Showing papers on "Non-uniform discrete Fourier transform published in 1981"

Estimation of Periods from Unequally Spaced Observations

Abstract: A better estimation of the power spectrum of a time series formed with unequally spaced observations may be obtained by means of a data-compensated discrete Fourier transform. This transform is defined so as to include the uneven spacing of the dates of observation and weighting of the corresponding data. The accurate determination of the peak heights allows one to design harmonic filters and thus to make a more certain choice among peaks of similar height and also to discriminate peaks that are just aliases of other peaks. The theory is applied to simulated time series and also to true observational data.

The Phase Retrieval Problem

Abstract: A method for solving the phase retrieval problem is proposed. The method consists of measuring the modulus of the Fourier transform of the unknown function and the modulus of the Fourier transform of the product of the unknown function and an exponential. From these two measurements, the location of the complex zeros of the analytic continuation of the Fourier transform of the unknown function may easily and quickly be deduced and the unknown function constructed.

Short-time Fourier analysis of sampled speech

Abstract: The theoretical basis for the representation of a speech signal by its short-time Fourier transform is developed. A time-frequency representation for linear time-varying systems is applied to the speech-production model to formulate a quasi-stationary representation for the speech waveform. Short-time Fourier analysis of the resulting representation yields the relationship between the short-time Fourier transform of the speech and the speech-production model.

Limited-Angle Three-Dimensional Reconstructions Using Fourier Transform Iterations And Radon Transform Iterations

Abstract: The principles of limited-angle reconstruction of space-limited objects using the concepts of "allowed cone" and "missing cone" in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time.

Method for continuing Fourier spectra given by the fast Fourier transform

Abstract: A new method for continuing the Fourier spectrum of data of finite extent has been developed. Almost perfect restoration was obtained for noise-free data. Much improved resolution was obtained for error-laden data. Many forms of peak data lend themselves easily to the application of additional constraints that further enhance resolution almost to the theoretical limit.

Non-linear wave propagation solutions by Fourier transform perturbation

Abstract: A Fourier transform perturbation method is developed and used to obtain uniformly valid asymptotic approximations of the solution of a class of one-dimensional second order wave equations with small non-linearities. Multiple time scales are used and the initial-value problem on the infinite line is solved by Fourier transforming the wave equation and expanding the Fourier transform in powers of the small parameter. The non-linearity involves only the first partial derivatives of the dependent variable and the determination of the leading approximation is reduced to the solution of a pair of coupled non-linear ordinary differential equations in Fourier space. Examples are given involving a convolution non-linearity and a Van-der-Pol non-linearity.

Fourier transform signal processor

Abstract: A hybrid opto-electronic method and apparatus for Fourier transform measurements of temporal signals are disclosed. The magnitude and phase of the signal transform are system outputs. High resolution spectral analysis operation is accomplished by proper spatial phase corrections, equivalent to aperture synthesis. Configurations for one-dimensional and two-dimensional input data formats are described. The disclosed method and apparatus can process signals with continuous spectral content as well as narrow spectral lines.

Achromatic Fourier transform holography.

Abstract: A method for producing Fourier transform holograms in spatially coherent but temporally broadband light is presented. The technique employs a broadband Fourier transforming system incorporated into an achromatic grating interferometer. The theory has been experimentally verified by producing a Fourier transform hologram in temporally broadband light from a high pressure Hg arc lamp.

Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique

Abstract: Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/πx is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high-frequency components.

The fast calculation of the exact distribution of pearson's chi-squared and of the number of repeats within the cells of a mltltinomial by using a fast fourier transform

Abstract: (1981). The fast calculation of the exact distribution of pearson's chi-squared and of the number of repeats within the cells of a mltltinomial by using a fast fourier transform. Journal of Statistical Computation and Simulation: Vol. 14, No. 1, pp. 71-78.

Fast computation of Fourier transforms at arbitrary frequencies

Abstract: An algorithm is proposed for computing the Fourier Transform (FT) of a uniformly sampled signal at arbitrary frequencies. In most of the applications, the algorithm retains the computational efficiency of the Fast Fourier Transform (FFT) algorithm. The method is based on the fact that the FT at an arbitrary frequency can be expressed as a weighted sum of its Discrete Fourier Transform (DFT) coefficients. In the proposed method, these weights are suitably approximated so that the desired FT is very nearly the sum of (i) a few dominant terms of the sum of the DFT which are computed directly, and (ii) the DFT of a new sequence obtained by multiplying the original sequence with a sawtooth function. The number of directly computed terms is so chosen that the error of approximation does not exceed the specified limits. The computational aspects of the algorithm and its error behavior with typical signals have been critically examined.

