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The reflection and transmission of rectangular and Gaussian pulses impinging on a periodically stratified slab are studied and a number of examples are illustrated and analyzed. The coupled waves approach is used to derive the reflection and transmission coefficient, then the fast Fourier transform is used to illustrate the transient responses.
Recent developments in the use of numerical methods for fluid flow simulation show an increasing tendency to use numerical operators that can, in various ways, be factored. Use of methods having this property often increases the accuracy and efficiency of computer codes. Tracing the factorization property provides a unity to the basic concepts involved in the development of cyclic reduction, predictor-corrector, splitting, fast Fourier transform, and pseudospectral methods.-
The effect on the buckling load of a hinge at the center of an infinite beam supported by a semiinfinite elastic continuum is analyzed using the complex Fourier transforms. An expression is obtained for the relationship between the surface deflection of the elastic continuum and the pressure distribution acting on the surface, and solutions are obtained for the assumed form of the pressure distribution below the beam. The analysis is applied to cases of uniform pressure over the width of the beam and a pressure distribution that occurs below a rigid stamp. The results show that the buckling loads for an infinite beam with a hinge at the center and supported by a semiinfinite elastic continuum are approximately one half of those for a beam without a hinge, and that this ratio is exactly one half for an infinite beam resting on a Winkler foundation.
Experimental results in astronomy obtained with the aid of infrared heterodyne detection techniques are considered, taking into account the detection of thermal emission with no dispersion at the intermediate frequency and observations involving molecular line detection. The tuning range of a heterodyne spectrometer and of a Fourier transform spectrometer is considered and attention is given to the selection of the appropriate technique for a specific investigative problem.-
Over a three-year period 800 thermal line scans of power plant plumes were made by an airborne scanner, with ground truth measured concurrently at the plants. Computations using centered finite differences in the thermal scanning imagery show a lower bound in the horizontal temperature gradient in excess of 1.6 C/m. Gradients persist to 3 m below the surface. Vector plots of the velocity of thermal fronts are constructed by tracing the front motion in successive thermal images. A procedure is outlined for the two-point ground calibration of a thermal scanner from an equation describing the scanner signal and the voltage for two known temperatures. The modulation transfer function is then calculated by input of a thermal step function and application of digital time analysis techniques using Fast Fourier Transforms to the voltage output. Field calibration tests are discussed. Data accuracy is limited by the level of ground truth effort chosen.
Fourier transformation improves aerodynamic coefficients.
Employing scanning transmission electron microscope as interferometer, relative phases of diffraction maximums can be determined by analysis of dark field images. Synthetic aperture technique and Fourier-transform computer processing of amplitude and phase information provide high resolution images at approximately one angstrom.
External cavity for monolithic array of three GaAs lasers phase-coherently couples individual outputs to produce single spatially coherent beam. Fourier transform properties of lens and spatial filter are used to select coherent mode.
Ground reflections generate undesirable effects on acoustic measurements such as those conducted outdoors for jet noise research, aircraft certification, and motor vehicle regulation. Cepstral techniques developed in speech processing are adapted to identify echo delay time and to correct for ground reflection effects. A sample result is presented using an actual narrowband sound pressure level spectrum. The technique can readily be adapted to existing fast Fourier transform type spectrum measurement instrumentation to provide field measurements/of echo time delays.
The first phase of a research project directed toward development of a high speed automatic process to be used to match gun barrel signatures imparted to fired bullets was documented. An optical projection technique has been devised to produce and photograph a planar image of the entire signature, and the phototransparency produced is subjected to analysis using digital Fourier transform techniques. The success of this approach appears to be limited primarily by the accuracy of the photographic step since no significant processing limitations have been encountered.
A method of implementing a pipelined fast Fourier transform (FFT) is presented that makes full use of the elements that comprise it. For a given bandwidth and spectral resolution, this approach requires 25 percent less memory, and needs only half the logic speed required for the conventional implementation. Since the spectrum is broken into two parts, two analog-to-digital converters, and attendant mixer-filters, are needed. These two input elements need only operate at half the speed of the one they replaced.
