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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Computing Instantaneous Frequency by normalizing Hilbert Transform

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Huang, Norden E.↗
NASA NTRS2015

Comparison of Instantaneous Frequency Scaling from Rain Attenuation and Optical Disdrometer Measurements at K/Q bands

Rain attenuation is strongly dependent on the rain rate, but also on the rain drop size distribution (DSD). Typically, models utilize an average drop size distribution, such as those developed by Laws and Parsons, or Marshall and Palmer. However, individual rain events may possess drop size distributions which could be significantly different from the average and will impact, for example, fade mitigation techniques which utilize channel performance estimates from a signal at a different frequency. Therefore, a good understanding of the characteristics and variability of the raindrop size distribution is extremely important in predicting rain attenuation and instantaneous frequency scaling parameters on an event-toevent basis. Since June 2014, NASA Glenn Research Center (GRC) and the Politecnico di Milano (POLIMI) have measured the attenuation due to rain in Milan, Italy, on the 20/40 GHz beacon signal broadcast from the Alphasat TDP#5 Aldo Paraboni Q/V-band Payload. Concomitant with these measurements are the measurements of drop size distribution and rain rate utilizing a Thies Clima laser precipitation monitor (disdrometer). In this paper, we discuss the comparison of the predicted rain attenuation at 20 and 40 GHz derived from the drop size distribution data with the measured rain attenuation. The results are compared on statistical and real-time bases. We will investigate the performance of the rain attenuation model, instantaneous frequency scaling, and the distribution of the scaling factor. Further, seasonal rain characteristics will be analysed.

millimeter wave↗
NASA NTRS1992

Hysteresis effects in instantaneous frequency scaling of attenuation on 20 and 30 GHz satellite links

It has been observed with 20/30 GHz satellite beacon measurements that the ratio of 30 GHz to 20 GHz attenuation changes during some fade events. This ratio displays a hysteresis effect. This effect can be explained by a change in the drop size distribution (DSD) during the event. However, it appears only above approximately 6-8 dB of attenuation at 20 GHz. Instantaneous frequency scaling of attenuation is being proposed as part of an algorithm for uplink power control (ULPC) and the dynamic range of such an algorithm must be appropriately limited to avoid the hysteresis.

Sweeney, D. G.↗
NASA NTRS2016

Statistical Analysis of Instantaneous Frequency Scaling Factor as Derived From Optical Disdrometer Measurements At KQ Bands

The rain rate data and statistics of a location are often used in conjunction with models to predict rain attenuation. However, the true attenuation is a function not only of rain rate, but also of the drop size distribution (DSD). Generally, models utilize an average drop size distribution (Laws and Parsons or Marshall and Palmer. However, individual rain events may deviate from these models significantly if their DSD is not well approximated by the average. Therefore, characterizing the relationship between the DSD and attenuation is valuable in improving modeled predictions of rain attenuation statistics. The DSD may also be used to derive the instantaneous frequency scaling factor and thus validate frequency scaling models. Since June of 2014, NASA Glenn Research Center (GRC) and the Politecnico di Milano (POLIMI) have jointly conducted a propagation study in Milan, Italy utilizing the 20 and 40 GHz beacon signals of the Alphasat TDP#5 Aldo Paraboni payload. The Ka- and Q-band beacon receivers provide a direct measurement of the signal attenuation while concurrent weather instrumentation provides measurements of the atmospheric conditions at the receiver. Among these instruments is a Thies Clima Laser Precipitation Monitor (optical disdrometer) which yields droplet size distributions (DSD); this DSD information can be used to derive a scaling factor that scales the measured 20 GHz data to expected 40 GHz attenuation. Given the capability to both predict and directly observe 40 GHz attenuation, this site is uniquely situated to assess and characterize such predictions. Previous work using this data has examined the relationship between the measured drop-size distribution and the measured attenuation of the link]. The focus of this paper now turns to a deeper analysis of the scaling factor, including the prediction error as a function of attenuation level, correlation between the scaling factor and the rain rate, and the temporal variability of the drop size distribution both within a given rain event and across different varieties of rain events. Index Terms-drop size distribution, frequency scaling, propagation losses, radiowave propagation.

Statistics↗
NASA NTRS2016

Statistical Analysis of Instantaneous Frequency Scaling Factor as Derived From Optical Disdrometer Measurements At KQ Bands

