3,499 research outputs found
Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets
A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method
Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects
AbstractâThis paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index TermsâFinite difference methods, time-domain analysis, transmission lines, wavelet transforms. I
Time-varying signal processing using multi-wavelet basis functions and a modified block least mean square algorithm
This paper introduces a novel parametric modeling and identification method for linear time-varying systems using a modified block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be used to track rapidly or even sharply varying processes and is more suitable for recursive estimation of process parameters by combining wavelet approximation theory with a modified block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstatinoary processes
Separating Gravitational Wave Signals from Instrument Artifacts
Central to the gravitational wave detection problem is the challenge of
separating features in the data produced by astrophysical sources from features
produced by the detector. Matched filtering provides an optimal solution for
Gaussian noise, but in practice, transient noise excursions or ``glitches''
complicate the analysis. Detector diagnostics and coincidence tests can be used
to veto many glitches which may otherwise be misinterpreted as gravitational
wave signals. The glitches that remain can lead to long tails in the matched
filter search statistics and drive up the detection threshold. Here we describe
a Bayesian approach that incorporates a more realistic model for the instrument
noise allowing for fluctuating noise levels that vary independently across
frequency bands, and deterministic ``glitch fitting'' using wavelets as
``glitch templates'', the number of which is determined by a trans-dimensional
Markov chain Monte Carlo algorithm. We demonstrate the method's effectiveness
on simulated data containing low amplitude gravitational wave signals from
inspiraling binary black hole systems, and simulated non-stationary and
non-Gaussian noise comprised of a Gaussian component with the standard
LIGO/Virgo spectrum, and injected glitches of various amplitude, prevalence,
and variety. Glitch fitting allows us to detect significantly weaker signals
than standard techniques.Comment: 21 pages, 18 figure
Sparse Linear Models applied to Power Quality Disturbance Classification
Power quality (PQ) analysis describes the non-pure electric signals that are
usually present in electric power systems. The automatic recognition of PQ
disturbances can be seen as a pattern recognition problem, in which different
types of waveform distortion are differentiated based on their features.
Similar to other quasi-stationary signals, PQ disturbances can be decomposed
into time-frequency dependent components by using time-frequency or time-scale
transforms, also known as dictionaries. These dictionaries are used in the
feature extraction step in pattern recognition systems. Short-time Fourier,
Wavelets and Stockwell transforms are some of the most common dictionaries used
in the PQ community, aiming to achieve a better signal representation. To the
best of our knowledge, previous works about PQ disturbance classification have
been restricted to the use of one among several available dictionaries. Taking
advantage of the theory behind sparse linear models (SLM), we introduce a
sparse method for PQ representation, starting from overcomplete dictionaries.
In particular, we apply Group Lasso. We employ different types of
time-frequency (or time-scale) dictionaries to characterize the PQ
disturbances, and evaluate their performance under different pattern
recognition algorithms. We show that the SLM reduce the PQ classification
complexity promoting sparse basis selection, and improving the classification
accuracy
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