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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Update on EMD and Hilbert-Spectra Analysis of Time Series

This method is especially well suited for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method is based principally on the concept of empirical mode decomposition (EMD), according to which any complicated signal (as represented by digital samples) can be decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum.

Huang, Norden E.↗
NASA NTRS2007

Maintaining Stability During a Conducted-Ripple EMC Test

An improved technique, and electronic circuitry to implement the technique, have been developed for a military-standard electromagnetic-compatibility (EMC) test in which one analyzes susceptibility to low-frequency ripple conducted into the equipment under test via a DC power line. In the traditional technique for performing the particular test, the ripple is coupled onto the DC power line via a transformer. Depending upon some design details of the equipment under test, the inductance of the transformer can contribute a degree of instability that results in an oscillation of amplitude large enough to destroy the equipment. It is usually possible to suppress the oscillation by connecting a damping resistor to the primary terminals of the ripple-injection transformer. However, it is important to emphasize the usually in the preceding sentence: sometimes, the resistive damping becomes insufficient to suppress destructive oscillation. In addition, undesirably, the resistor contributes to power dissipation and power demand, and thereby also necessitates the use of a larger ripple voltage amplifier. Yet another disadvantage of the transformer-coupling technique is that the transformer introduces low-frequency distortion of the injected ripple voltage. The improved technique makes it possible to inject ripple with very low distortion at low frequency, without inducing oscillation. In this technique, a transformer is not used: Instead, power is fed to the equipment under test via series power field-effect transistors (FETs) controlled by a summing operational amplifier. One of the inputs to the amplifier controls the DC component of the power-line voltage; the other input, generated by an external oscillator, controls the ripple component. The circuitry for implementing this technique includes panel displays, an internal power supply for the operational amplifier and panel displays, and amplitude controls for the DC and ripple powerline voltage components.

Vorperian, Vatche↗
NASA NTRS1973

Reduction of truncation errors in modal analysis

A condensation method and computer program are described for large discrete parameter vibration analysis of complex structures that greatly reduces truncation errors and provides accurate definition of modes in a selected frequency range. A dynamic transformation is obtained from the partitioned equations of motion that relates modes not explicitly in the condensed solution to the retained modes at a selected system frequency. The generalized mass and stiffness matrices, obtained with existing modal synthesis methods, are reduced using this transformation and solved. Revised solutions are then obtained using new transformations at the calculated eigenvalues and are also used to assess the accuracy of the results. Computations are made tractable by simplified forms of the transformation that result with various modal synthesis methods. Three examples using the dynamic transformation in conjunction with a General Electric stiffness coupling method and the method of Craig and Bampton indicate large reductions in truncation errors and demonstrate the method for sequential groups of modes.

Kuhar, E. J.↗
NASA NTRS1994

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗
NASA NTRS1978

Ocean waves

Ocean wave data can be obtained from such active microwave probe techniques as monostatic HF and VHF, bistatic HF, HF synthetic aperture radar, altimeters, satellite and airborne synthetic aperture radar, carrier wave or pulsed dual-frequency radars, and coastal surveillance radar. Approaches to texture analysis of ocean wave imagery are discussed, with attention given to transform techniques or spatial frequency analysis, and the analysis of second-order gray level statistics. In addition, recommendations are made for further work on the modulation of short gravity waves by longer waves as a function of wind speed and wave direction, and the derivation of transfer functions for the ocean response of dual-frequency radars.

Bartsch, N.↗
NASA NTRS1990

The Cortex Transform as an image preprocessor for sparse distributed memory: An initial study

An experiment is described which was designed to evaluate the use of the Cortex Transform as an image processor for Sparse Distributed Memory (SDM). In the experiment, a set of images were injected with Gaussian noise, preprocessed with the Cortex Transform, and then encoded into bit patterns. The various spatial frequency bands of the Cortex Transform were encoded separately so that they could be evaluated based on their ability to properly cluster patterns belonging to the same class. The results of this study indicate that by simply encoding the low pass band of the Cortex Transform, a very suitable input representation for the SDM can be achieved.

