Showing papers on "Discrete Fourier transform published in 1997"

Ground-roll suppression using the wavelet transform

Abstract: Low-frequency, high-amplitude ground roll is an old problem in land-based seismic field records. Current processing techniques aimed at ground-roll suppression, such as frequency filtering, f - k filtering, and f - k filtering with time-offset windowing, use the Fourier transform, a technique that assumes that the basic seismic signal is stationary. A new alternative to the Fourier transform is the wavelet transform, which decomposes a function using basis functions that, unlike the Fourier transform, have finite extent in both frequency and time. Application of a filter based on the wavelet transform to land seismic shot records suppresses ground roll in a time-frequency sense; unlike the Fourier filter, this filter does not assume that the signal is stationary. The wavelet transform technique also allows more effective time-frequency analysis and filtering than current processing techniques and can be implemented using an algorithm as computationally efficient as the fast Fourier transform. This new filtering technique leads to the improvement of shot records and considerably improves the final stack quality.

Fractional wavelet transform.

Abstract: The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform. Optical implementation of this transform is briefly discussed.

A new frequency tracking and phasor estimation algorithm for generator protection

Abstract: Digital generator protection is a complex and difficult problem. Analog and solid state methods have been successfully applied to generator protection in the past and implementation of these functions in a digital device is a continuing trend. This paper explores a new method to implement frequency tracking and phasor estimation in a numerical relay. A new algorithm is presented which utilizes a variable window discrete Fourier transform (DFT) for frequency tracking. Use of the DFT to compute the phasor estimates at a frequency other than the assumed frequency is outlined first. Next, a new technique for tracking the frequency is outlined. The paper concludes with testing of the new algorithm.

Use of Fourier and Karhunen-Loeve decomposition for fast pattern matching with a large set of templates

Abstract: We present a fast pattern matching algorithm with a large set of templates. The algorithm is based on the typical template matching speeded up by the dual decomposition; the Fourier transform and the Karhunen-Loeve transform. The proposed algorithm is appropriate for the search of an object with unknown distortion within a short period. Patterns with different distortion differ slightly from each other and are highly correlated. The image vector subspace required for effective representation can be defined by a small number of eigenvectors derived by the Karhunen-Loeve transform. A vector subspace spanned by the eigenvectors is generated, and any image vector in the subspace is considered as a pattern to be recognized. The pattern matching of objects with unknown distortion is formulated as the process to extract the portion of the input image, find the pattern most similar to the extracted portion in the subspace, compute normalized correlation between them at each location in the input image, and find the location with the best score. Searching for objects with unknown distortion requires vast computation. The formulation above makes it possible to decompose highly correlated reference images into eigenvectors, as well as to decompose images in frequency domain, and to speed up the process significantly.

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

Abstract: Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp z-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

Short Term Spectral Analysis, Synthesis, and Modification by Discrete Fourier Transform

Abstract: A theory of short term spectral analysis, synthesis, and modification is presented with an attempt at pointing out certain practical and theoretical questions. The methods discussed here are useful in designing filter banks when the filter bank outputs are to be used for synthesis after multiplicative modifications are made to the spectrum.

Efficient algorithm for discrete sinc interpolation

Abstract: A new computing method for discrete-signal sinc interpolation suitable for use in image and signal processing and the synthesis of holograms is described. It is shown to be superior to the commonly used zero-padding interpolation method in terms of interpolation accuracy, flexibility, and computational complexity.

Extraction of spectral peak parameters using a short-time Fourier transform modeling and no sidelobe windows

Abstract: A new method which improves the estimation of frequency, amplitude and phase of the partials of a sound is presented. It allows the reduction of the analysis-window size from four periods to two periods. It therefore gives better accuracy in parameter determination, and has proved to remain efficient at low signal-to-noise ratios. The basic idea consists of using a parametric modeling of the short-time Fourier transform. The method alternately estimates the complex amplitudes and the frequencies starting from the result of the classical analysis method. It uses the least-square procedure and a first-order limited expansion of the model around previous estimations. This method leads us to design new windows which do not have any sidelobes in order to help the convergence. Finally an analysis algorithm which has been built according to the observed behavior of the method for various kinds of sound is presented.

