1,386 research outputs found
Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing
nonstationary data that provides a localized time-frequency representation by
decomposing the data into adaptively defined modes. EMD can be used to estimate
a signal's instantaneous frequency (IF) but suffers from poor performance in
the presence of noise. To produce a meaningful IF, each mode of the
decomposition must be nearly monochromatic, a condition that is not guaranteed
by the algorithm and fails to be met when the signal is corrupted by noise. In
this work, the extraction of modes containing both signal and noise is
identified as the cause of poor IF estimation. The specific mechanism by which
such "transition" modes are extracted is detailed and builds on the observation
of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing
pure noise. The mechanism is shown to be dependent on spectral leak between
modes and the phase of the underlying signal. These ideas are developed through
the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel
Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk
Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?
The performances of a new data processing technique, namely the Empirical
Mode Decomposition, are evaluated on a fully developed turbulent velocity
signal perturbed by a numerical forcing which mimics a long-period flapping.
First, we introduce a "resemblance" criterion to discriminate between the
polluted and the unpolluted modes extracted from the perturbed velocity signal
by means of the Empirical Mode Decomposition algorithm. A rejection procedure,
playing, somehow, the role of a high-pass filter, is then designed in order to
infer the original velocity signal from the perturbed one. The quality of this
recovering procedure is extensively evaluated in the case of a "mono-component"
perturbation (sine wave) by varying both the amplitude and the frequency of the
perturbation. An excellent agreement between the recovered and the reference
velocity signals is found, even though some discrepancies are observed when the
perturbation frequency overlaps the frequency range corresponding to the
energy-containing eddies as emphasized by both the energy spectrum and the
structure functions. Finally, our recovering procedure is successfully
performed on a time-dependent perturbation (linear chirp) covering a broad
range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid
Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis
The Hilbert transform (HT) and associated Gabor analytic signal (GAS)
representation are well-known and widely used mathematical formulations for
modeling and analysis of signals in various applications. In this study, like
the HT, to obtain quadrature component of a signal, we propose the novel
discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine
quadrature transforms (FSQTs), designated as Fourier quadrature transforms
(FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal
(FSAS) representations with following properties: (1) real part of eight FSAS
representations is the original signal and imaginary part is the FCQT of the
real part, (2) imaginary part of eight FSAS representations is the original
signal and real part is the FSQT of the real part, (3) like the GAS, Fourier
spectrum of the all FSAS representations has only positive frequencies, however
unlike the GAS, the real and imaginary parts of the proposed FSAS
representations are not orthogonal to each other. The Fourier decomposition
method (FDM) is an adaptive data analysis approach to decompose a signal into a
set of small number of Fourier intrinsic band functions which are AM-FM
components. This study also proposes a new formulation of the FDM using the
discrete cosine transform (DCT) with the GAS and FSAS representations, and
demonstrate its efficacy for improved time-frequency-energy representation and
analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure
Enhanced monopulse radar tracking using empirical mode decomposition
Monopulse radar processors are used to track targets that appear in the look direction beamwidth. The target tracking information (range, azimuth angle, and elevation angle) are affected when manmade high power interference (jamming) is introduced to the radar processor through the radar antenna main lobe (main lobe interference) or antenna side lobe (side lobe interference). This interference changes the values of the error voltage which is responsible for directing the radar antenna towards the target. A monopulse radar structure that uses filtering in the empirical mode decomposition (EMD) domain is presented in this paper. EMD is carried out for the complex radar chirp signal with subsequent denoising and thresholding processes used to decrease the noise level in the radar processed data. The performance enhancement of the monopulse radar tracking system with EMD based filtering is included using the standard deviation angle estimation error (STDAE)
A tutorial review on time-frequency analysis of non-stationary vibration signals with nonlinear dynamics applications
Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equation
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