Showing papers on "Harmonic wavelet transform published in 1972"

A Recurrence Technique for Expanding a Function in Spherical Harmonics

Abstract: A recurrence technique is described that enables the use of proven efficient Fourier transform techniques to be applied to the expansion of a given function in terms of spherical harmonics.

Real-time Fourier transform with a surface-wave convolver

Abstract: The generation of Fourier transforms of electronic signals in real time with an acoustic-surface-wave convolver is demonstrated. Two matched chirps propagating through each other behave as a narrowband filter in wavevector space, with the filter centre moving at a rate proportional to the acoustic velocity and the chirp rate.

Accurate calculation of Fourier transform of two-center Slater orbital products†

Abstract: A method is presented which leads to accurate Fourier transform values of any 1s−1s Slater-type orbital overlap distribution. The numerical merits are discussed and illustrated by some examples.

Spectral errors resulting from random sampling-position errors in fourier transform spectroscopy.

Abstract: In the design and operation of a two-beam interferometer in Fourier spectroscopy, it is important to known how much the lack of precision in the setting of the optical path differences will affect the measured spectra. This problem has been considered by Surh, and by Sakai, who has given a relation for the stan­ dard deviation in the size of the \"ghost\" lines due to the random error in the sampling of the interferogram of a monochromatic spectral line. We will reformulate and extend the results to apply to a more general spectrum. Consider an interferogram P(x) which is sampled at optical path differences x = jΔx giving values Pj for N, conveniently an even integer, values of the integer j in the range — N/2 ≤ j < N/2. The discrete Fourier transform pair

The Application of Filtered Transforms to the General Classification Problem

Abstract: An image classification model based on nearest prototypes in filtered Fourier and Walsh transform domains is presented. A computer simulation of the model applied to handwritten English letters, Russian letters, numerals, and electromagnetic signals is also presented. Experiments to date fail to refute the working hypothesis that generalized harmonic analysis can be used to reliably classify alphabet characters, time-varying signals, and other images.

A Parallel Implementation of the Fast Fourier Transform Algorithm

Abstract: For many real-time signal processing problems, correlations, convolutions, and Fourier analysis must be performed in special-purpose digital hardware. At relatively high levels of performance, it becomes necessary for this hardware to perform some of its computations in parallel. A parallel FFT algorithm is described that segments the fast Fourier transform algorithm into groups of identical parallel operations that can be performed concurrently and independently. A hardware implementation of the algorithm is described in the context of the parallel element processing ensemble (PEPE) previously described by Githens [7], [8].

Computer Processing of Radiographic Images with the Finite Fourier Transform

Abstract: This paper considers the optimal design and implementation of two-dimensional, nonrecursive digital filters for use in the processing of radiographic images. A stochastic system model is used for the image-forming process, and the filter is designed to a mean-square error criterion. Both the design algorithm and filter realization are mechanized by using a Fast Fourier Transform code, thereby ensuring the computational efficiency of the method.

Automated design of large-signal amplifiers for minimum distortion

Abstract: A technique for the design of large-signal amplifiers for minimum distortion is presented. This technique takes advantage of the frequency-domain aspects of the problem by using the fast Fourier transform.

Automatic equalization and discrete Fourier transform techniques (Ph.D. Thesis abstr.)

Abstract: The primary objective of this thesis is the study and analysis of techniques that use discrete Fourier transforms (DFT) in conjunction with fast Fourier transform (FFT) algorithms for automatic equalization of synchronous data transmission. W e show that the problem of minimizing mean-square intersymbol interference can be analyzed in the discrete f requency domain as an optimization problem with constraints. Various solutions to this problem are studied including Rosen’s gradient projection method, Lagrange multipliers, and direct substitution. W e prove that the rate of convergence toward the opt imum parameter setting is faster for the gradient projection scheme, for channels usually d iscussed in the literature, than for the corresponding t ime-domain technique. W e then develop an alternative gradient projection method that provides savings proport ional to N/log, N in the number of required computat ions, where N is the number of discrete f requency parameters. Finally, we devise a scheme for finding an approximate solution in one iteration using gradient projection. This solution was found to be almost exact for the particular cases we simulated, even in the presence of noise. The speed of convergence for all the schemes is dependent on the overall channel characteristics and each method has advantages in certain special situations. W e show that all the aforement ioned methods converge in the mean in the presence of noise. A var iance bound indicates that the var iance about this setting is finite and can be made as small as desired by reducing the gradient step size and hence the speed of convergence. Our second objective is to use the DFT and FFT algorithms to make time domain equalization computationally more efficient. W e show that the number of computat ions needed to set a time domain equalizer can be made proport ional to M log, M instead of MZ, where M is the number of adjustable parameters, by use of FFT algorithms. Savings always ensue for sufficiently large M and grow rapidly thereafter. The breakeven point is approximately M = 16. W e also derive tight and easily obtainable bounds on the eigenvalues of the t ime-domain iteration matrix in terms of DFT coefficients. This allows us to increase the speed of convergence. Leonard P. W inkler, “Opt imum and adapt ive detector arrays,” Ph.D., Dep. Elec. Eng., Polytech. Inst. Brooklyn, Brooklyn, N.Y., June 1971. Adviser: Mischa Schwartz.

A note on the spectral analysis of periodic functions

Abstract: An analysis of the Fourier transform for a truncated cosine waveform is given that illustrates the dependence of the transform on the phase as the period of the waveform becomes large with respect to the record length. The effects of sampling on the transform are then discussed and illustrated.

Hadamard Transform for Speech Wave Analysis

Abstract: : Two methods of speech wave analysis using the Hadamard transform are discussed The first method is a direct application of the Hadamard transform for speech waves The reason this method yields poor results is discussed The second method is the application of the Hadamard transform to a log-magnitude frequency spectrum After the application of the Fourier transform the Hadamard transform is applied to detect a pitch period or to get a smoothed spectrum This method shows some positive aspects of the Hadamard transform for the analysis of a speech wave with regard to the reduction of processing time required for smoothing, but at the cost of precision A formant tracking program for voiced speech is implemented by using this method and an edge following technique used in scene analysis

Integral transform and fourier transform by fiber optics network.

Abstract: where S, x, u, and g(u) are the input plane, input plane coordi­ nates, the output plane coordinates, and the output light intensity. By selecting the kernel h(u,x), various types of transform are realized. In the pat tern recognition field, the Fourier transform is available since the Fourier spectrum gives the shift invariant features. Further, the matched filter, Hadamard or Walsh -Fourier transform, binary mask, etc. are also essentially the integral transform. Since the fiber optics bundle is composed of small areas, the input-output relationship is expressed by a discrete form rather than the integral form [Eq. (1)]; i.e., we have

On the efficient processing of sonar signals

Abstract: Techniques for processing active sonar signals using Fourier and Walsh transforms are discussed. A method is introduced which uses the Walsh-Hadamard transform and permits excellent processing economy. This economy plus the observed ability of the resultant processor to maintain quality estimation of target range and range rate may make this system quite practical for certain sonar detection applications.