Abstract: A scheme based on conjugate Fourier series is proposed for the determination of the dissipative mode of an optical constant from the corresponding dispersive mode, and vice versa. The connection between the conjugate Fourier series and Fourier integral method is discussed. The advantages of the method in relation to the Kramers-Kronig approach are outlined.

Abstract: A new coded-aperture configuration for gamma-ray imaging is described. It measures a single Fourier component of the object distribution at a time and does not require a position-sensitive detector. If, however, a position-sensitive detector is used, three-dimensional information about the source can be obtained.

Abstract: The use of simple off-the-shelf lenses as Fourier transform elements in an optical computer is considered. Several schemes for measuring those lens parameters that determine the performance of such simple lenses as Fourier transform elements are provided with emphasis on lens phase errors. It is assumed that no lens design data are available for the lens under test.

Abstract: The description of texture is an important problem in image analysis. Several methods in the literature require that local two-dimensional discrete Fourier transforms be computed as a first step in the texture description process. A chief limitation in these approaches has been the computational complexity of the transform calculation which has tended to limit the resolution of subsequent description and/or segmentation. It is shown here that through a suitable ordering of calculations, the transforms over a complete set of overlapping "texture windows" can be obtained efficiently. An algorithm is given and is shown to be time-optimal to within a constant factor.

Abstract: : Fourier transforms are efficient and convenient for analyzing local gravity data, but the accuracy of Fourier methods is restricted by the flat-earth approximation. In this paper, the theory of matched asymptotic (inner and outer) expansions is used to develop improved flat-earth approximations, determine regions of convergence, and match global (round-earth) and local (flat-earth) gravity models. Accurate solutions in the terms of Fourier transforms are given for the integrals of Poisson, Stokes, and Vening Meinesz. The new theory provides an error analysis of flat-earth algorithms and a systematic procedure for improving their accuracy. (Author)

Abstract: Fourier transforms are often useful in characterizing measured transient signals. It is shown that the amplitudes of such transforms are overestimated in the presence of normal zero-mean random noise. This bias is shown to be significant (greater than 5 percent) for signals with signal-to-noise ratios less than approximately 2.5:1. The result is independent of signal waveform.

Abstract: Interference techniques can be used to measure both the amplitude and phase of optically generated Fourier transforms. Because phase information is recovered by observing an interference pattern, source coherence can significantly influence phase accuracy. System performance is analyzed using simple test functions and the phase error is estimated in terms of the source transverse coherence length and space-bandwidth product of the input function.

Abstract: A short survey of some of the real variable methods recently developed in Fourier analysis for the study of the maximal operator associated to a sequence of operators.

Abstract: Procedures using cross-correlation functions to analyze telluric and magnetotelluric field data can be designed which, in certain applications, are more efficient than conventional techniques using fast Fourier transforms. One such application, involving the processing ofband-limited data, is presented here. The linear coupling relations between fields in a limited frequency band are estimated from transient time series by minimizing, in a least squares sense, the residuals between observed and predicted values of the frequency coefficients. The resulting normal equations contain integral averages over the continuous auto- and cross-energy spectra which are efficiently evaluated as Fourier transforms of windowed auto- and cross-correlation functions in the time domain.

Abstract: In the fast Fourier processor, Fourier analysis of the first signals and Fourier synthesis of the second signals takes place in brief alternation. The same fast fourier processor is used for Fourier analysis and Fourier synthesis and has the same linking instruction and the same store with the same coefficient. A sorting device controlled by the word cycle of the input signals of the processor separates the components of the signals generated by Fourier analysis from the components of the signals generated by Fourier synthesis. The sorting device also arranges the sequences of the signal components.