Uniform time-sampling Fourier transform spectroscopy

Abstract: We show that uniform time sampling of both the reference and the target channels in a continuous scanning Fourier transform spectrometer is a simple and versatile way of extending the Nyquist limit shorter than the wavelength of the reference channel. We also discuss the benefits of recording the reference channel when intensity calibrating the target data.

Modified Fourier transform method for interferogram fringe pattern analysis.

Abstract: A modified Fourier transform method for interferogram fringe pattern analysis is proposed. While it retains most of the advantages of the Fourier transform method, the new method overcomes some drawbacks of the previous method. It eliminates the assumptions of slowly varying phase variation in the test section and the constant spatial carrier frequency. It also extends the frequency bandwidth and avoids phase distortion caused by discreteness of the sampling frequency. Both numerical simulation and experimental examination are performed to evaluate the performance of the method.

Simulation of Multivariate Nonstationary Random Processes: Hybrid DFT and Digital Filtering Approach

Abstract: A numerical simulation scheme is presented that combines the advantages of the discrete Fourier transform algorithm and a digital filtering scheme to generate nonstationary multivariate random processes. The resulting time histories provide piecewise continuous evolutionary spectra and the proposed simulation technique offers significant computational efficiency. The effectiveness of the proposed technique is demonstrated with examples. The simulated records are in excellent agreement with the prescribed probabilistic characteristics. The proposed technique has immediate applications to the simulation of ground motions, evolutionary sea states, and fast-moving gust fronts.

Adaptive short-time Fourier analysis

Abstract: This article presents a method of adaptively adjusting the window length used in short-time Fourier analysis, related to our earlier work in which we developed a means of adaptively optimizing the performance of the cone kernel distribution (CKD). The optimal CKD cone length is, by definition, a measure of the interval over which the signal has constant or slowly changing frequency structure. The article shows that this length can also be used to compute a time-varying short-time Fourier transform (STFT). The resulting adaptive STFT shares many desirable properties with the adaptive CKD, such as the ability to adapt to transient as well as long-term signal components. The optimization requires O(N) operations per step, less than the fast Fourier transform (FFT) used in computing each time slice, making it competitive in complexity with nonadaptive time-frequency algorithms.

Optical implementation of the fractional Hilbert transform for two-dimensional objects.

Abstract: The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is π-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.

Demodulation using a time domain guard interval with an overlapped transform

Abstract: A system and method for demodulation of an RF signal on a transmission channel is provided. The RF signal is demodulated to baseband as an in-phase (I) data signal and a quadrature (Q) data signal. A first block of I data is captured and a first block of Q data is captured. A time domain guard interval is provided in the captured first blocks of I and Q data. A complex discrete Fourier transform is performed on the captured first I and Q data blocks. An inverse frequency response for the transmission channel is determined. The inverse frequency response is multiplied by the complex discrete Fourier transform of the guard-interval protected first I and Q data blocks to generate a frequency domain product signal. An inverse Fourier transform on the product of the multiplying step is performed to generate a first equalized time domain signal. In a preferred embodiment, the method also includes using an overlapped Fourier transform and discarding a first portion of each equalized time domain signal.

Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive.

Abstract: Optical-computing technology offers new challenges to algorithm designers since it can perform an n-point discrete Fourier transform (DFT) computation in only unit time. Note that the DFT is a nontrivial computation in the parallel random-access machine model, a model of computing commonly used by parallel-algorithm designers. We develop two new models, the DFT–VLSIO (very-large-scale integrated optics) and the DFT–circuit, to capture this characteristic of optical computing. We also provide two paradigms for developing parallel algorithms in these models. Efficient parallel algorithms for many problems, including polynomial and matrix computations, sorting, and string matching, are presented. The sorting and string-matching algorithms are particularly noteworthy. Almost all these algorithms are within a polylog factor of the optical-computing (VLSIO) lower bounds derived by Barakat Reif [Appl. Opt.26, 1015 (1987) and by Tyagi Reif [Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing (Institute of Electrical and Electronics Engineers, New York, 1990) p. 14].