Olshausen, Bruno↗
NASA NTRS1976

Transformation of apparent ocean wave spectra observed from an aircraft sensor platform

The problem considered was transformation of a unidirectional apparent ocean wave spectrum observed from an aircraft sensor platform into the true spectrum that would be observed from a stationary platform. Spectral transformation equations were developed in terms of the linear wave dispersion relationship and the wave group speed. An iterative solution to the equations was outlined and used to transform reference theoretical apparent spectra for several assumed values of average water depth. Results show that changing the average water depth leads to a redistribution of energy density among the various frequency bands of the transformed spectrum. This redistribution is most severe when much of the energy density is expected, a priori, to reside at relatively low true frequencies.

Poole, L. R.↗
NASA NTRS1997

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

Morelli, Eugene A.↗
NASA NTRS2001

On the Application of Hilbert Spectral Analysis for Climate Studies

The Hilbert spectral analysis (Huang et al, 1998, Proceedings of the Royal Society of London, A 454, pp 903-995) consisted of two steps: First, the data has to be reduced into a finite number of Intrinsic Mode Function by the Empirical Mode Decomposition method, then the resulting Intrinsic Mode Functions are converted to time-frequency-energy distribution through Hilbert transform. In this approach, the Empirical Mode Functions served as the basis functions with which the data is expanded. This basis function is adaptive, and the decomposition is nonlinear. Furthermore, as the Hilbert transform is a singular transform, it retains a high degree of local information. The instantaneous frequency is determined by differentiation of the phase function; therefore, there is no restriction of the 'uncertainty principle' for all the time-frequency analysis resulting from a priori basis approach. With the adaptive basis and the instantaneous frequency, the Hilbert Spectral analysis can represent data from nonlinear and nonstationary processes without resorting to the harmonics. Another advantage of using instantaneous frequency is the ability to find out frequency from limited length of data, which is a critical problem in climate studies. As the processes driving the climate changes could be both nonlinear and nonstationary, the Hilbert Spectral Analysis could be of great use in examining the underlying mechanisms. A preliminary study based on the length of day data will be presented as example for the application of the Hilbert Spectral Analysis for climate study.

Huang, Norden E.↗
NASA NTRS2006

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.

Brenner, Martin J.↗
NASA NTRS2005

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

This paper investigates the utility of the Hilbert-Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert-Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert-Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this paper is to demonstrate the potential applications of the Hilbert-Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized/online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F/A-18 Active Aeroelastic Wing aircraft, an Aerostructures Test Wing, and pitch-plunge simulation.

Brenner, Marty↗
NASA NTRS1994

Multi-velocity component LDV

A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components. Ames Research Center, Mail Code 200-11A, Moffett Field, California, 94035. Approved NASA forms for application for nonexclusive or exclusive license are available from the above address.

Johnson, Dennis A.↗
NASA NTRS1996

Multi-Velocity Component LDV

A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components.

Johnson, Dennis A.↗
NASA NTRS1995

Time-Domain Computation Of Electromagnetic Fields In MMICs

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

Lansing, Faiza S.↗
NASA NTRS1991

Discrete-time model reduction in limited frequency ranges

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Horta, Lucas G.↗
NASA NTRS1988

High-dynamic GPS tracking

The results of comparing four different frequency estimation schemes in the presence of high dynamics and low carrier-to-noise ratios are given. The comparison is based on measured data from a hardware demonstration. The tested algorithms include a digital phase-locked loop, a cross-product automatic frequency tracking loop, and extended Kalman filter, and finally, a fast Fourier transformation-aided cross-product frequency tracking loop. The tracking algorithms are compared on their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. The measured results are shown to agree with simulation results carried out and reported previously.

Hinedi, S.↗