Karin Blank

ON INSTANTANEOUS FREQUENCY

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the m...

On certain theoretical developments underlying the Hilbert-Huang transform

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier integral transform and its high performance digital equivalent - the fast Fourier transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the empirical mode decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source numerical data vector into a finite set of intrinsic mode functions (IMF). These functions form a nearly orthogonal, derived from the data basis (adaptive basis). The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT data processing system (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT EMD algorithm. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2D processing using field programmable gate array (FPGA) computational resources, enhanced HHT synthesis, and will broaden the scope of HHT applications for signal processing

On the Hilbert-Huang transform data processing system development

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the fast Fourier transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang transform (HHT) proposes an approach to the solution for the nonlinear class of spectrum analysis problems. Using the empirical mode decomposition (EMD) followed by the Hilbert transform of the empirical decomposition data (HT) as stated in N.E. Huang et al. (1998), N. E. Huang (1999), and N. E. Huang (2001), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of intrinsic mode functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert transform. This paper describes phase one of the development of a new engineering tool, the HHT data processing system (HHTDPS). The HHTDPS allows applying the HHT to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a composite waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

REDUCTIONS OF NOISE AND UNCERTAINTY IN ANNUAL GLOBAL SURFACE TEMPERATURE ANOMALY DATA

Global climate variability is currently a topic of high scientific and public interest, with potential ramifications for the Earths ecologic systems and policies governing world economy. Across the broad spectrum of global climate variability, the least well understood time scale is that of decade-to-century.1 The bases for investigating past changes across that period band are the records of annual mean Global Surface Temperature Anomaly (GSTA) time series, produced variously in many painstaking efforts.2–5 However, due to incipient instrument noise, the uneven distribution of sensors spatially and temporally, data gaps, land urbanization, and bias corrections to sea surface temperature, noise and uncertainty continue to exist in all data sets.1, 2, 6–8 Using the Empirical Mode Decomposition method as a filter, we can reduce this noise and uncertainty and produce a cleaner annual mean GSTA dataset. The noise in the climate dataset is thus reduced by one-third and the difference between the new and the commonly used, but unfiltered time series, ranges up to 0.1506°C, with a standard deviation up to 0.01974°C, and an overall mean difference of only 0.0001°C. Considering that the total increase of the global mean temperature over the last 150 years to be only around 0.6°C, we believe this difference of 0.1506°C is significant.

Earth Observations from DSCOVR EPIC Instrument

The NOAA Deep Space Climate Observatory (DSCOVR) spacecraft was launched on February 11, 2015, and in June 2015 achieved its orbit at the first Lagrange point or L1, 1.5 million km from Earth towards the Sun. There are two NASA Earth observing instruments onboard: the Earth Polychromatic Imaging Camera (EPIC) and the National Institute of Standards and Technology Advanced Radiometer (NISTAR). The purpose of this paper is to describe various capabilities of the DSCOVR/EPIC instrument. EPIC views the entire sunlit Earth from sunrise to sunset at the backscattering direction (scattering angles between 168.5° and 175.5°) with 10 narrowband filters: 317, 325, 340, 388, 443, 552, 680, 688, 764 and 779 nm. We discuss a number of pre-processingsteps necessary for EPIC calibration including the geolocation algorithm and the radiometric calibration for each wavelength channel in terms of EPIC counts/second for conversion to reflectance units. The principal EPIC products are total ozone O3amount, scene reflectivity, erythemal irradiance, UV aerosol properties, sulfur dioxide SO2 for volcanic eruptions, surface spectral reflectance, vegetation properties, and cloud products including cloud height. Finally, we describe the observation of horizontally oriented ice crystals in clouds and the unexpected use of the O2 B-band absorption for vegetation properties.

On development of Hilbert-Huang Transform data processing real-time system with 2D capabilities

Unlike other digital signal processing techniques such as the Fast Fourier Transform for one-dimensional (1D) and two-dimensional (2D) data (FFT1 and FFT2) that assume signal linearity and stationarity, the Hilbert-Huang Transform (HHT) utilizes relationships between arbitrary signals local extrema to find the signal instantaneous spectral representation. This is done in two steps. Firstly, the Huang Empirical Mode Decomposition (EMD) is separating input signal of one variable s(t) into a finite set of narrow-band Intrinsic Mode Functions {IMF1(t), IMF2(t)... IMFk(t)} that add up to the signal s(t). The IMFs comprise the signal adaptive basis that is derived from the signal, as opposed to artificial basis imposed by the FFT or other heritage frequency analysis methods. Secondly, the HHT is applying the Hilbert Transform to each IMFi(t) signal constituents to obtain the corresponding analytical signal Si(t). From the analytical signal the HHT generates the Hilbert-Huang Spectrum. Namely, a single instantaneous frequency ωi(t) for signal Si(t) at each argument t is obtained for each of the k-Huang IMFs. This yields the Hilbert-Huang spectrum {ω(IMF1(t)), ω(IMF2(t))... ω(IMFk(t))} at each domain argument t for s(t) that was not obtainable otherwise. The HHT and its engineering implementation - the HHT Data Processing System (HHT-DPS) for 1D was developed at the NASA Goddard Space Flight Center (GSFC). The HHT-DPS is the reference system now used around the world. However, the state-of-the-art HHT-DPS works only for 1D data, as designed, and it is not a real-time system. This paper describes the development of the reference HHT Data Processing Real-Time System (HHTPS-RT) with 2D capabilities or HHT2 to process large images as the development goal. This paper describes the methodology of research and development of the new reference HHT2 Empirical Mode Decomposition for 2D (EMD2) system and its algorithms that require high capability computing. It provides this system prototype test results and also introduces the HHT2 spectrum concepts. It concludes with suggested areas for future research.