The rain rate data and statistics of a location are often used in conjunction with models to predict rain attenuation. However, the true attenuation is a function not only of rain rate, but also of the drop size distribution (DSD). Generally, models utilize an average drop size distribution (Laws and Parsons or Marshall and Palmer [1]). However, individual rain events may deviate from these models significantly if their DSD is not well approximated by the average. Therefore, characterizing the relationship between the DSD and attenuation is valuable in improving modeled predictions of rain attenuation statistics. The DSD may also be used to derive the instantaneous frequency scaling factor and thus validate frequency scaling models. Since June of 2014, NASA Glenn Research Center (GRC) and the Politecnico di Milano (POLIMI) have jointly conducted a propagation study in Milan, Italy utilizing the 20 and 40 GHz beacon signals of the Alphasat TDP#5 Aldo Paraboni payload. The Ka- and Q-band beacon receivers provide a direct measurement of the signal attenuation while concurrent weather instrumentation provides measurements of the atmospheric conditions at the receiver. Among these instruments is a Thies Clima Laser Precipitation Monitor (optical disdrometer) which yields droplet size distributions (DSD); this DSD information can be used to derive a scaling factor that scales the measured 20 GHz data to expected 40 GHz attenuation. Given the capability to both predict and directly observe 40 GHz attenuation, this site is uniquely situated to assess and characterize such predictions. Previous work using this data has examined the relationship between the measured drop-size distribution and the measured attenuation of the link [2]. The focus of this paper now turns to a deeper analysis of the scaling factor, including the prediction error as a function of attenuation level, correlation between the scaling factor and the rain rate, and the temporal variability of the drop size distribution both within a given rain event and across different varieties of rain events. Index Terms-drop size distribution, frequency scaling, propagation losses, radiowave propagation.

Radio Attenuation↗
NASA NTRS2017

Statistical Analysis of Instantaneous Frequency Scaling Factor as Derived from Optical Disdrometer Measurements at VW Bands

Since October 2015, NASA Glenn Research Center (GRC) and the Air Force Research Laboratory (AFRL) have collaboratively operated an RF terrestrial link in Albuquerque, New Mexico to characterize atmospheric propagation phenomena at 72 and 84 GHz. The WV-band Terrestrial Link Experiment (WTLE) consists of coherent transmitters at each frequency on the crest of the Sandia Mountains and a corresponding pair of receivers in south Albuquerque. The beacon receivers provide a direct measurement of the link attenuation, while concurrent weather instrumentation provides a measurement of the atmospheric conditions.Among the available weather instruments is an optical disdrometer which yields an optical measurement of rain rate, as well as droplet size and velocity distributions (DSD, DVD). In particular, the DSD can be used to derive an instantaneous scaling factor (ISF) by which the measured data at one frequency can be scaled to another for example, scaling the 72 GHz to an expected 84 GHz timeseries. Given the availability of both the DSD prediction and the directly observed 84 GHz attenuation, WTLE is thus uniquely able assess DSD-derived instantaneous frequency scaling at the VW-bands. Previous work along these lines has investigated the DSD-derived ISF at Ka and Q-band (20 GHz to 40 GHz) using a satellite beacon receiver experiment in Milan, Italy [1-3]. This work will expand the investigation to terrestrial links in the VW-bands, where the frequency scaling factor is lower and where the link is also much more sensitive to attenuation by rain, clouds, and other atmospheric effects.

Radio Attenuation↗
NASA NTRS2017

Statistical Analysis of Instantaneous Frequency Scaling Factor as Derived from Optical Disdrometer Measurements at V/W Bands

Since October 2015, NASA Glenn Research Center (GRC) and the Air Force Research Laboratory (AFRL) have collaboratively operated an RF terrestrial link in Albuquerque, New Mexico to characterize atmospheric propagation phenomena at 72 and 84 GHz. The W/V-band Terrestrial Link Experiment (WTLE) consists of coherent transmitters at each frequency on the crest of the Sandia Mountains and a corresponding pair of receivers in south Albuquerque. The beacon receivers provide a direct measurement of the link attenuation, while concurrent weather instrumentation provides a measurement of the atmospheric conditions. Among the available weather instruments is an optical disdrometer which yields an optical measurement of rain rate, as well as droplet size and velocity distributions (DSD, DVD). In particular, the DSD can be used to derive an instantaneous scaling factor (ISF) by which the measured data at one frequency can be scaled to another - for example, scaling the 72 GHz to an expected 84 GHz timeseries. Given the availability of both the DSD prediction and the directly observed 84 GHz attenuation, WTLE is thus uniquely able assess DSD-derived instantaneous frequency scaling at the V/W-bands. Previous work along these lines has investigated the DSD-derived ISF at Ka and Q-band (20 GHz to 40 GHz) using a satellite beacon receiver experiment in Milan, Italy. This work will expand the investigation to terrestrial links in the V/W-bands, where the frequency scaling factor is lower and where the link is also much more sensitive to attenuation by rain, clouds, and other atmospheric effects.

Radio Transmission↗
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 NTRS2003

Beam-Switch Transient Effects in the RF Path of the ICAPA Receive Phased Array Antenna

When the beam of a Phased Array Antenna (PAA) is switched from one pointing direction to another, transient effects in the RF path of the antenna are observed. Testing described in the report has revealed implementation-specific transient effects in the RF channel that are associated with digital clocking pulses that occur with transfer of data from the Beam Steering Controller (BSC) to the digital electronics of the PAA under test. The testing described here provides an initial assessment of the beam-switch phenomena by digitally acquiring time series of the RF communications channel, under CW excitation, during the period of time that the beam switch transient occurs. Effects are analyzed using time-frequency distributions and instantaneous frequency estimation techniques. The results of tests conducted with CW excitation supports further Bit-Error-Rate (BER) testing of the PAA communication channel.

