Kalman filters are based on linear dynamical systems discretised **in** the time domain. They are modeled on a Markov chain built on linear operators perturbed by Gaussian noise. The state of the system is represented as a vector of real numbers. At each discrete time increment, a linear operator is applied to the state to generate the new state, with some noise mixed **in**, and optionally some information from the controls on the system if they are known. Then, another linear operator mixed with more noise generates the visible outputs from the hidden state. The Kalman filter may be regarded as analogous to the hidden Markov model, with the key difference that the hidden state variables take values **in** a continuous space (as opposed to a discrete state space as **in** the hidden Markov model). Additionally, the hidden Markov model can represent an arbitrary distribution for the next value of the state variables, **in** contrast to the Gaussian noise model that is used for the Kalman filter. There is a strong duality between the equations of the Kalman Filter and those of the hidden Markov model.

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60 Hz AC interference can be a problem **in** any biopotential measurement situation. The source of such interference is the AC potential of the electrical power supply network that is inevitably present **in** any clinical situation, either for lighting the environment or as a source of supply for the measuring equipment. Electrical interference at 60 Hz can be difficult to detect visually on signals having non-regular waveforms such as EEG or EMG. Nevertheless, the interference is easily visible when present **in** signals with well-defined waveforms, such as the **ECG** (Electrocardiogram) **signal**. **In** any case, the power spectrum of the **signal** shall provide a clear indication of the presence of the network interference as a 60 Hz pulse. The harmonics, if present, appear as additional pulses **in** integral multiples of the fundamental frequency. **In** this work, a **filtering** technique is demonstrated, using a digital Notch filter, which removes the 60 Hz artifact from the **ECG** **signal**, increasing the reliability of the clinical diagnosis from its interpretation.

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Numerous methods have been reported to denoise **ECG** signals based on filter banks, principal component analysis (PCA), independent component analysis (ICA), neural networks (NNs), adaptive **filtering**, empirical mode decomposition (EMD), and wavelet transform [24]-[5]. The filter bank based denoising process smoothes the P and R amplitude of the **ECG** **signal**, and it is more sensitive to different levels of noise [22]. By exploiting PCA or ICA or NNs, a statistical model of the **ECG** **signal** and noise is first extracted and then, the **in**-band noise is removed by discarding the dimensions corresponding to the noise [8]-[34]. Although PCA, ICA and NNs based schemes are powerful for **in**-band noise **filtering**, the statistical model derived therein is not only fairly arbitrary but also extremely sensitive to small changes **in** either the **signal** or the noise unless the basis functions are trained on a global set of **ECG** beat types. **In** particular, one of the difficulties with the application of ICA is the determination of the order of the independent components (ICs). Thus for further processing, visual inspection is required, which is undesirable **in** routine clinical **ECG** analysis [35]. The limitations of the adaptive **filtering** based **ECG** denoising lies **in** the fact that a reference **signal** has to be additionally recorded together with the **ECG** [36].

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Hence, the development of novel, non-invasive, accurate and home-bound techniques based on a reduced and simplified set of biometric signals [13] may represent a feasible and accurate alternative method to PSG. **In** fact, this scenario may enable an affordable and ubiquitous recording of patient data **in** the comfort of their houses, offering the opportunity for broader and more effective monitoring of the population, using less resources of the public and/or private health systems. However, since the sleep apnea detection is based on a reduced set of signals, the use of **signal** processing techniques such as **filtering**, wrapping, feature extraction, and feature selection becomes critical and challenging regarding the design of specialized computerized systems. On the one hand, the wise selection of the most informative and/or rep- resentative features may lead to improve the overall accuracy of the system. On the other hand, methods for feature selection are prone to produce new suggested features which require further evaluation that may lead to additional computational costs.

