Thomas P. Flatley

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.

Keynote 2 — SpaceCube — A family of reconfigurable hybrid on-board science data processors

SpaceCube is a family of Field Programmable Gate Array (FPGA) based on-board science data processing systems developed at the NASA Goddard Space Flight Center (GSFC). The goal of the SpaceCube program is to provide 10× to 100× improvements in on-board computing power while lowering relative power consumption and cost. SpaceCube is based on the Xilinx Virtex family of FPGAs, which include processor, FPGA logic and digital signal processing (DSP) resources. These processing elements are leveraged to produce a hybrid science data processing platform that accelerates the execution of algorithms by distributing computational functions to the most suitable elements. This approach enables the implementation of complex on-board functions that were previously limited to ground based systems, such as on-board product generation, data reduction, calibration, classification, event/feature detection, data mining and real-time autonomous operations. The system is fully reconfigurable in flight, including data parameters, software and FPGA logic, through either ground commanding or autonomously in response to detected events/features in the instrument data stream.

Adapting the SpaceCube v2.0 data processing system for mission-unique application requirements

The SpaceCube™ v2.0 system is a high performance, reconfigurable, hybrid data processing system that can be used in a multitude of applications including those that require a radiation hardened and reliable solution. This paper provides an overview of the design architecture, flexibility, and the advantages of the modular SpaceCube v2.0 high performance data processing system for space applications. The current state of the proven SpaceCube technology is based on nine years of engineering and operations. Five systems have been successfully operated in space starting in 2008 with four more to be delivered for launch vehicle integration in 2015. The SpaceCube v2.0 system is also baselined as the avionics solution for five additional flight projects and is always a top consideration as the core avionics for new instruments or spacecraft control. This paper will highlight how this multipurpose system is currently being used to solve design challenges of three independent applications. The SpaceCube hardware adapts to new system requirements by allowing for application-unique interface cards that are utilized by reconfiguring the underlying programmable elements on the core processor card. We will show how this system is being used to improve on a heritage NASA GPS technology, enable a cutting-edge LiDAR instrument, and serve as a typical command and data handling (C&DH) computer for a space robotics technology demonstration.

Comparison between Hilbert-Huang transform and scalogram methods on non-stationary biomedical signals: application to laser Doppler flowmetry recordings.

A significant transient increase in laser Doppler flowmetry (LDF) signals is observed in response to a local and progressive cutaneous pressure application on healthy subjects. This reflex may be impaired in diabetic patients. The work presents a comparison between two signal processing methods that provide a clarification of this phenomenon. Analyses by the scalogram and the Hilbert-Huang transform (HHT) of LDF signals recorded at rest and during a local and progressive cutaneous pressure application are performed on healthy and type 1 diabetic subjects. Three frequency bands, corresponding to myogenic, neurogenic and endothelial related metabolic activities, are studied at different time intervals in order to take into account the dynamics of the phenomenon. The results show that both the scalogram and the HHT methods lead to the same conclusions concerning the comparisons of the myogenic, neurogenic and endothelial related metabolic activities-during the progressive pressure and at rest-in healthy and diabetic subjects. However, the HHT shows more details that may be obscured by the scalogram. Indeed, the non-locally adaptative limitations of the scalogram can remove some definition from the data. These results may improve knowledge on the above-mentioned reflex as well as on non-stationary biomedical signal processing methods.