Showing papers on "Phase correlation published in 1982"

NMR chemical shift imaging in three dimensions

Abstract: A method for obtaining the three-dimensional distribution of chemical shifts in a spatially inhomogeneous sample using Fourier transform NMR is presented. The method uses a sequence of pulsed field gradients to measure the Fourier transform of the desired distribution on a rectangular grid in (k,t) space. Simple Fourier inversion then recovers the original distribution. An estimated signal/noise ratio of 20 in 10 min is obtained for an "image" of the distribution of a 10 mM phosphorylated metabolite in the human head at a field of 20 kG with 2-cm resolution.

A Complete Set of Fourier Descriptors for Two-Dimensional Shapes

Abstract: A set of Fourier descriptors for two-dimensional shapes is defined which is complete in the sense that two objects have the same shape if and only if they have the same set of Fourier descriptors. It also is shown that the moduli of the Fourier coefficients of the parameterizing function of the boundary of an object do not contain enough information to characterize the shape of an object. Further a relationship is established between rotational symmetries of an object and the set of integers for which the corresponding Fourier coefficients of the parameterizing function are nonzero.

Signal reconstruction from the short-time Fourier transform magnitude

Abstract: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude. For applications such as speech processing, these conditions place very mild restrictions on the signal as well as the analysis window of the transform. Examples of such reconstruction for speech signals are included in the paper.

A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent

Abstract: The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.

Iterative Procedures For Signal Reconstruction From Fourier Transform Phase

Abstract: Recently, a set of conditions has been developed under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are distinctly different from the minimum or maximum phase requirement and are applicable to both one-dimensional and multi-dimensional sequences. Under the specified conditions, several numerical algorithms have been developed to reconstruct a sequence from its phase. In this paper, we review the recent theoretical results pertaining to the phase-only reconstruction problem, and we discuss in detail two iterative numerical algorithms for performing the reconstrucction.

Some approaches for location of centroids of quartz grain outlines to increase homology between Fourier amplitude spectra

Abstract: The ability to test for similarities and differences among families of shapes by closed-form Fourier expansion is greatly enhanced by the concept of homology. Underlying this concept is the assumption that each term of a Fourier series, when compared to the same term in another series, represents the “same thing”. A method that ensures homology is one which minimizes the “centering error,” as reflected in the first harmonic term of the Fourier expansion. The problem is to chose a set of edge points derived from a much larger, but variable, number of edge points such that a valid homologous Fourier series can be calculated. Methods are reviewed and criteria given to define a “proper” solution. An algorithm is presented which takes advantage of the fact that minimization of the “error term” can be accomplished by minimizing the distance between the origin of the polar coordinate system in the calculation of the Fourier series and the shape centroid. The use of this algorithm has produced higher quality solutions for quartz grain provenance studies.

Direct Fourier Transform NMR Tomography with Modified Kumar-Welti-Ernst(MKWE) Method

Abstract: Direct Fourier transform NMR tomographic method originally proposed by Kumar-Welti-Ernst(KWE) has been modified by double spin echo technique to improve the image quality. This new Modified-KWE(MKWE) method provides two quadrant data set in 2-D Fourier space which is essential for the accurate image representation of the NMR spin density. Further improvement of the MKWE method using the slice encoding technique and spin echo measurement time is also investigated.

Effects of noise on signal reconstruction from Fourier transform phase

Abstract: The effects of noise in the given phase on signal reconstruction from the Fourier transform phase are studied. Specifically, the effects of different methods of sampling the degraded phase, of the number of non-zero points in the sequence, and of the noise level on the sequence reconstruction are examined. A sampling method is developed to significantly reduce the error in the reconstructed sequence, and the error is found to increase as the number of non-zero points in the sequence increases and as the noise level increases. In addition, an averaging technique is developed which reduces the effects of noise when the continuous phase function is known. Finally, as an illustration of how the results in this paper may be applied in practice, Fourier transform signal coding is considered. Coding only the Fourier transform phase and reconstructing the signal from the coded phase is found to be considerably less efficient (i.e. a higher bit rate is required for the same mean square error) than reconstructing from both the coded phase and magnitude.

Simplified time-integrating acousto-optical processor for Fourier transformation.

Abstract: Novel concepts for simplification of the optical design of a time-integrating acousto-optical signal processor for real-time Fourier transformation are described. Fourier transforms of both pulsed and continuous signals, obtained from the triangular common-path interferometric setup, are demonstrated. Because of their simplicity, these concepts are suitable for designing ultracompact devices.

Analysis of a Magnetic Sphere Using the Fourier Transform: A New Approach

Abstract: A novel interpretation of the vertical magnetic effect of a sphere is developed using Fourier transforms Since the analytical expression of the magnetic effect of a sphere defies Fourier transformation, it is squared and the Fourier transform of the square is obtained From the real and imaginary components of the Fourier transform the depth to the centre of the sphere, the angle of magnetic polarization, and the radius of the sphere are obtained The validity of the method is tested on four theoretical models Also, a field example from the Bankura area in West Bengal (India) is tested and the evaluated parameters agree with those previously obtained by Rao et al (1977) An advantage of the present method is that location of the origin is not necessary The method can be run by computer to determine the parameters of the causative body

Bipolar VLSI facilitates Fourier transformation

Abstract: This paper describes an integrated address sequencer for the Fast Fourier Transform. It also shows how this may be included in a high-speed signal processing peripheral.