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NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper discusses the Dynamic Mode Decomposition (DMD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected with four Phantom high-speed cameras at a constant sample frequency in the Ascent Transient Aerodynamics Test (ATAT) of the Space Launch System (SLS) Block 1 cargo vehicle with the Unitary Plan Wind Tunnel (UPWT) 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD). For the data with zero mean, the DMD is equivalent to the Discrete Fourier Transform (DFT). Since the uPSP is mainly used to determine the unsteady property of the aerodynamic flow, the DMD of the uPSP measurements is implemented in two steps: (1) subtract the mean value from the uPSP measurement; (2) apply the Fast Fourier Transform (FFT) on the resulting data with zero mean. The DMD of the uPSP measurements with FFT has two advantages: (1) the FFT algorithm is well known for its computational efficiency, therefore, compared to the SVD-based DMD algorithm, the DMD with FFT reduces the computation time; (2) the DMD with FFT can be easily implemented in parallel processing. The DMD outputs were generated with the execution in parallel of a code in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, on the NASA Pleiades supercomputer. In this paper, the results of DMD of the uPSP measurements in the tests of Mach sweep runs of the SLS ATAT are presented, and the effectiveness of the DMD of the uPSP measurements in the diagnosis of the unsteady, aerodynamic phenomena is demonstrated. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding for this research was provided by the NASA Aeroscience Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
NASA NTRS1990

Propagation characteristics of optical fiber structures with arbitrary shape and index variation

The application of the scalar wave-fast Fourier transform (SW-FFT) technique to the computation of the propagation characteristics of some complex optical fiber structures is presented. The SW-FFT technique is based on the numerical solution of the scalar wave equation by a forward-marching fast Fourier transform method. This solution yields the spatial configuration of the fields as well as its modal characteristics in and around the guiding structure. The following are treated by the SW-FFT method: analysis of coupled optical fibers and computation of their odd and even modes and coupling length; the solution of tapered optical waveguides (transitions) and the study of the effect of the slope of the taper on mode conversion; and the analysis of branching optical fibers and demonstration of their mode-filtering and/or power-dividing properties.

Manshadi, F.↗
NASA NTRS1990

Time-dependent treatment of scattering - Integral equation approaches using the time-dependent amplitude density

The time-dependent form of the Lippmann-Schwinger integral equation is used as the basis of several new wave packet propagation schemes. These can be formulated in terms of either the time-dependent wave function or a time-dependent amplitude density. The latter is nonzero only in the region of configuratiaon space for which the potential is nonzero, thereby in principle obviating the necessity of large grids or the use of complex absorbing potentials when resonances cause long collision times (leading, consequently, to long propagation times). Transition amplitudes are obtained in terms of Fourier transforms of the amplitude density from the time to the energy domain. The approach is illustrated by an application to a standard potential scattering model problem where, as in previous studies, the action of the kinetic energy operator is evaluated by fast Fourier transform (FFT) techniques.

Hoffman, David K.↗
NASA NTRS2004

Temporal Characterization of Aircraft Noise Sources

Current aircraft source noise prediction tools yield time-independent frequency spectra as functions of directivity angle. Realistic evaluation and human assessment of aircraft fly-over noise require the temporal characteristics of the noise signature. The purpose of the current study is to analyze empirical data from broadband jet and tonal fan noise sources and to provide the temporal information required for prediction-based synthesis. Noise sources included a one-tenth-scale engine exhaust nozzle and a one-fifth scale scale turbofan engine. A methodology was developed to characterize the low frequency fluctuations employing the Short Time Fourier Transform in a MATLAB computing environment. It was shown that a trade-off is necessary between frequency and time resolution in the acoustic spectrogram. The procedure requires careful evaluation and selection of the data analysis parameters, including the data sampling frequency, Fourier Transform window size, associated time period and frequency resolution, and time period window overlap. Low frequency fluctuations were applied to the synthesis of broadband noise with the resulting records sounding virtually indistinguishable from the measured data in initial subjective evaluations. Amplitude fluctuations of blade passage frequency (BPF) harmonics were successfully characterized for conditions equivalent to take-off and approach. Data demonstrated that the fifth harmonic of the BPF varied more in frequency than the BPF itself and exhibited larger amplitude fluctuations over the duration of the time record. Frequency fluctuations were found to be not perceptible in the current characterization of tonal components.

Grosveld, Ferdinand W.↗
NASA NTRS1981

Study of high speed complex number algorithms

A method of evaluating the radiation integral on the curved surface of a reflecting antenna is presented. A three dimensional Fourier transform approach is used to generate a two dimensional radiation cross-section along a planer cut at any angle phi through the far field pattern. Salient to the method is an algorithm for evaluating a subset of the total three dimensional discrete Fourier transform results. The subset elements are selectively evaluated to yield data along a geometric plane of constant. The algorithm is extremely efficient so that computation of the induced surface currents via the physical optics approximation dominates the computer time required to compute a radiation pattern. Application to paraboloid reflectors with off-focus feeds in presented, but the method is easily extended to offset antenna systems and reflectors of arbitrary shapes. Numerical results were computed for both gain and phase and are compared with other published work.

Heisler, R.↗
NASA NTRS1990

Spatial heterodyne spectroscopy - Interferometric performance at any wavelength without scanning

Spatial heterodyne spectroscopy (SHS) employing a two-beam dispersive interferometer producing a Fizeau fringe pattern having wavelength-dependent spatial frequencies is presented. The pattern is recorded on an imaging detector and Fourier transformed to recover the input stream. It is pointed out that spectrometers operating on the SHS principle can achieve the theoretical resolution limit of the gratings without scanning, retaining at the same time the large angular input tolerance and multiplexing properties of conventional scanning Fourier-transform spectrometers. Additionally, broad spectral coverages can be achieved, and field widening can be accomplished without moving parts.

