Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fMRI

Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp 30:452-461, 2009. (C) 2007 Wiley-Liss, Inc.

Grayscale and colour image Codec based on matching pursuit in the spatio-frequency domain

This report presents and evaluates a novel idea for scalable lossy colour image coding with Matching Pursuit (MP) performed in a transform domain. The benefits of the idea of MP performed in the transform domain are analysed in detail. The main contribution of this work is extending MP with wavelets to colour coding and proposing a coding method. We exploit correlations between image subbands after wavelet transformation in RGB colour space. Then, a new and simple quantisation and coding scheme of colour MP decomposition based on Run Length Encoding (RLE), inspired by the idea of coding indexes in relational databases, is applied. As a final coding step arithmetic coding is used assuming uniform distributions of MP atom parameters. The target application is compression at low and medium bit-rates. Coding performance is compared to JPEG 2000 showing the potential to outperform the latter with more sophisticated than uniform data models for arithmetic coder. The results are presented for grayscale and colour coding of 12 standard test images.

Colour image coding with matching pursuit in the spatio-frequency domain

We present and evaluate a novel idea for scalable lossy colour image coding with Matching Pursuit (MP) performed in a transform domain. The idea is to exploit correlations in RGB colour space between image subbands after wavelet transformation rather than in the spatial domain. We propose a simple quantisation and coding scheme of colour MP decomposition based on Run Length Encoding (RLE) which can achieve comparable performance to JPEG 2000 even though the latter utilises careful data modelling at the coding stage. Thus, the obtained image representation has the potential to outperform JPEG 2000 with a more sophisticated coding algorithm.

Information theoretic interpretation of frequency domain connectivity measures

In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.

Frequency-domain receiver design for doubly-selective channels

This work is devoted to the broadband wireless transmission techniques, which are serious candidates to be implemented in future broadband wireless and cellular systems, aiming at providing high and reliable data transmission and concomitantly high mobility. In order to cope with doubly-selective channels, receiver structures based on OFDM and SC-FDE block transmission techniques, are proposed, which allow cost-effective implementations, using FFT-based signal processing. The first subject to be addressed is the impact of the number of multipath components, and the diversity order, on the asymptotic performance of OFDM and SC-FDE, in uncoded and for different channel coding schemes. The obtained results show that the number of relevant separable multipath components is a key element that influences the performance of OFDM and SC-FDE schemes. Then, the improved estimation and detection performance of OFDM-based broadcasting systems, is introduced employing SFN (Single Frequency Network) operation. An initial coarse channel is obtained with resort to low-power training sequences estimation, and an iterative receiver with joint detection and channel estimation is presented. The achieved results have shown very good performance, close to that with perfect channel estimation. The next topic is related to SFN systems, devoting special attention to time-distortion effects inherent to these networks. Typically, the SFN broadcast wireless systems employ OFDM schemes to cope with severely time-dispersive channels. However, frequency errors, due to CFO, compromises the orthogonality between subcarriers. As an alternative approach, the possibility of using SC-FDE schemes (characterized by reduced envelope fluctuations and higher robustness to carrier frequency errors) is evaluated, and a technique, employing joint CFO estimation and compensation over the severe time-distortion effects, is proposed. Finally, broadband mobile wireless systems, in which the relative motion between the transmitter and receiver induces Doppler shift which is different or each propagation path, is considered, depending on the angle of incidence of that path in relation to the direction of travel. This represents a severe impairment in wireless digital communications systems, since that multipath propagation combined with the Doppler effects, lead to drastic and unpredictable fluctuations of the envelope of the received signal, severely affecting the detection performance. The channel variations due this effect are very difficult to estimate and compensate. In this work we propose a set of SC-FDE iterative receivers implementing efficient estimation and tracking techniques. The performance results show that the proposed receivers have very good performance, even in the presence of significant Doppler spread between the different groups of multipath components.

