On Hilbert-Huang Transform Based Synthesis of a Signal Contaminated by Radio Frequency Interference or Fringes

Norden E. Huang et al. had proposed and published the Hilbert-Huang Transform (HHT) concept correspondently in 1996, 1998 [1]. The HHT is a novel method for adaptive spectral analysis of non-linear and non-stationary signals. The HHT comprises two components: – the Huang Empirical Mode Decomposition (EMD), resulting in an adaptive dataderived basis of Intrinsic Mode functions (IMFs), and the Hilbert Spectral Analysis (HSA1) based on the Hilbert Transform for 1-dimension (1D) applied to the EMD IMF’s outcome. Although paper [1] describes the HHT concept in great depth, it does not contain all needed methodology to implement the HHT computer code [2]. In 2004, Semion Kizhner and Karin Blank implemented the reference digital HHT real-time data processing system for 1D (HHT-DPS Version 1.4) [3-4]. The case for 2-Dimension (2D) (HHT2) proved to be difficult due to the computational complexity of EMD for 2D (EMD2) and absence of a suitable Hilbert Transform for 2D spectral analysis (HSA2) [7], [9]. The real-time EMD2 and HSA2 comprise the real-time HHT2. Kizhner completed the real-time EMD2 and the HSA2 reference digital implementations respectively in 2013 & 2014 [56]. Still, the HHT2 outcome synthesis remains an active research area. This paper presents the initial concepts and preliminary results of HHT2-based synthesis and its application to processing of signals contaminated by Radio-Frequency Interference (RFI), as well as optical systems’ fringe detection and mitigation at design stage. The Soil Moisture Active Passive (SMAP mission (SMAP) carries a radiometer instrument that measures Earth soil moisture at L1 frequency (1.4 GHz polarimetric H, V, 3 and 4 Stokes parameters). There is abundant RFI at L1 and because soil moisture is a strategic parameter, it is important to be able to recover the RFIcontaminated measurement samples (15% of telemetry). State–of–the-art only allows RFI detection and removes RFI-contaminated measurements. The HHT-based analysis and synthesis facilitates recovery of measurements contaminated by all kinds of RFI, including jamming [7-8]. The fringes are inherent in optical systems and multi-layer complex contour expensive coatings are employed to remove the unwanted fringes. HHT2-based analysis allows test image decomposition to analyze and detect fringes, and HHT2based synthesis of useful image.