41 research outputs found
Cumulant based identification approaches for nonminimum phase FIR systems
Cataloged from PDF version of article.In this paper, recursive and least squares methods
for identification of nonminimum phase linear time-invariant
(NMP-LTI) FIR systems are developed. The methods utilize the
second- and third-order cumulants of the output of the FIR
system whose input is an independent, identically distributed
(i.i.d.) non-Gaussian process. Since knowledge of the system
order is of utmost importance to many system identification algorithms,
new procedures for determining the order of an FIR
system using only the output cumulants are also presented. To
illustrate the effectiveness of our methods, various simulation
examples are presented
Cumulant-based identification of non gaussian moving average signals
In this paper, an overview on higher-order statistics based identification methods is presented, and tree batch blind estimation
methods are proposed . One of them use both autocorrelation and cumulant sequences, the others are cumulant-based only .
The cumulant-based ones are respectively a generalization of Zhang et al.'s method and a reformulation of Giannakis-Mendel's
method without autocorrelation . By simulations, we evaluate their performances and compare them together and with the existing
approaches. The results show that the generalization of Zhang et al.'s method give good estimates, specially in noise environment
(white or colored noises) .Dans ce papier, nous donnons un aperçu des méthodes classiques d'identification des signaux linéaires non gaussiens de type à moyenne ajustée basées sur les statistiques d'ordre supérieur (SOS). Puis, nous proposons trois méthodes d'estimation globale : la première combine l'autocorrélation et les cumulants et les deux autres exploitent les cumulants seuls. L'une d'entre elles généralise la méthode de Zhang et al., La deuxième est une modification de l'approche reformulée de Giannakis et Mendel. Elle est obtenue en remplaçant les moments d'ordre deux, sensibles aux bruits gaussiens, par des cumulants, grâce à une relation qu'on développera. Finalement nous testons par simulations les performances des trois méthodes proposées et nous les comparons à d'autres approches existantes. Les résultats montrent que la méthode proposée généralisant celle de Zhang et al., fournit de bons résultats et qu'elle est plus résistante aux effets des bruits blancs ou colorés
Impulse response recovery of linear systems through weighted cumulant slice
Identifiability of the so-called ω-slice algorithm is proven for ARMA linear systems. Although proofs were developed in the past for the simpler cases of MA and AR models, they were not extendible to general exponential linear systems. The results presented in this paper demonstrate a unique feature of the ω-slice method, which is unbiasedness and consistency when order is overdetermined, regardless of the IIR or FIR nature of the underlying system, and numerical robustness.Peer Reviewe
Blind Separation of Independent Sources from Convolutive Mixtures
International audienceThe problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the para-unitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks
Blind, MIMO system estimation based on PARAFAC decomposition of higher order output tensors
IEEE Transactions on Signal Processing, 54(11): pp. 4156-4168.We present a novel framework for the identification of
a multiple-input multiple-output (MIMO) system driven by white,
mutually independent unobservable inputs. Samples of the system
frequency response are obtained based on parallel factorization
(PARAFAC) of three- or four-way tensors constructed based on,
respectively, third- or fourth-order cross spectra of the system outputs.
The main difficulties in frequency-domain methods are frequency-
dependent permutation and filtering ambiguities.We show
that the information available in the higher order spectra allows
for the ambiguities to be resolved up to a constant scaling and permutation
ambiguities and a linear phase ambiguity. Important features
of the proposed approach are that it does not require channel
length information, needs no phase unwrapping, and unlike the
majority of existing methods, needs no prewhitening of the system
outputs
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Advanced robust non-invasive foetal heart detection techniques during active labour using one pair of transabdominal electrodes
The thesis proposes and evaluates three state-of-the-art signal processing techniques to detect fetal heartbeats within each maternal cardiac cycle, during labour contractions, using only a pair of transabdominal electrodes. The first and second techniques are, namely, the structured third- order cumulant-slice-template matching and the bispectral-contours-template matching for fetal QRS identification, respectively. The third technique is based on the modified and appropriately weighted spectral multiple signal classification (MUSIC) with incorporated covariance matrix for uterine contraction noise-like interfering signals also contaminated with noise. Essentially, two modifications to the standard MUSIC have been developed in order to enhance the performance of the spectral estimator in our applied work. The first modification involves the introduction of an optimised weighting function to the segmented ECG covariance matrix, and is chiefly aimed at enhancing the fetal QRS major spectral peak which occurs at around 30 Hz against the mother QRS major spectral peak usually occurring around 17 Hz and all other noise contributions. Additional optional pseudo-bispectral enhancement to sharpen the maternal and fetal spectral peaks, in particular when the mother and fetal R-waves are temporally coincident, have been achieved. The second modification to the spectral MUSIC is the removal of the unjustified assumption that only white Gaussian noise is present and the incorporation of the actual measured labour uterine contraction covariance matrix in reconfigured subspace analysis. This inevitably leads to the generalised eigenvectors - eigenvalues decomposition modern signal processing. This is now coined the modified, interference incorporated pseudo-spectral MUSIC. The above mentioned first and second techniques are higher-order statistics-based (HOS) and hybrid involving both signal processing and NN classifiers. The third technique is second-order statistics-based (SOS). In all techniques, the removal of signal non-linearity with the aid of non-linear Volterra synthesisers plays a crucial part in the fetal detection integrity.
Accurately assessed fetal heart classification rates as high as 95% have been achieved during labour, thus helping to provide non-invasive transparency to fetal intrapartum welfare. Performance analysis and evaluation processes involved more than 30 critical cases classified as “fetal under stress in labour” recorded in a London hospital database and used both transbadominal ECG electrodes and fetal scalp electrodes. The latter facilitates detection of the instantaneous fetal heart rate which is then used as the Reference Fetal Heart Rate in the assessment of the classification rate of each of the above mentioned techniques. It will be shown that the fetal heartbeats are completely masked by uterine activity and noise artefacts in all the recorded transabdominal maternal ECG signals. The fetal scalp electrode was, therefore, deemed necessary to provide the highest accurate measure of fetal heart functionality (from the hospital viewpoint), and in the assessment of the three non-invasive techniques presented in this thesis. The techniques may also be used during gestation and as early as 10 weeks
Computation of the one-dimensional unwrapped phase
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M