Atrial activation during sinus rhythm in patients with rheumatic and non-rheumatic paroxysmal atrial fibrillation. Frequency-domain analysis using signal-averaged electrocardiography

OBJECTIVE: Using P-wave signal-averaged electrocardiography, we assessed the patterns of atrial electrical activation in patients with idiopathic atrial fibrillation as compared with patterns in patients with atrial fibrillation associated with structural heart disease. METHODS: Eighty patients with recurrent paroxysmal atrial fibrillation were divided into 3 groups as follows: group I - 40 patients with atrial fibrillation associated with non-rheumatic heart disease; group II - 25 patients with rheumatic atrial fibrillation; and group III - 15 patients with idiopathic atrial fibrillation. All patients underwent P-wave signal-averaged electrocardiography for frequency-domain analysis using spectrotemporal mapping and statistical techniques for detecting and quantifying intraatrial conduction disturbances. RESULTS: We observed an important fragmentation in atrial electrical conduction in 27% of the patients in group I, 64% of the patients in group II, and 67% of the patients in group III (p=0.003). CONCLUSION: Idiopathic atrial fibrillation has important intraatrial conduction disturbances. These alterations are similar to those observed in individuals with rheumatic atrial fibrillation, suggesting the existence of some degree of structural involvement of the atrial myocardium that cannot be detected with conventional electrocardiography and echocardiography.

Time- and frequency-domain modeling of passive interconncection structured in field and circuit analysis

PEEC, computational electromagnetics

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Frequency-Domain and Wide-Pulse Time-Domain Measurements of Lanthanide Luminescence and Lanthanide-Based Resonance Energy Transfer

Resonance energy transfer (RET) is a non-radiative transfer of the excitation energy from the initially excited luminescent donor to an acceptor. The requirements for the resonance energy transfer are: i) the spectral overlap between the donor emission spectrum and the acceptor absorption spectrum, ii) the close proximity of the donor and the acceptor, and iii) the suitable relative orientations of the donor emission and the acceptor absorption transition dipoles. As a result of the RET process the donor luminescence intensity and the donor lifetime are decreased. If the acceptor is luminescent, a sensitized acceptor emission appears. The rate of RET depends strongly on the donor–acceptor distance (r) and is inversely proportional to r6. The distance dependence of RET is utilized in binding assays. The proximity requirement and the selective detection of the RET-modified emission signal allow homogeneous separation free assays. The term lanthanide-based RET is used when luminescent lanthanide compounds are used as donors. The long luminescence lifetimes, the large Stokes’ shifts and the intense, sharply-spiked emission spectra of the lanthanide donors offer advantages over the conventional organic donor molecules. Both the organic lanthanide chelates and the inorganic up-converting phosphor (UCP) particles have been used as donor labels in the RET based binding assays. In the present work lanthanide luminescence and lanthanide-based resonance energy transfer phenomena were studied. Luminescence lifetime measurements had an essential role in the research. Modular frequency-domain and time-domain luminometers were assembled and used successfully in the lifetime measurements. The frequency-domain luminometer operated in the low frequency domain ( 100 kHz) and utilized a novel dual-phase lock-in detection of the luminescence. One of the studied phenomena was the recently discovered non-overlapping fluorescence resonance energy transfer (nFRET). The studied properties were the distance and temperature dependences of nFRET. The distance dependence was found to deviate from the Förster theory and a clear temperature dependence was observed whereas conventional RET was completely independent of the temperature. Based on the experimental results two thermally activated mechanisms were proposed for the nFRET process. The work with the UCP particles involved the measurement of the luminescence properties of the UCP particles synthesized in our laboratory. The goal of the UCP particle research is to develop UCP donor labels for binding assays. In the present work the effect of the dopant concentrations and the core–shell structure on the total up-conversion luminescence intensity, the red–green emission ratio, and the luminescence lifetime was studied. Also the non-radiative nature of the energy transfer from the UCP particle donors to organic acceptors was demonstrated for the first time in aqueous environment and with a controlled donor–acceptor distance.

A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed.

A MATLAB GUI for learning controller design in the frequency domain

A MATLAB GUI is presented which is used to help students learn to design controllers in the frequency domain. It complements the author’s two previous GUIs for plotting and identification of systems in the frequency domain. It also incorporates the concept used in the “electronic calculator that makes students think” to assist learning. Positive student feedback affirms that the GUI has helped their understanding.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.