A performance analysis of adaptive line enhancer-augmented spectral detectors

Abstract: This paper discusses the receiver operating characteristic performance of Adaptive Line Enhancer (ALE) augmented spectral detectors for sinusoidal signals in both stationary white Gaussian noise and in nonstationary noise. The detectors considered are based on the discrete Fourier transform (DFT) and include both cases with and without incoherent integration. Analytical expressions are provided for the detector output probability density functions in the stationary noise case. Extensive Monte Carlo simulation results are used to verify these expressions, and to treat the nonstationary noise case.

Spectral Decomposition of EEG Intervals Using Walsh and Fourier Transforms

Abstract: This paper presents a comparison of the use of features derived from Walsh and Fourier transforms for classification of short segments of EEG data. The result was that features obtained from Fourier transforms produced consistently better classification results than Walsh function-derived features.

Walsh Versus Fourier Estimators of the EEG Power Spectrum

Abstract: Walsh-based discrete algorithms offer a fast, simple alternative to Fourier methods for estimating EEG power spectra, but their performance has been criticized. Previous comparisons of Fourier and Walsh estimators are reexamined, and they are compared experimentally, on simulated EEG. The evidence suggests that they should perform comparably for EEG monitoring.

A DFT-based residual-excited linear predictive coder (RELP) for 4.8 and 9.6kb/s

Abstract: The proposed RELP system is based on a DFT (discrete Fourier transform) of the linear prediction residual. The base-band Fourier coefficients, derived from frequencies 0 to 800 Hz, are transmitted to the receiver. For encoding, the Fourier coefficients are converted to polar representation reiφ. The quantization accuracy of both magnitude and phase angle is controlled by an adaptive-bit assignment algorithm. At the receiver, the non-transmitted Fourier coefficients are replaced by base-band coefficients which have been frequency-shifted pitch-synchronously. In the 4.8 kb/s version, the spectral translation algorithm is controlled only by the transmitted pitch frequency. In the 9.6 kb/s version, however, additional information for reconstruction of the harmonic structure in the high-frequency region is computed at the transmitter. Audio tapes of both versions are presented.

A new prime factor FFT algorithm

Abstract: This paper presents an approach to calculating the discrete Fourier transform (DFT) using a prime factor algorithm (PFA). A very simple indexing scheme is employed that results in a flexible, modular program that very efficiently calculates the DFT in-place. A modification of this indexing scheme gives a new algorithm with the output both in-place and in-order at a slight cost in flexibility. This means only 2N data storage is needed for a length N complex FFT and no unscrambling is necessary. The basic part of a FORTRAN program is given. A speed comparison shows the new algorithm to be faster than both the Cooley-Tukey and the nested Winograd algorithms.

New fast discrete sine transform with offset

Abstract: A new fast even discrete sine transform with offset (FEDSTo) has been developed and implemented for use in picture processing. This FEDSTo is faster than FDCTs for many block sizes and produces pictures that are subjectively much better than those of other available fast discrete transforms when only one-dimensional blocks are used and low sequency coefficients are retained for transmission.

An interpolation technique for periodically sampled two-dimensional signals

Abstract: Two-dimensional signals are usually represented for the purpose of digital processing as rectangularly sampled functions of two orthogonal independent variables. It has been previously noted that sampling a signal on a hexagonal grid can offer substantial savings in digital storage and computation. In this paper these two sampling schemes will be generalized, via a matrix description, to include arbitrarily sampled 2-D signals. Using this matrix description and a generalized discrete Fourier transform, a technique will be presented for interpolating a set of sample points from one sampling grid to an alternative one. Since the analog signal from which the original samples were obtained is frequently unavailable for resampling, the ability to easily convert from one sampling scheme to another can be important in the efficient processing of a particular signal.

Apparatus for inspecting average size of fundamental patterns

Abstract: An apparatus for determining the average size of fundamental patterns contained in a given region of an object to be inspected, which includes Fourier transform means for producing output data corresponding to a Fourier transform pattern image of the given region of the object, and processor means for processing the output data to provide the actual pattern size information. The Fourier transform means includes a Fourier converter for providing the output data corresponding to Fourier transform patterns. The processor means includes an extractor coupled to the Fourier transform means for extracting a single magnitude data (In) representing the order n of spatial frequency component (e.g. 200) from the output data, the magnitude of the order n component changing with variation (e.g. ΔaH) of the size of patterns; and a data processor coupled to the extractor for determining the average size of patterns in the given region according to the single magnitude (In) and providing the actual pattern size information indicating the averge size of the patterns.

A Time Domain Reflectometer Using a Semiautomatic Network Analyzer and the Fast Fourier Transform

Abstract: A time domain reflectometer system is simulated by measuring the reflection coefficient in the frequency domain and then computing the time domain signal by the Fourier transform. The program has been written for the Hewlett-Packard 8409A Semiautomatic Network Analyzer. The computation time has been minimized by using the fast Fourier transform. The problems imposed by the difficulty of switching the HP 8409A between low- and high-frequency ranges are also discussed.