Numerical investigation of phase retrieval in a fractional Fourier transform

Abstract: Recently the combination of the Gerchberg–Saxton (GS) algorithm and a fractional Fourier transform was proposed to implement beam shaping in the fractional Fourier domain [ Zalevsky , Opt. Lett.21, 842 (1996)]. We generalize this idea to deal with the problem of phase retrieval from two intensity measurements in a fractional Fourier transform system. The relevant equations for determining the unknown phases are derived, based on the general theory of amplitude–phase retrieval in an optical system. The unitarity condition of the fractional Fourier transform in a practical optical system with finite aperture is discussed. For different fractional orders P, the phase retrieval of several typical model images is studied in detail. A comparison of the GS and our algorithms is given, based on numerical simulations. It follows that our algorithm can offer the desired phase in all cases considered. However, the GS algorithm may fail when the transform system is nonunitary.

Decoding real block codes: activity detection Wiener estimation

Abstract: New decoding procedures for real-number block codes which are constructed by imposing constraints in the discrete Fourier transform (DFT) domain are examined. The codewords are corrupted by small levels of roundoff noise and possibly occasionally by a few large excursions of random disturbances. The error-correcting procedure is separated into two parts, large activity detection followed by error value estimation, particularly the larger errors. The first part determines if large excursions are present, roughly identifying their locations, while the second part is a Wiener minimum mean-squared error estimation technique providing a stochastic correction to the corrupted components. The activity-detecting part determines locations for large increases in the Wiener estimator's gain. A computationally intensive Bayes hypothesis testing approach is shown to be very effective at locating large activity positions, but a more efficient modified Berlekamp-Massey (1969) algorithm is developed which leads to excellent mean-squared error performance. Extensive simulations demonstrate individual codeword corrective actions and compare the average mean-squared error performance between coded and unprotected data. The error level improvement ranges from three to four orders of magnitude.

The Time Variant Discrete Fourier Transform as an Order Tracking Method

Abstract: Present order tracking methods for solving noise and vibration problems are reviewed, both FFT and resampling based order tracking methods. The time variant discrete Fourier transform (TVDFT) is developed as an alternative order tracking method. This method contains many advantages which the current order tracking methods do not possess. This method has the advantage of being very computationally efficient as well as the ability to minimize leakage errors. The basic TVDFT method may also be extended to a more complex method through the use of an orthogonality compensation matrix (OCM) which can separate closely spaced orders as well as separate the contributions of crossing orders. The basic TVDFT is a combination of the FFT and the re-sampling based methods. This method can be formulated in several different manners, one of which will give results matching the re-sampling based methods very closely. Both analytical and experimental data are used to establish the behavioral characteristics of this new method.

Optimal selection of parameters for the angular spectrum approach to numerically evaluate acoustic fields

Abstract: Optimal selection of parameters is presented for the angular spectrum approach (ASA) to the numerical calculation of acoustic fields radiated by planar transducers and linear arrays with and without focusing. The parameters include spatial sampling interval, discretization size of a source plane in which a source is located, and the angular range over which the plane waves decomposed from the source using the discrete Fourier transform (DFT) are chosen to superimpose and construct the fields. The concept of instantaneous frequency is applied to the Fourier transformed Green’s function to determine the angular range of the plane waves used for the construction with minimal spatial aliasing error. Based on the minimization of spatial frequency and spatial aliasing errors in a constructed field, optimal selection of the parameters is worked out. The ASA with the optimal selection is then applied to computing the fields radiated by planar transducers and linear arrays into water and a layered (oil/water) medi...

