous -Time Signals. Modification of the Variable t. Continuous-Time Convolution. PART B Discrete-Time Signals. Basic Discrete-Time Signals. Modification of the Variable n. Discrete-Time Convolution. 3. Linear Time-Invariant Systems. PART A Continuous-Time Systems. System Attributes. Continuous-Time LTI Systems. Properties of LTI Systems. Differential Equations and Their Implementation. PART B Discrete-Time Systems. System Attributes. Discrete-Time LTI Systems. Properties of LTI Systems. Difference Equations and the Their Implementation. 4. Fourier Analysis for Continuous-Time Signals. The Eigenfunctions of Continuous-Time LTI Systems. Periodic Signals and the Fourier Series. The Continuous-Time Fourier Transform. Properties and Applications of the Fourier Transform. APPLICATION 4.1 Amplitude Modulation. APPLICATION 4.2 Sampling. 5.Frequency Response of LTI Systems. APPLICATION 4.3 Filtering. 5. The Laplace Transform. The Region of Convergence. The Inverse Laplace Transform. Properties of the Laplace Transform. The System Function for LTI Systems. Differential Equations. APPLICATION 5.1 Butterworth Filters. Structures for Continuous-Time Filters. Appendix 5A The Unilateral Laplace Transform. Appendix 5B Partial-Fraction Expansion for Multiple Poles. 6. The z Transform. The Eigenfunctions of Discrete-Time LTI Systems. The Region of Convergence. The Inverse z Transform. Properties of the z Transform. The System Function to LTI Systems. Difference Equations. APPLICATION 6.1 Second-Order IIR Filters. APPLICATION 6.2 Linear-Phase FIR Filters. Structures for Discrete-Time Filters. APPENDIX 6A The Unilateral z Transform. APPENDIX 6B Partial-Fraction Expansion for Multiple Poles. 7. Fourier Analysis for Discrete-Time Signals. The Discrete-Time Fourier Transform. 2.Properties of the DTFT. APPLICATION 7.1 Windowing. 3.Sampling. 4.Filter Design by Transformation. 5.The Discrete Fourier Transform/Series. APPLICATION 7.2 FFT Algorithm. 8. State Variables. Discrete-Time Systems. Continuous-Time Systems. Operational-Amplifier Networks. Bibliography. Index.

Weighting effect on the discrete time Fourier transform of noisy signals

Abstract: The effect of weighting on the uncertainty of the discrete time Fourier transform (DTFT) samples of a signal corrupted by additive noise is investigated. Making very weak assumptions, it is shown how the adopted window sequence and the autocovariance function of the noise affect the second-order stochastic moments of the frequency-domain data. The relationship obtained extends the results reported in the literature and is useful in many frequency-domain estimation problems. It is shown how the knowledge of the second-order moments of the transform has allowed the application of the least squares technique for the estimation of the parameters of a multifrequency signal in the frequency-domain. The estimator obtained is very useful when high-accuracy results are required under real-time constraints. The procedure exhibits a better accuracy than similar frequency-domain methods proposed in the literature. >

A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms

Abstract: The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder Theorem.

Signal processing apparatus and method for iteratively determining Arithmetic Fourier Transform

Abstract: A signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signal. The signal processing apparatus and method utilize a process in which a data set of samples is used to iteratively compute a set of frequency samples, wherein each computational iteration utilizes error information which is calculated between the initial data and data synthesized using the AFT. The iterative computations converge and provide AFT values at the Farey-fraction arguments which are consistent with values given by a zero-padded Discrete Fourier Transform (DFT), thus obtaining dense frequency domain samples without interpolation or zero-padding.

A quantitative comparison of the TERA modeling and DFT magnetic resonance image reconstruction techniques.

Abstract: The resolution of magnetic resonance images reconstructed using the discrete Fourier transform (DFT) algorithm is limited by the effective window generated by the finite data length. The transient error reconstruction approach (TERA) is an alternative reconstruction method based on autoregressive moving average (ARMA) modeling techniques. Quantitative measurements comparing the truncation artifacts present during DIT and TERA image reconstruction show that the modeling method substantially reduces these artifacts on “full” (256 × 256), “truncated” (256 × 192), and “severely truncated” (256 × 128) data sets without introducing the global amplitude distortion found in other modeling techniques. Two global measures for determining the success of modeling are suggested. Problem areas for one-dimensional modeling are examined and reasons for considering two-dimensional modeling discussed. Analysis of both medical and phantom data reconstructions are presented. © 1991 Academic Press, Inc.

Spectral peak interpolation with application to LDA signal processing

Abstract: The discrete Fourier transform (DFT) finds widespread use in laser anemometry for the estimation of frequency, phase and signal-to-noise ratio (SNR) of individual Doppler signals. Peak interpolation is a common method for increasing the accuracy of these estimates without significantly adding to the computational load. Many methods for peak interpolation do not account for large variations in the peak width due to signal length variations, and thus often result in biased SNR estimates and/or frequency estimates. A new interpolation procedure is introduced which accounts for variable peak width and is adaptive, to avoid the usual periodicities inherent to this interpolation problem. Estimators of frequency and SNR based on this interpolation are compared with other commonly used methods using simulated LDA signals. The new estimators are shown to be more accurate and robust.