Sands, O. Scott↗
NASA NTRS2001

Applications of the Hilbert-Huang Transform

A new method, the Hilbert-Huang Transform, has been developed for analyzing nonlinear and nonstationary data. The key part of the method is the Empirical Mode Decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An M is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies'as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. With this technique we can examine the detailed dynamics characteristics of a nonlinear system through the instantaneous frequency rather than harmonics. Thus it constitutes a new view of the nonlinear dynamics. Examples of classic nonlinear equations and other nonlinear and nonstationary data sets will be used as examples to illustrate the advantage of the application of this new data analysis method.

Huang, Norden E.↗
NASA NTRS1999

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Huang, Norden E.↗
NASA NTRS2002

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.↗
NASA NTRS2003

Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Huang, Norden Eh↗
NASA NTRS2004

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.↗
NASA NTRS2005

Development of a Coherent Lidar for Aiding Precision Soft Landing on Planetary Bodies

Coherent lidar can play a critical role in future planetary exploration missions by providing key guidance, navigation, and control (GNC) data necessary for navigating planetary landers to the pre-selected site and achieving autonomous safe soft-landing. Although the landing accuracy has steadily improved over time to approximately 35 km for the recent Mars Exploration Rovers due to better approach navigation, a drastically different guidance, navigation and control concept is required to meet future mission requirements. For example, future rovers will require better than 6 km landing accuracy for Mars and better than 1 km for the Moon plus maneuvering capability to avoid hazardous terrain features. For this purpose, an all-fiber coherent lidar is being developed to address the call for advancement of entry, descent, and landing technologies. This lidar will be capable of providing precision range to the ground and approach velocity data, and in the case of landing on Mars, it will also measure the atmospheric wind and density. The lidar obtains high resolution range information from a frequency modulated-continuous wave (FM-CW) laser beam whose instantaneous frequency varies linearly with time, and the ground vector velocity is directly extracted from the Doppler frequency shift. Utilizing the high concentration of aerosols in the Mars atmosphere (approx. two order of magnitude higher than the Earth), the lidar can measure wind velocity with a few watts of optical power. Operating in 1.57 micron wavelength regime, the lidar can use the differential absorption (DIAL) technique to measure the average CO2 concentration along the laser beam using, that is directly proportional to the Martian atmospheric density. Employing fiber optics components allows for the lidar multi-functional operation while facilitating a highly efficient, compact and reliable design suitable for integration into a spacecraft with limited mass, size, and power resources.

Amzajerdian, Farzin↗
NASA NTRS1971

A real-time statistical time-series analyzer

Device extracts average frequency of human speech and produces second, third, and fourth moments of instantaneous frequency about this average. It operates on electrical time representation of input signal, performs statistical analysis on zero-crossing of almost any signal, and does not require specialized personnel to operate it.

Stewart, C. H.↗
NASA NTRS2017

Global Observations of Magnetospheric High-m Poloidal Waves During the 22 June 2015 Magnetic Storm

We report global observations of high-m poloidal waves during the recovery phase of the 22 June 2015 magnetic storm from a constellation of widely spaced satellites of five missions including Magnetospheric Multiscale (MMS), Van Allen Probes, Time History of Events and Macroscale Interactions during Substorm (THEMIS), Cluster, and Geostationary Operational Environmental Satellites (GOES). The combined observations demonstrate the global spatial extent of storm time poloidal waves. MMS observations confirm high azimuthal wave numbers (m approximately 100). Mode identification indicates the waves are associated with the second harmonic of field line resonances. The wave frequencies exhibit a decreasing trend as L increases, distinguishing them from the single-frequency global poloidal modes normally observed during quiet times. Detailed examination of the instantaneous frequency reveals discrete spatial structures with step-like frequency changes along L. Each discrete L shell has a steady wave frequency and spans about 1 RE, suggesting that there exist a discrete number of drift-bounce resonance regions across L shells during storm times.

Le, G.↗
NASA NTRS2006

Computing frequency by using generalized zero-crossing applied to intrinsic mode functions

This invention presents a method for computing Instantaneous Frequency by applying Empirical Mode Decomposition to a signal and using Generalized Zero-Crossing (GZC) and Extrema Sifting. The GZC approach is the most direct, local, and also the most accurate in the mean. Furthermore, this approach will also give a statistical measure of the scattering of the frequency value. For most practical applications, this mean frequency localized down to quarter of a wave period is already a well-accepted result. As this method physically measures the period, or part of it, the values obtained can serve as the best local mean over the period to which it applies. Through Extrema Sifting, instead of the cubic spline fitting, this invention constructs the upper envelope and the lower envelope by connecting local maxima points and local minima points of the signal with straight lines, respectively, when extracting a collection of Intrinsic Mode Functions (IMFs) from a signal under consideration.

Huang, Norden E.↗