How do you make a time series sing like a choir? Using the Hilbert-Huang transform to extract embedded frequencies from economic or financial time series

The Hilbert-Huang transform (HHT) was developed late last century but has still to be introduced to the vast majority of economists. The HHT transform is a way of extracting the frequency mode features of cycles embedded in any time series using an adaptive data method that can be applied without making any assumptions about stationarity or linear data-generating properties. This paper introduces economists to the two constituent parts of the HHT transform, namely empirical mode decomposition (EMD) and Hilbert spectral analysis. Illustrative applications using HHT are also made to two financial and three economic time series.business cycles; growth cycles; Hilbert-Huang transform (HHT); empirical mode decomposition (EMD); economic time series; non-stationarity; spectral analysis

Operation of the Hilbert-Huang Transform: basic overview with examples

This learning object provides a simple explanation of the operation of the Hilbert-Huang transform. This is a tool which has been employed with success in the signal processing field and, more especifically, in the analysis of non-stationary signals. The work reviews the mathematical bases of the transform and it focuses on its operation. It describes its two main parts: Empirical Mode Decomposition algorithm and the Hilbert Spectral Analysis. Several simple examples illustrating the operation of the transform are also provided.Antonino Daviu, JA. (2013). Operation of the Hilbert-Huang Transform: basic overview with examples. http://hdl.handle.net/10251/3074

Applying the Hilbert--Huang Decomposition to Horizontal Light Propagation C_n^2 data

The Hilbert Huang Transform is a new technique for the analysis of non--stationary signals. It comprises two distinct parts: Empirical Mode Decomposition (EMD) and the Hilbert Transform of each of the modes found from the first step to produce a Hilbert Spectrum. The EMD is an adaptive decomposition of the data, which results in the extraction of Intrinsic Mode Functions (IMFs). We discuss the application of the EMD to the calibration of two optical scintillometers that have been used to measure C_n^2 over horizontal paths on a building rooftop, and discuss the advantage of using the Marginal Hilbert Spectrum over the traditional Fourier Power Spectrum.Comment: 9 pages, 11 figures, proc. SPIE 626

Caracterización multicanal no lineal de señales EMG con la transformada Hilbert-Huang

En este documento se presenta una propuesta de caracterización multicanal no lineal y adaptativa de señales electromiográficas de superficie usando la transformada Hilbert-Huang, la cual es una técnica de procesamiento digital reciente basada en la descomposición empírica y la transformada Hilbert propuesta por el Huang et. al [14]. Los resultados obtenidos con esta propuesta (96.6%) mejora los resultados reportados en [10] para 4 movimientos (87.5%) y son muy comparables con la metodología propuesta en [7] para 5 movimientos con la transformada wavelet adaptativa (97.3%).This document present a procedure for non-lineal non-stationary characterization of multichannel EMG signals. Its main key is the novel digital signal processing Hilbert-Huang transform, which is a recent tool for analyzing these kinds of signals based on both the empirical mode decomposition and the Hilbert transform

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

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

Statistical Movement Classification based on Hilbert-Huang Transform

The goal of this project is to introduce an automatic movement classification technique of finger movement signals using Hilbert-Huang Transform (HHT). Due to the nonlinear and nonstationary processing behavior, movement signals are analyzed with the Hilbert-Huang Transform (HHT). The slope of auto-correlation function and mean of frequency from first three Intrinsic Mode Functions (IMFs) was used as feature parameters for each category. Finally, performing support vector machine (SVM) for pattern classification completes clas- sifying types of finger movement. According to the records of 669 trial samples of two types of finger movement signals (thumb and pinky), average accuracy is 93.28%. In another case of movement (thumb and pinky), average accuracy is 100%. All in all, the feature extraction method based on Hilbert-Huang transform (HHT) can be used to achieve effective movement classification

Detection and Classification of Double Line to Ground Faults in a 138 kV Six Phase Transmission Line Using Hilbert Huang Transform

In this paper, Hilbert Huang transform based technique is introduced to detect and classify double line to ground faults in a 138 kV, 60 Hz, 68 km long six phase transmission line. Hilbert Huang transform is used to extract the hidden features contained in fault current signal in the form of Hilbert coefficients. The proposed technique does not requires the communication link between the two terminals of six phase transmission line since the fault current signals are recorded at the first terminal only i.e. at bus-1. For the justification of the proposed technique, wide variety of fault test studies were carried out in MATLAB/ Simscape power system toolbox for different types of three phase to ground faults by varying fault type, fault location, fault inception time, fault resistance and ground resistance. Test results shows that the Hilbert Huang transform based proposed technique effectively detects/ classifies the double line to ground faults

Analysis of an oscillating plate coupled with fluid

Thesis (M.S.) University of Alaska Fairbanks, 2013The mechanical vibration of an oscillating cantilever plate is studied to determine the interaction of a plate coupled with air and with water. Experimental data was collected and analyzed using multiple methods including Fast Fourier Transform, wavelet analysis, and the Hilbert-Huang Transform (HHT) to characterize the behavior of the plate. The HHT is able to process nonlinear and nonstationary signals and provides more meaningful information compared to the traditionally used Fourier transform for similar applications. The HHT was found to be appropriate and more descriptive for the analysis of coupled fluid-structure systems. Digital Particle Image Velocimetry (DPIV) was also used to analyze the circulation and energy transferred to the fluid.Chapter 1. Introduction -- Chapter 2. Method -- 2.1. Equipment setup -- 2.2. Data collection parameters -- 2.3. Analysis methods -- 2.3.1. Fast Fourier transform -- 2.3.2. Wavelet -- 2.3.3. Hilbert-Huang transform -- 2.3.4. Digital particle image velocimetry -- Chapter 3. Experiment -- 3.1. Design of experiment -- Chapter 4. Analysis -- 4.1. Raw data -- 4.2. Data analysis -- 4.2.1. Waveform -- 4.2.2. Fast Fourier transform -- 4.2.3. Wavelet -- 4.2.4. Hilbert-Huang transform -- 4.2.5. Digital particle image velocimetry -- Chapter 5. Conclusions -- References