Roesler, F. L.↗
NASA NTRS1999

Determination of Spectroscopic Properties of Atmospheric Molecules from High Resolution Vacuum Ultraviolet Cross Section and Wavelength Measurements

We have studied the spectroscopy and the cross sections of the simple molecules of atmospheric interest such as oxygen, nitric oxide, carbon dioxide, and water. We have made cross section measurements on an absolute base without the effects from the limited instrumental resolution. We have used the following different instruments- the grating spectrometer (6.65-m at CfA, 3-m at Photon Factory), VUV Fourier transform spectrometer at Imperial College, and then moved the same one to the Photon Factory. Selection of the instruments depend on the appearance of molecular bands, and their wavelength region. For example, the cross section measurements of Doppler limited bands can been done with the Fourier transform spectrometer at the very high resolution (0.025/ cm resolution). All of these spectroscopic measurements are needed for accurate calculations of the production of atomic oxygen penetration of solar radiation into the Earth's atmosphere, and photochemistry of minor molecules.

Parkinson, W. H.↗
NASA NTRS2005

Two-Dimensional Ffowcs Williams/Hawkings Equation Solver

FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.

Lockard, David P.↗
NASA NTRS1980

Servomechanism for Doppler shift compensation in optical correlator for synthetic aperture radar

A method and apparatus for correcting Doppler shifts in synthetic aperture radar data is described. An optical correlator for synthetic aperture radar data has a means for directing a laser beam at a signal film having radar return pulse intensity information recorded on it. A resultant laser beam passes through a range telescope, an azimuth telescope, and a Fourier transform filter located between the range and azimuth telescopes, and forms an image for recording on an image film. A compensation means for Doppler shift in the radar return pulse intensity information includes a beam splitter for reflecting the modulated laser beam, after having passed through the Fourier transform filter, to a detection screen having two photodiodes mounted on it.

Constaninides, N. J.↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
NASA NTRS1988

High resolution infrared absorption spectra of various trace gases present in the upper atmosphere of the Earth

The objective of NASA Grant NsG 7473 was to obtain and analyze high resolution infrared absorption spectra of various trace gases present in the Earth's upper atmosphere. The goal of the spectral analysis was to obtain values of absorption line strengths, widths and frequencies of sufficient accuracy for use in upper atmosphere trace gas monitoring. During the early phase of the grant, high resolution spectra were obtained from two instruments. One was the 0.02/cm resolution vacuum grating spectrometer at the Florida State University and the other was the 0.01/cm resolution Fourier transform spectrometer at the McMath solar telescope at the Kitt Peak Observatory. Using these instruments, a considerable amount of spectra of methane and hydrogen peroxide were obtained and analyzed. During the latter years of the project, data taking was halted while efforts were devoted to building a new 0.0025/cm resolution vacuum Fourier transform spectrometer. Progress during this phase of the grant then became greatly slowed due to a lack of suitable graduate students in the program. However, the instrument was completed and brought to the point of producing interferograms.

Hunt, Robert H.↗
NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗
NASA NTRS1973

On the normality and accuracy of simulated random processes.

Efficient methods of simulating stationary and nonstationary random processes and envelopes, by using a series of sine or cosine functions or by using the fast Fourier transform, have been proposed previously. Without applying the central limit theorem, it is shown in this paper that the simulated random processes are asymptotically Gaussian processes as the number of terms, N, of sine or cosine functions approaches infinity. The accuracy of the first-order probability densities of the simulated random processes is investigated by using the fast Fourier transform. Numerical results are computed with respect to the variation of the number of terms, N, of sine or cosine functions used for simulation. It is shown that within the practical range of N, such as 500, the accuracy is remarkably satisfactory even outside the region of 3 standard deviations.

Yang, J.-N.↗
NASA NTRS1972

An evaluation of random analysis methods for the determination of panel damping

An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.

Bhat, W. V.↗
NASA NTRS1989

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.↗
NASA NTRS1972

Improved methods of performing coherent optical correlation

Coherent optical correlators are described in which complex spatial filters are recorded by a quasi-Fourier transform method. The high-pass spatial filtering effects (due to the dynamic range of photographic films) normally encountered in Vander Lugt type complex filters are not present in this system. Experimental results for both transmittive as well as reflective objects are presented. Experiments are also performed by illuminating the object with diffused light. A correlator using paraboloidal mirror segments as the Fourier-transforming element is also described.

Husain-Abidi, A. S.↗
NASA NTRS1994

Dynamic Stability Instrumentation System (DSIS). Volume 1: Hardware description

This paper is a hardware description manual for the Dynamic Stability Instrumentation System that is used in specific NASA Langley wind tunnels. The instrumentation system performs either a synchronous demodulation or a fast Fourier transform on dynamic balance strain gage signals, and ultimately computes aerodynamic coefficients. The DSIS consists of a double rack of instruments, a remote motor-generator set, two special stings each with motor driven shafts, and specially designed balances. The major components in the instrumentation rack include a personal computer, digital signal processor microcomputers, computer-controlled signal conditioners, function generator, digital multimeter, and an optional fast Fourier transform analyzer.

Jordan, T. L.↗
NASA NTRS2011

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↗