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

Nonlinear denoising of transient signals with application to event related potentials

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

A Wideband Direct Data Domain Genetic Algorithm Beamforming

In this paper, a wideband direct data-domain genetic algorithm beamforming is presented. Received wideband signals are decomposed to a set of narrow sub-bands using fast Fourier transform. Each sub-band is transformed to a reference frequency using the steering vector transformation. So, narrowband approaches could be used for any of these sub-bands. Hence, the direct data-domain genetic algorithm beamforming can be used to form a single ‘hybrid’ beam pattern with sufficiently deep nulls in order to separate and reconstruct frequency components of the signal of interest efficiently. The proposed approach avoids most of drawbacks of already-existing statistical and gradient-based approaches since formation of a covariance matrix is not needed, and a genetic algorithm is used to solve the beamforming problem

Channel Estimation for Millimeter-Wave Massive MIMO with Hybrid Precoding over Frequency-Selective Fading Channels

Channel estimation for millimeter-wave (mmWave) massive MIMO with hybrid precoding is challenging, since the number of radio frequency (RF) chains is usually much smaller than that of antennas. To date, several channel estimation schemes have been proposed for mmWave massive MIMO over narrow-band channels, while practical mmWave channels exhibit the frequency-selective fading (FSF). To this end, this letter proposes a multi-user uplink channel estimation scheme for mmWave massive MIMO over FSF channels. Specifically, by exploiting the angle-domain structured sparsity of mmWave FSF channels, a distributed compressive sensing (DCS)-based channel estimation scheme is proposed. Moreover, by using the grid matching pursuit strategy with adaptive measurement matrix, the proposed algorithm can solve the power leakage problem caused by the continuous angles of arrival or departure (AoA/AoD). Simulation results verify that the good performance of the proposed solution.Comment: 4 pages, 3 figures, accepted by IEEE Communications Letters. This paper may be the first one that investigates the frequency selective fading channel estimation for mmWave massive MIMO systems with hybrid precoding. Key words: Millimeter-wave (mmWave) massive MIMO, frequency-selective fading, channel estimation, compressive sensing, hybrid precodin

How Predictable are Temperature-series Undergoing Noise-controlled Dynamics in the Mediterranean

Mediterranean is thought to be sensitive to global climate change, but its future interdecadal variability is uncertain for many climate models. A study was made of the variability of the winter temperature over the Mediterranean Sub-regional Area (MSA), employing a reconstructed temperature series covering the period 1698 to 2010. This paper describes the transformed winter temperature data performed via Empirical Mode Decomposition for the purposes of noise reduction and statistical modeling. This emerging approach is discussed to account for the internal dependence structure of natural climate variability

Is current disruption associated with an inverse cascade?

Current disruption (CD) and the related kinetic instabilities in the near-Earth magnetosphere represent physical mechanisms which can trigger multi-scale substorm activity including global reorganizations of the magnetosphere. Lui et al. (2008) proposed a CD scenario in which the kinetic scale linear modes grow and reach the typical dipolarization scales through an inverse cascade. The experimental verification of the inverse nonlinear cascade is based on wavelet analysis. In this paper the Hilbert-Huang transform is used which is suitable for nonlinear systems and allows to reconstruct the time-frequency representation of empirical decomposed modes in an adaptive manner. It was found that, in the Lui et al. (2008) event, the modes evolve globally from high-frequencies to low-frequencies. However, there are also local frequency evolution trends oriented towards high-frequencies, indicating that the underlying processes involve multi-scale physics and non-stationary fluctuations for which the simple inverse cascade scenario is not correct.Comment: 6 pages, 4 figure