A new systolic array algorithm for discrete Fourier transform

Abstract: A new systolic algorithm for computing the discrete Fourier transform (DFT) is presented. The algorithm exhibits the minimum required time O(Nt/sub a/) and the computational complexity O(2N/sup 2/), which are much better than the time O(Nt/sub a/+Nt/sub m/) and the complexity O(4N/sup 2/) in existing systolic algorithms, where t/sub a/ and t/sub m/ are the computation time for a complex addition and a complex multiplication, respectively, and N is the DFT length. By exerting the benefits of the algorithm and adopting the scheme of tag control, a systolic array and a two-level pipelined systolic array are designed. The resulting arrays have outstanding performance on computing speeds, hardware cost, and the number of input/output (I/O) channels. >

Fourier transform of a linear distribution with triangular support and its applications in electromagnetics

Abstract: A three-dimensional Fourier transform (FT) of a linear function with triangular support is derived in its coordinate-free representation. The Fourier transform of this distribution is derived in three steps. First, the 2-D FT of a constant (top hat) function is obtained. Next, the distribution is generalized to a linearly varying function. Finally, the formulation is extended to a coordinate-free representation which is the 3-D FT of the 2-D function defined over a surface. This formulation is applied to the near-field computation, yielding accurate numerical solutions. >

Fast calculation apparatus for carrying out a forward and an inverse transform

Abstract: In an apparatus for carrying out a linear transform calculation on a product signal produced by multiplying a predetermined transform window function and an apparatus input signal, an FFT part (23) carries out fast Fourier transform on a processed signal produced by processing the product signal in a first processing part (21). As a result, the FFT part produces an internal signal which is representative of a result of the fast Fourier transform. A second processing part (22) processes the internal signal into a transformed signal which represents a result of the linear transform calculation. The apparatus is applicable to either of forward and inverse transform units (11, 12).

A new, efficient structure for the short-time Fourier transform, with an application in code-division sonar imaging

Abstract: Although most applications which use the short-time Fourier transform (STFT) temporally downsample the output, some applications exploit a dense temporal sampling of the STFT. One example, coded-division multiple-beam sonar, is discussed. Given a need for the densely sampled STFT, the complexity of the computation can be reduced from O(N log N) for the general short-time FFT structure to O(N) using the Goertzel algorithm. The authors introduce the pruned short-time FFT, a novel computational structure for efficiently computing the STFT with dense temporal sampling. The pruned FFT achieves the same computational savings as the Goertzel algorithm, but is unconditionally stable. >

Aliasing effects in Fourier transforms of monotonically decaying functions and the calculation of viscoelastic moduli by combining transforms over different time periods

Abstract: An analysis is presented of the discrete Fourier transform of a monotonically decaying function, represented by a sum of exponentials with negative exponents. The results are compared with those of a previous analysis based on the analytical Fourier transform, which proposed a method for extending the frequency range of the Fourier transform of experimental data by combining transforms performed over different time periods. The principle of the method is confirmed but comparison shows that results derived for the analytical transform cannot always be applied directly to the discrete transform. Modifications are therefore proposed which improve the accuracy and mitigate the aliasing effects evident in short-time transforms while keeping the computing time to a minimum. These results are particularly applicable to stress relaxation and creep in viscoelastic materials and an example from articular cartilage shows the compliance modulus over a frequency range from 10-3 Hz to 230 Hz from one creep experiment of duration 18.7 min.

Use of Fourier domain real-plane zeros to overcome a phase retrieval stagnation

Abstract: The iterative Fourier transform algorithm, although it has been demonstrated to be a practical phase retrieval algorithm, suffers from certain stagnation problems. Specifically, there exists a stripe stagnation problem, in which stagnated reconstructed images exhibit stripelike features throughout the image, which is particularly difficult to overcome. Previous solutions to this problem used multiple reconstructions and did not address the cause. In this paper a new procedure that uses only a single image is developed that estimates the locations of real-plane zeros from either the measured Fourier modulus data or a stagnated reconstruction and uses this information in the iterative Fourier transform algorithm to force the complex-valued Fourier data to have real-plane zeros at the correct locations. It is shown that this procedure overcomes the stripe stagnation.

