Showing papers on "Harmonic wavelet transform published in 1971"
TL;DR: The Fourier transform data communication system is described and the effects of linear channel distortion are investigated and a differential phase modulation scheme is presented that obviates any equalization.
Abstract: The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.
2,507 citations
TL;DR: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the Fast Fourier Transform (FFT) algorithm as discussed by the authors.
Abstract: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the 'fast Fourier transform' algorithm. The transform may be applied to the problem of calculating convolutions of long integer sequences by means of integer arithmetic.
431 citations
01 Feb 1971
TL;DR: In this paper, a technique is discussed and illustrated for transforming a sequence to a new sequence whose discrete Fourier transform is equal to samples of the z transform of the original sequence at unequally spaced angles around the unit circle.
Abstract: The discrete Fourier transform of a sequence, which can be computed using the fast Fourier transform algorithm, represents samples of the z transform equally spaced around the unit circle. In this letter, a technique is discussed and illustrated for transforming a sequence to a new sequence whose discrete Fourier transform is equal to samples of the z transform of the original sequence at unequally spaced angles around the unit circle.
189 citations
TL;DR: In this paper, the orthogonal nature of the Fourier transform (FT) is maintained by using the trapezoidal rule for the mechanical quadrature of the FT of one, two, and three dimensions.
128 citations
TL;DR: An arbitrary-radix fast Fourier transform algorithm and the design of its implementing signal processing machine are introduced, which yields an implementation with a level of parallelism proportional to the radix r of factorization of the discrete Fouriertransform.
Abstract: An arbitrary-radix fast Fourier transform algorithm and a design of its implementing signal processing machine are introduced. The algorithm yields an implementation with a level of parallelism proportional to the radix r of factorization of the discrete Fourier transform, allows 100 percent utilization of the arithmetic unit, and yields properly ordered Fourier coefficients without the need for pre- or postordering of data.
44 citations
TL;DR: In this article, the Fast Fourier Transform (FFT) was used to calculate time-displaced correlation functions from molecular dynamics data much more rapidly (less expansively) than by using the standard integration technique.
40 citations
TL;DR: The design of a class of special-purpose computers for time-series analysis by Fourier transformation is described, which implement machine-oriented fast Fourier transform algorithms obtained by factoring the discrete Fouriertransform to an arbitrary radix.
Abstract: The design of a class of special-purpose computers for time-series analysis by Fourier transformation is described. The computers are sequential machines which implement machine-oriented fast Fourier transform algorithms obtained by factoring the discrete Fourier transform to an arbitrary radix.
38 citations
29 citations
TL;DR: This paper investigates the use of the fast Fourier transform as an aid in the analysis and classification of spectroscopic data and sees how the pattern obtained after transformation is viewed as a weighted average and/or as a frequency representation of the original spectroscopy data.
Abstract: This paper investigates the use of the fast Fourier transform as an aid in the analysis and classification of spectroscopic data. The pattern obtained after transformation is viewed as a weighted average and/or as a frequency representation of the original spectroscopic data. In pattern recognition the Fourier transform allows a different (i.e., a frequency) representation of the data which may prove more amenable to linear separation according to various categories of the patterns. The averaging property means that the information in each dimension of the original pattern is distributed over all dimensions in the pattern resulting from the Fourier transformation. Hence the arbitrary omission or loss of data points in the Fourier spectrum has less effect on the original spectrum. This property is exploited for reducing the dimensionality of the Fourier data so as to minimize data storage requirements and the time required for development of pattern classifiers for categorization of the data. Examples of applications are drawn from low resolution mass spectrometry.
27 citations
TL;DR: In this paper, a method for refining and/or extending a set of crystallographic phases by real-space convolution utilizing the fast Fourier transform (FFT) algorithm was proposed.
Abstract: A method is formulated for refining and/or extending a set of crystallographic phases by real-space convolution utilizing the fast Fourier-transform algorithm. The method is applied to extending a set of myoglobin phases and the results show that high-resolution structural information can be obtained from high-resolution intensities and low-resolution phases.
TL;DR: In this letter, two methods for elim inating the entire zero order are described and the detectability of low spatial frequency components is thereby greatly improved and is now limited only by the background due to scattered light.
Abstract: For coherent optical fourier transformers, aperture tapering (apodization) has been discussed' as a method of improving the detectability of low spatial frequency signals that would other wise be obscured by zero-order light. By zero-order light we mean the light distribution in the transform plane, centered at the zero frequency point, due to the average of dc bias light at the input aperture. In this letter, two methods for elim inating the entire zero order are described. The detectability of low spatial frequency components is thereby greatly improved and is now limited only by the background due to scattered light.
TL;DR: The generalized matrix elements on the Poincaré group are used to write the Fourier transform explicitly as discussed by the authors, which realizes a mapping between positive type functions on the group and generalized density matrices.
Abstract: The generalized matrix elements on the Poincaré group are used to write the Fourier transform explicitly. This realizes a mapping between positive type functions on the group and generalized density matrices.
TL;DR: Some problems associated with Fourier analysis of reaction time data are indicated and convenient ways to overcome some of the difficulties are suggested.
Abstract: The popularity of the assumption of stages in models of the reaction time process and the availability of fast and efficient means of computing approximations to the Fourier transform makes the Fourier analysis of reaction time data attractive. This paper indicates some problems associated with such analyses and suggests convenient ways to overcome some of the difficulties.
TL;DR: In this paper, a time-varying Fourier transform is defined along with its related power and phase spectra and a convenient recursive technique to compute this transform is also presented.
Abstract: A time-varying Fourier transform is defined along with its related power and phase spectra. A convenient recursive technique to compute this transform is also presented.
01 Jan 1971
TL;DR: In this paper, the detection and estimation of a long-period wave function can be accomplished by a generalization of harmonic analysis along the framework of regression analysis, which computes a squared multiple correlation coefficient corresponding to any frequency, by regressing sine and cosine weights on the observed data.
Abstract: : Successive ordinates of the line spectrum as computed by means of the discrete Fourier transform indicate how the variance of a given time series is apportioned among the members of a set of orthogonal, i.e. harmonic, frequencies. The continuous Fourier transform provides a means of interpolation between these frequencies. However, when the original data include a long-period sinusoid whose frequency is below the fundamental, then neither the discrete nor the continuous Fourier transform gives a good indication of the presence of long-period wave function. The detection and estimation of such a function can be accomplished by a generalization of harmonic analysis along the framework of regression analysis. The procedure computes a squared multiple correlation coefficient corresponding to any frequency, by regressing sine and cosine weights on the observed data. The method and its applications are illustrated by simple numerical examples. (Author)
01 Jan 1971