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At least 127 records · Page 7

Efficient detection of a CW signal with a linear frequency drift

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series.

Swarztrauber, Paul N.↗

Impact on multilayered composite plates

Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.

Kim, B. S.↗

Broad-Bandwidth FPGA-Based Digital Polyphase Spectrometer

With present concern for ecological sustainability ever increasing, it is desirable to model the composition of Earth s upper atmosphere accurately with regards to certain helpful and harmful chemicals, such as greenhouse gases and ozone. The microwave limb sounder (MLS) is an instrument designed to map the global day-to-day concentrations of key atmospheric constituents continuously. One important component in MLS is the spectrometer, which processes the raw data provided by the receivers into frequency-domain information that cannot only be transmitted more efficiently, but also processed directly once received. The present-generation spectrometer is fully analog. The goal is to include a fully digital spectrometer in the next-generation sensor. In a digital spectrometer, incoming analog data must be converted into a digital format, processed through a Fourier transform, and finally accumulated to reduce the impact of input noise. While the final design will be placed on an application specific integrated circuit (ASIC), the building of these chips is prohibitively expensive. To that end, this design was constructed on a field-programmable gate array (FPGA). A family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved analog-to-digital converters (ADCs). This 6-Gsps (gigasample per second) digital representation of the analog signal is then processed through an FPGA-based streaming fast Fourier transform (FFT). Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers.

Jamot, Robert F.↗

Application of Fourier transforms for microwave radiometric inversions

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

Holmes, J. J.↗

Transient wave propagation in composite plates due to impact

Stress-wave propagation in a composite plate due to an impact has been examined using anisotropic elasticity theory. The plate is modelled as a number of identical anisotropic layers whose elastic moduli are given. Mindlin's (1959) approximate theory of plates is then applied to each layer to obtain a set of difference-differential equations of motion by using the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions these equations are solved for an arbitrary number of layers in the plate, and the transient propagation of a stress wave is calculated by means of a fast Fourier transform algorithm.

Sung Kim, B.↗

Wideband Spectroscopy: The Design and Implementation of a 3 GHz, 2048 Channel Digital Spectrometer

A state-of-the-art digital Fourier Transform spectrometer has been developed, with a combination of high bandwidth and fine resolution unavailable elsewhere. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved Analog-to-Digital Converters (ADC). This 6 Gsps (giga sample per second) digital representation of the analog signal is then processed through an FPGA-based streaming Fast Fourier Transform (FFT), the key development described below. Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers. The implementation, results and underlying math for this spectrometer, as well as potential for future extension to even higher bandwidth, resolution and channel orthogonality, needed to support proposed future advanced atmospheric science and radioastronomy, are discussed.

field programmable gate array↗

Wideband Spectroscopy: The Design and Implementation of a 3 GHz Bandwidth, 8192 Channel, Polyphase Digital Spectrometer

A family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution unavailable elsewhere. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved Analog-to-Digital Converters, (ADC). This 6 Gsps (giga-sample per second) digital representation of the analog signal is then processed through an FPGA-based streaming Fast Fourier Transform (FFT), the key development described below. Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers. the implementation, results and underlying math for this spectrometer, as well as, potential for future extension to even higher bandwidth, resolution and channel orthogonality, needed to support proposed future advanced atmospheric science and radioastronomy, are discussed.

field programmable gate array↗

Fourier analysis and signal processing by use of the Moebius inversion formula

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

Reed, Irving S.↗

Fast-Polynomial-Transform Program

Computer program uses fast-polynomial-transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional cyclic convolutions converted to one-dimensional convolutions in polynomial rings. Program decomposes cyclic polynomials into polynomial convolutions of same length. Only FPT's and fast Fourier transforms of same length required. Modular approach saves computional resources. Program written in C.

Truong, T. K.↗

Quantum Entanglement Molecular Absorption Spectrum Simulator

Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.

Nguyen, Quang-Viet↗

Rapid data comparison technique development for N-ray/X-ray analysis

An operational N-ray/X-ray computer analysis system for nondestructive testing problems was realized by developing: (1) more efficient data transfer routines for use in existing image processing systems; (2) the capability to store and analyze multiple N-ray/X-ray images; (3) an efficient 2-D Fast Fourier Transform; and (4) transfer functions compensation capability to correct for distortions and nonlinearities of N-rays/X-rays. Applications of the technique are summarized for the following: thermal protection system tile with hydraulic fluid; thermal protection system tile with corrosion; thermal protection system tile debonding; stainless steel tubing corrosion; defective electrical devices; fast film restoration and deblur; corrosion tracking over time; reduction of source vignetting, and identification of materials (0 rings, Teflon parts, soft goods) via table look up.