Application of the Hartley transform for the analysis of the propagation of nonsinusoidal waveforms in power systems

Abstract: Because the Fourier transform causes the convolution operation to become a simple complex product, it has been used to solve power system problems. A similar convolution property of the Hartley transform is used to calculate transients and nonsinusoidal waveshape propagation in electric power systems. The importance of this type of calculation relates to the impact of loads, particularly electronic loads, whose demand currents are nonsinusoidal. An example is given in which the Hartley transform is used to assess the impact of an electronic load with a demand which contains rapidly changing current. The authors also present a general introduction to the use of Hartley transforms for electric circuit analysis. A brief discussion of the error characteristics of discrete Fourier and Hartley solutions is presented. Because the Hartley transform is a real transformation, it is more computationally efficient then the Fourier or Laplace transforms. >

The techniques of the generalized fast Fourier transform algorithm

Abstract: A general method of deriving DFT (discrete Fourier transform) algorithms, generalised fast Fourier transform algorithms, is presented. It is shown that a special case of the method is equivalent to nesting of FFTs. The application of the method to the case where N has mutually prime factors results in a new interpretation of the permutations characteristic of this class of algorithms. It is shown that the equalization of FFTs leads to results which are different from the widely used intuitive ones. The high efficiency of split-radix FFTs is explained. It is shown that the formulae of the method can be easily adapted for deriving algorithms for the cosine/sine DFT. A set of FFTs that has smaller arithmetical and/or memory complexities than any algorithm known is presented. In particular, a method of deriving split-radix-2/sup s/ FFTs requiring N log/sub 2/ N-3N+4 real multiplications and 3N log/sub 2/ N-3N+4 additions for any s>1 is presented. >

Efficient DFT-based model reduction for continuous systems

Abstract: A method for online identification of reduced-order models (ROM) of stable continuous systems is presented. The method is unique because it utilizes the moving discrete Fourier transform (MDFT) to continuously monitor the frequency-domain profile of the plant input and output signals. These signals need not be sinusoidal, although they must be accurately represented by their DFTs. Also, the input must contain at least n frequency components (for an nth-order ROM). A computer simulation demonstrates the method. >

Fast computation of real discrete Fourier transform for any number of data points

Abstract: In many applications, it is desirable to have a fast algorithm (RFFT) for the computation of the real discrete Fourier transform (RDFT) for any number of data points N. To achieve this, the two-factor Cooley-Tukey decimation-in-time and decimation-in-frequency RFFT algorithms are first developed and expressed in terms of matrix factorization using Kronecker products. This is generalized to any number of factors with arbitrary radices. Each factor M involves the computation of the size-M RDFT, which is carried out by the best size-M RFFT algorithm available. The RFFT algorithm for the case where M is a prime number is also developed. The RFFT algorithms are more efficient in the number of operations when the factors are arranged in a certain order, unlike the Cooley-Tukey complex FFT algorithms. which have the same number of operations for any order of the factors. >

Multi-velocity component LDV

Abstract: A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components.

Algorithms for processing fourier transform phase of signals

Abstract: The studies presented in this thesis represent an attempt to process the Fourier transform (FT) phase of signals for feature extraction. Although the FT magnitude and phase spectra are independent functions of frequency features of a signal, most techniques for feature extraction from a signal are bked upon manipulating the the FT magnitude only. The phase spectrum of the signal corresponds to time delay corresponding to each of the sinusoidal components of the signal. In the context of additive noise, the time delay may not be significantly corrupted and the phase spectrum might be considered to be a more reliable source for estimating the features in a noisy signal. Although the importance of phase in signals is realised by researchers, very few attempts have been made to process the FT phase of signals for the extraction of features. Features of a signal, for example, resonance information, is completely masked by the inevitable wrapping of the phase spectrum. An alternative to processing the phase spectrum is processing the group delay function. The group delay function is the negative derivative of the (unwrapped) FT phase spectrum. The group delay function can be computed directly from the time domain signal.The group delay function possesses additive and high resolution properties, in that it shows a squared magnitude behaviour in the vicinity of a resonance. But the group delay function in general is not well behaved for all classes of signals. Zeros in the z-transform of a signal that are close to the unit circle cause large amplitude spikes to appear in the group delay function. The polarity of a spike depends on the location of the zero with respect to the unit circle. These large amplitude spikes mask the information about resonances. The research effort in this thesis focusses on the development of algorithms for manipulating the group delay function to suppress the information corresponding to the zeros of th signal that are close to unit circle in the z-domain and emphasise the features of of a signal. To demonstrate the usefulness of the algorithms developed, these algorithms are used to estimate (a) formant and pitch data from speech signals and ( b ) estimate spectra of auto-regressive processes and sinusoids in noise. The research effort in this thesis shows that the phase spectrum (or rather the group delay function) of a signal can be usefully processed to reliably extract features of a signal. ACKNOWLEDCEMENT I express my appreciation to Prof.B.Yegnanarayana for his constant help, excellent guidance and constructive criticisms throughout the course of this work. I thank Prof. R. ~a~arajan, Head, Department of Computer Science and Engineering, for making the various facilities in the department available to me: I owe my special thanks to Madhu Murthy and C.P.Mariadassou for some fruitful discussions. I thank G. V. Ramana Rao and R. Ramaseshan for reading my thesis and making useful suggestions. I would like to thank all my colleagues of the Speech and Vision Lab who have helped me in one way or the other. I thank Vatsala for providing me a shoulder whenever I was depressed. Finally, I thank my husband M. V. N. Murthy for his support and perseverence throughout the course of this work.

Polyphase-discrete Fourier transform spectrum analysis for the Search for Extraterrestrial Intelligence sky survey

Abstract: The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch An improvement in sensitivity of approx 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI)