Abstract: In this paper we consider algorithms of phase and group correlation which are based on different assumptions regarding the character of wave field. In order to construct the correlation algorithm, the wave field is presented as a product of an envelope and a normalized seismogram. Phase correlation is performed on the normalized seismogram, while group correlation is performed on the perigram, a low cut version of the envelope function. The central point of the correlation algorithm is the construction of a functional which characterizes the main correlation properties of the wave field. This functional is computed for different values of parameters which appear in the expressions approximating phase and group traveltime curves. Several types of correlation functionals are considered. The next step of the correlation algorithm is analysis of the previously obtained functionals; this is performed using a system of inequalities based on a number of assumptions regarding the properties of wave fields. The re...

Abstract: An iterative technique has been used to improve the design and performance of the binary phase version of a tandem-component correlation filter. The results are compared to a regular matched filter, a phase-only filter (POF), and a binary phase POF, in terms of optical efficiency, SNR, and peak correlation intensity.

Abstract: Users of the Cooley–Tukey Fast Fourier Transform algorithm may wish to test the hypothesis that their data contain genuine periodicities rather than a sequence of independent values. Tables are provided to enable them to do this at three different levels of significance.

Abstract: The realization of the Fourier image of a two-dimensional object without using a lens is described. The two-dimensional Fourier transform is generated optically by means of a periodic array of pin-holes (the sampling filter). The object is illuminated by a monochromatic, coherent plane wave and sampled by the pin-hole array. Multiple Fourier images of the object appear in certain planes behind the sampling filter. The simple theory of this phenomenon, together with experimental results, is given.

Abstract: This paper presents a silhouette-slice theorem for convex opaque 3-D objects. The theorem states that the 2-D Curvature Transform (CT) of any silhouette contour is a slice of the 3-D CT of the object surface at some appropriate orientation. The 2-D and 3- D CT's are defined as curvature functions on the Gaussian circle and sphere of the silhouette and object, respectively. The new theorem and transforms are shown to be the counterparts in silhouette imaging of the projection-slice theorem and Fourier Transforms of line-integral projection imaging.

Abstract: In a recent paper we investigated the problem of reconstructing the magnitude of a 2-D complex signal f from samples of the Fourier transform of f lying in a small region off-set from the origin. The primary application of interest was synthetic aperture radar. We showed that high quality speckle reconstructions are possible so long as the phase of f is highly random. In this paper we explore the possibility of Fourier-offset reconstruction from just the phase of the Fourier transform. We provide and compare a large number of computer simulated image reconstructions from phase plus magnitude, phase only (constant magnitude), magnitude only (zero phase), and from magnitude plus quantized phase. A number of conclusions are drawn regarding Fourier-offset phase-only reconstruction and several topics are suggested for further research.

Abstract: Autoregressive prediction is adapted to double the resolution of Angle-Resolved Photoemission Extended Fine Structure (ARPEFS) Fourier transforms. Even with the optimal taper (weighting function), the commonly used taper-and-transform Fourier method has limited resolution: it assumes the signal is zero beyond the limits of the measurement. By seeking the Fourier spectrum of an infinite extent oscillation consistent with the measurements but otherwise having maximum entropy, the errors caused by finite data range can be reduced. Our procedure developed to implement this concept applies autoregressive prediction to extrapolate the signal to an extent controlled by a taper width. Difficulties encountered when processing actual ARPEFS data are discussed. A key feature of this approach is the ability to convert improved measurements (signal-to-noise or point density) into improved Fourier resolution.

Abstract: A method of producing nuclear magnetic resonance image data which represent a characteristic of a target, is described which comprises, at least, the steps of: a) exciting the target with a magnetic field and a radio frequency pulse; b) applying at least one time-varying magnetic field gradient to the target; c) collecting data from the target during the step of applying the at least one time varying magnetic field gradient, by acquiring a data signal from target which data signal is dependent on the values of a Fourier transform of the characteristic of the target at a plurality of sample points in the Fourier space occupied by the Fourier transform; d) determining the positions of the data signal sample points on a path in the Fourier space which path is defined as a constant times the integral of the timvarying gradient; e) interpolating the value of the data signals at a plurality of Cartesian grid points in the Fourier space using the positions and values of the data signal at the sample points in the Fourier space; and f) converting the value of the data signals at the Cartesian grid points in the Fourier space by Fourier transform to a spatial domain to produce the image data of the characteristic of the target.

Abstract: This paper suggests a new data multiplication window for use with the Fourier Transform. The window is complex and consists of a linear FM chirp which spans the range 0 to 21r. Windowing in this manner is shown to be particularly useful for complex data signals such as those observed at the outputs of in-phase and quadrature component receivers. As such, it has application to both communications and radar problems. For the case of an input consisting of a single complex sinusoid, the new window produces an extremely sharp null located exactly at the frequency of the input sinusoid. As such, it has resolution properties far superior to those available via more conventional windowing techniques such as the raised cosine. Examples are presented showing clear indications of frequency shifts as small as 1/8 bin. Applications to real data environments are discussed.

Abstract: When the cross spectrum is estimated where there is a delay between the two input signals, it is shown that the corresponding misalignment gives both magnitude and phase errors. The existence of the phase error is a new result. The importance of the errors depend on the algorithms used. It is shown that the misalignment may either be given by the total observation time or by the section length in the processor. In the latter case the effect of phase errors must be considered when the section length is low, that is when the cross spectrum is smooth, requiring little resolution.

Abstract: To estimate the position of a subpicture P1 (with unknown angular misaligment) in a contour map P2, a method based on Fourier descriptors of multidirectional gradient codes is suggested It is assumed that P2 is characterized by a set of magnitudes at equally spaceddiscrete points over a rectangular area; and P1 is described by a set of magnitudes at discrete points on directional axes emanated from a point with magnitude c* Using the measurements of P1, the multidirectional gradient or successive-gradient codes and their Fourier descriptors are generated A contour map for P2 having c* as one of the isopleth values is then obtained For each point on all c*-isopleths, a two-level classifier, utilizing information derived from the Fourier descriptors and the phase correlation function, is used to estimate the possible location of P1 in P2 Simulation has indicated that in many cases the angular misalignment and the position of P1 with respect to P2 can be determined