Short-time Fourier analysis via optimal harmonic FIR filters

Abstract: The Fourier coefficients (FCs) of quasiperiodic signals are assumed to be in random walk motion in order to represent a broader class. A state model for such quasiperiodic signals is derived. The optimal short-time estimate of the Fourier coefficients is obtained via the suggested optimal harmonic FIR filter (OHFF) based on this state-space signal model. The optimal harmonic FIR filter can be considered to be a generalization of the discrete Fourier transform (DFT) in the sense that it becomes the same as the DFT when the state model is for periodic signals and the filter length is equal to the order of the state model. The optimal harmonic FIR filter derived from the model, even with nonzero state noise and measurement noise, gives an exact harmonic estimate when an incoming signal is periodic and noiseless. It is shown by examples that the ability to suppress noise and the ability to resolve changes of the Fourier coefficients can be adjusted by the filter length and the noise covariance of the state model. Finally, the suggested scheme is compared with existing short-time Fourier analysis methods in a test signal that has time-varying Fourier coefficients.

A novel FSK demodulation method using short-time DFT analysis for LEO satellite communication systems

Abstract: This paper proposes a novel frequency-shift keying (FSK) demodulation method using short-time discrete Fourier transform (ST-DFT) analysis for low-Earth-orbit (LEO) satellite communication systems. The ST-DFT-based FSK demodulation method is simple and robust to a large and time-variant frequency offset because it expands the received signal in a time-frequency plane and demodulates it only by searching the instantaneous spectral peaks with no complicated carrier-recovery circuit. Two kinds of demodulation strategies are proposed: a bit-by-bit demodulation algorithm and an efficient demodulation-algorithm frequency-sequence estimation (FSE) based on the Viterbi algorithm. In addition, in order to carry out an accurate ST-DFT window synchronization, a simple DFT-based ST-DFT window-synchronization method is proposed.

An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

Abstract: Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general.

Fast resynchronization system for high-speed data transmission

Abstract: A system for resynchronizing the timing and carrier phases of a modem receiver signal to enable the receiver to quickly reacquire the timing phase and the carrier phase, and thereby restart the demodulation process. The system provides accurate estimates of the timing and carrier phases, as well as a gain correction factor to provide for proper alignment for decoding. The discrete Fourier transform of the received signal is multiplied by the complex conjugate of the discrete Fourier transform of the transmitted signal to produce estimates of the desired phases. Gain control and carrier phase control are performed to determine corresponding error signals to adapt the resultant estimated timing and carrier phases, and gain correction.

Wavelet transform based fast approximate Fourier transform

Abstract: We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coefficients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational complexity is on the same order of the FFT, i.e. O(N log/sub 2/ N). The main advantage of the proposed algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals resulting in much less computation. Thus the new algorithm provides an efficient complexity vs. accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability.

Analysis-/synthesis-filtering system with efficient oddly-stacked singleband filter bank using time-domain aliasing cancellation

Abstract: An efficient implementation of oddly-stacked critically-sampled single sideband analysis/synthesis filter banks is achieved by application of a set of functions to time-domain and frequency-domain values before and after transformation. In one embodiment of an analysis filter bank, a forward pre-transform function groups blocks of N samples into blocks of 1/4N modified samples, a discrete transform generates frequency-domain coefficients in response to the modified samples, and a forward post-transform function generates spectral information in response to the frequency-domain transform coefficients. In one embodiment of a synthesis filter bank, an inverse pre-transform function groups spectral information into blocks of 1/4N frequency-domain transform coefficients, a discrete transform generates blocks of 1/4N time-domain transform coefficients in response to the frequency-domain transform coefficients, and an inverse post-transform function generates blocks of N time-domain samples in response to the time-domain transform coefficients. An implementation of an oddly-stacked Time Domain Aliasing Cancellation transform permits the length of the transformation to be adaptively selected.