The conceptual differences between the following two approaches used to measure spatial variations in steady-state acoustic pressure amplitude were examined: taking the cross spectrum between two signals from probes in the same field or taking the difference in complex Fourier transform of enhanced probe signals. Each approach is used to analyze pressure data from the inlets of two different turbomachines. A complete mapping of this steady-state field may then be used to determine its modal content. A problem with long term nonstationarity was found with both methods. Conditions for equivalence of the two methods are discussed.
The foreign object damage resistance of composite fan blades was studied. Edge impact stresses in an anisotropic plate were first calculated incorporating a constrained layer damping model. It is shown that a very thin damping layer can dramatically decrease the maximum normal impact stresses. A multilayer model of a composite plate is then presented which allows computation of the interlaminar normal and shear stresses. Results are presented for the stresses due to a line impact load normal to the plane of a composite plate. It is shown that significant interlaminar tensile stresses can develop during impact. A computer code was developed for this problem using the fast Fourier transform. A marker and cell computer code were also used to investigate the hydrodynamic impact of a fluid slug against a wall or turbine blade. Application of fluid modeling of bird impact is reviewed.
Spatially coherent radiation from a monolithic array of three GaAs lasers in a free-running mode is reported. The lasers, with their mirror faces antireflection coated, are operated in an external optical cavity built of spherical lenses and plane mirrors. The spatially coherent-beam formation makes use of the Fourier-transformation property of the internal lenses. Transverse mode control is accomplished by a spatial filter. The optical cavity is similar to that used for the phase-controlled mode of spatially coherent-beam formation; only the spatial filters are different. In the far field (when restored by an external lens), the intensities of the lasers in the array are concentrated in a single laser beam of spatial coherence, without any grating lobes. The far-field distribution of the laser array in the free-running mode differs significantly from the interference pattern of the phase-controlled mode. The modulation characteristics of the optical waveforms of the two modes are also quite different because modulation is related to the interaction of the spatial filter with the longitudinal modes of the laser array within the optical cavity. The modulation of the optical waveform of the free-running mode is nonperiodic, confirming that the fluctuations of the optical fields of the lasers are random.
Motivated by the problem of Mach number and temperature discontinuity mismatch between the tailpipe and the surrounding medium, and the effect of this flow mismatch on aircraft engine noise, the radiation of spinning turbo-acoustic modes from a round duct is investigated. The model, based on a plug flow exhaust jet, solves the convected wave equations using Fourier transforms, inversion being accomplished via a coupled Wiener-Hopf and Carrier-Koiter technique. It is concluded that the Mach number discontinuity results in a conflict between convection and refraction effects, while the temperature mismatch results in a sharp beaming of sound off to the side.
The application of Fourier Transform Spectroscopy (FTS) to planetary research is reviewed. The survey includes FTS observations of the sun, all the planets except Uranus and Pluto, The Galilean satellites and Saturn's rings. Instrumentation and scientific results are considered. The prospects and limitations of FTS for planetary research in the forthcoming years are discussed.
Ground reflections generate undesirable effects on acoustic measurements such as those conducted outdoors for jet noise research, aircraft certification, and motor vehicle regulation. This paper shows how cepstral techniques developed in speech processing can be adapted to identify the echo delay time and to correct for ground reflection effects. A sample result is presented using an actual narrowband sound pressure level spectrum. The technique can readily be adapted to existing fast Fourier transform type spectrum measurement instrumentation to provide field measurement of echo time delays.
Stigmatic spectra between 4160 and 4385 A of the central regions of M31 and M32 as well as the K0 III star 51 Ori are presented which were obtained using a SEC-vidicon integrating television tube and the coude spectrograph of the Hale telescope. Line-of-sight velocity dispersions of approximately 130 and 55 km/s are determined for the nuclei of M31 and M32, respectively, by directly comparing their spectra with Gaussian-broadened spectra of 51 Ori. The analytical techniques are outlined, and alternative methods for estimating velocity dispersions are evaluated, including least-squares fitting of intensities and division of Fourier transforms. It is noted that the broadened spectrum of 51 Ori fits the nucleus of M32 and the bulge of M31 much better than the nucleus of M31 in the region between 4180 and 4370 A.