Butterfield, R. L.↗

NASA Tech Briefs, April 2011

Topics covered include: Amperometric Solid Electrolyte Oxygen Microsensors with Easy Batch Fabrication; Two-Axis Direct Fluid Shear Stress Sensor for Aerodynamic Applications; Target Assembly to Check Boresight Alignment of Active Sensors; Virtual Sensor Test Instrumentation; Evaluation of the Reflection Coefficient of Microstrip Elements for Reflectarray Antennas; Miniaturized Ka-Band Dual-Channel Radar; Continuous-Integration Laser Energy Lidar Monitor; Miniaturized Airborne Imaging Central Server System; Radiation-Tolerant, SpaceWire-Compatible Switching Fabric; Small Microprocessor for ASIC or FPGA Implementation; Source-Coupled, N-Channel, JFET-Based Digital Logic Gate Structure Using Resistive Level Shifters; High-Voltage-Input Level Translator Using Standard CMOS; Monitoring Digital Closed-Loop Feedback Systems; MASCOT - MATLAB Stability and Control Toolbox; MIRO Continuum Calibration for Asteroid Mode; GOATS Image Projection Component; Coded Modulation in C and MATLAB; Low-Dead-Volume Inlet for Vacuum Chamber; Thermal Control Method for High-Current Wire Bundles by Injecting a Thermally Conductive Filler; Method for Selective Cleaning of Mold Release from Composite Honeycomb Surfaces; Infrared-Bolometer Arrays with Reflective Backshorts; Commercialization of LARC (trade mark) -SI Polyimide Technology; Novel Low-Density Ablators Containing Hyperbranched Poly(azomethine)s; Carbon Nanotubes on Titanium Substrates for Stray Light Suppression; Monolithic, High-Speed Fiber-Optic Switching Array for Lidar; Grid-Tied Photovoltaic Power System; Spectroelectrochemical Instrument Measures TOC; A Miniaturized Video System for Monitoring Drosophila Behavior; Hydrofocusing Bioreactor Produces Anti-Cancer Alkaloids; Creep Measurement Video Extensometer; Radius of Curvature Measurement of Large Optics Using Interferometry and Laser Tracker n-B-pi-p Superlattice Infrared Detector; Safe Onboard Guidance and Control Under Probabilistic Uncertainty; General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets; Hidden Statistics of Schroedinger Equation; Optimal Padding for the Two-Dimensional Fast Fourier Transform; Spatial Query for Planetary Data; Higher Order Mode Coupling in Feed Waveguide of a Planar Slot Array Antenna; Evolutionary Computational Methods for Identifying Emergent Behavior in Autonomous Systems; Sampling Theorem in Terms of the Bandwidth and Sampling Interval; Meteoroid/Orbital Debris Shield Engineering Development Practice and Procedure; Self-Balancing, Optical-Center-Pivot, Fast-Steering Mirror; Wireless Orbiter Hang-Angle Inclinometer System; and Internal Electrostatic Discharge Monitor - IESDM.

Source record↗

Microprocessor implementation of an FFT for ionospheric VLF observations

A fast Fourier transform algorithm is implemented on a CMOS microprocessor for application to very low-frequency electric fields (less than 10 kHz) sensed on high-altitude scientific balloons. Two FFT's are calculated simultaneously by associating them with conjugate symmetric and conjugate antisymmetric results. One goal of the system was to detect spectral signatures associated with fast time variations present in natural signals such as whistlers and chorus. Although a full evaluation of the system was not possible for operational reasons, a measure of the system's success has been defined and evaluated.

Elvidge, J.↗

Rapid, high-order accurate calculation of flows due to free source or vortex distributions

Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.

Halsey, D.↗

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

White, Michael J.↗

On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

A fast algorithm is developed to compute two dimensional convolutions of an array of d sub 1 X d sub 2 complex number points, where d sub 2 = 2(M) and d sub 1 = 2(m-r+) for some 1 or = r or = m. This algorithm requires fewer multiplications and about the same number of additions as the conventional fast fourier transform method for computing the two dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

Truong, T. K.↗

Faster Processing for Inverting GPS Occultation Data

A document outlines a computational method that can be incorporated into two prior methods used to invert Global Positioning System (GPS) occultation data [signal data acquired by a low-Earth-orbiting satellite as either this or the GPS satellite rises above or falls below the horizon] to obtain information on altitude-dependent properties of the atmosphere. The two prior inversion methods, known as back propagation and canonical transform, are computationally expensive because for each occultation, they involve numerical evaluation of a large number of diffraction-like spatial integrals. The present method involves an angular-spectrum-based phase-extrapolation approximation in which each data point is associated with a plane-wave component that propagates in a unique direction from the orbit of the receiving satellite to intersect a straight line tangent to the orbit at a nearby point. This approximation enables the use of fast Fourier transforms (FFTs), which apply only to data collected along a straight-line trajectory. The computation of the diffraction-like integrals in the angular-spectrum domain by use of FFTs takes only seconds, whereas previously, it took minutes.

Ao, Chi↗

Tracking of Ice Edges and Ice Floes by Wavelet Analysis of SAR Images

This paper demonstrates the use of wavelet transforms in the tracking of sequential ice features in the ERS-1 synthetic aperture radar (SAR) imagery, especially in situations where feature correlation techniques fail to yield reasonable results. Examples include the evolution of the St. Lawrence polynya and summer sea ice change in the Beaufort Sea. For the polynya, the evolution of the region of young ice growth surrounding a polynya can be easily tracked by wavelet analysis due to the large backscatter difference between the young and old ice. Also within the polynya, a 2D fast Fourier transform (FFT) is used to identify the extent of the Langmuir circulation region, which is coincident with the wave-agitated frazil ice growth region, where the sea ice experiences its fastest growth. Therefore, the combination of wavelet and FFT analysis of SAR images provides for the large-scale monitoring of different polynya features. For summer ice, previous work shows that this is the most difficult period for ice trackers due to the lack of features on the sea ice cover. The multiscale wavelet analysis shows that this method delineates the detailed floe shapes during this period, so that between consecutive images, the floe translation and rotation can be estimated.

Liu, Antony K.↗