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Early diagnosis and early treatment is an effective method for the control of diabetic retinop- athy [5, 6]. Fundus imaging by digital fundus camera is a standard diagnostic mode **in** ophthal- mology, which captures the intensity of light reflected from the retinal surface **in** three different wavelength ranges [7, 8]. By reason of imaging mechanism and system of fundus retina imaging itself, and the disturbance of various noise **in** image formation process, one often obtain noisy and blurry retinal image with nonuniform and distorted illumination, which is difficult to inter- pret medically and to process subsequently [7, 9–11]. Thus, it is indispensable to remove noise and disturbances, to improve **signal**-to-noise rate of image, to adjust image contrast and to enhance vessels and fine details of retinal image data [9, 12, 13]. By above image preprocessing, useful information **in** retinal image is highlighted, while useless one is weakened or removed, to make the result more suitable to clinical diagnosis and treatment [3, 7, 9, 14–17].

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Conventionally used ANCs basically require two inputs: primary input and reference input. For an ANC to be feasible, the reference input must be correlated with the noise part of the primary input **in** order to cancel the noise therein. However, there are cases **in** which commonly used ANCs are limited **in** use. For example, if off-line processing of **ECG** recordings is required, the recordings themselves are the only data available for processing. Moreover, **in** the case when reference input cannot be well-correlated with the noise part of the primary input, ANC cannot perform well as the case with a well correlated reference input. **In** such cases, alternative approaches other than an ANC must be pursued. Figure 1 shows the example of conventional model of adaptive noise canceller with reference input.

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Abstract – The **ECG** **signal** is abruptly changing and continuous **in** nature. The heart disease such as paroxysmal of heart, arrhythmia diagnosing, are related with the intelligent health care decision this **ECG** **signal** need to be pre-process accurately for further action on it such as extracting the features, wavelet decomposition, distribution of QRS complexes **in** **ECG** recordings and related information such as heart rate and RR interval, classification of the **signal** by using various classifiers etc. Filters plays very important role **in** analyzing the low frequency components **in** **ECG** **signal**. The biomedical signals are of low frequency, the removal of power line interference and baseline wander is a very important step at the pre-processing stage of **ECG**. **In** these paper we deal with the study of Median **filtering** and FIR (Finite Impulse Response)**filtering** of **ECG** signals under noisy condition.

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A simple and promising method for reducing the PMEPR of DS-CDMA signals it to employ a **nonlinear** clipping operation **in** the time-domain followed by a linear, frequency-domain **filtering** operation so as to generate a low-PMEPR version of the DS-CDMA **signal**, occupying the same bandwidth of the corresponding conventional DS-CDMA **signal** [8], [9] (similar techniques have also been proposed for reducing the envelope fluctuations of orthogonal frequency division multi- plexing (OFDM) signals [10]). However, the **filtering** operation produces some envelope fluctuations regrowth, limiting the achievable PMEPR [9]. As with OFDM schemes [11], [12], by repeating the clipping and **filtering** procedures we can reduce the PMEPR regrowth **in** multicode DS-CDMA schemes [13]. However, **nonlinear** distortion levels increase when we repeat the clipping and **filtering** procedures, leading to performance degradation. This performance degradation can be particularly high when we have different powers assigned to different spreading codes, especially for the spreading codes with lower power [14]. A scenario where this effect might be significant is for multi-resolution broadcasting systems [15], [16], where we transmit simultaneously several parallel data streams with different powers so as to have different error protections. For DS-CDMA systems, this can be achieved by assigning to each resolution a subset of the available spreading codes and a different power to each subset (i.e., the spreading codes with higher power have higher error protection and, therefore, are associated to the basic (lower) resolution).

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have been proposed to reduce the envelope fluctuations of OFDMA signals namely through suitable pre-processing schemes [9]–[11]. As an alternative, we can employ clipping and **filtering** techniques, already shown to be effective for conventional OFDM signals [12]–[14], as well as MC-CDMA (Multi-Carrier Code Division Multiple Access) schemes [15]. The performance evaluation of multicarrier schemes with **nonlinear** transmission (either due to an imperfectly linear amplification or due to suitable **signal** processing schemes to reduce the envelope fluctuations of the transmitted signals), usually resorts to Monte-Carlo simulations that require a long computation time; heuristic, "semi-analytical", approaches have also been proposed so as to evaluate **nonlinear** distortion effects (see, e.g., [16]). When the number of subcarriers is high we can take advantage of the Gaussian nature of the transmitted signals to characterize statistically the transmitted signals [12], [15], [17]–[20]. The **nonlinear** devices considered **in** [12], [15], [17], [18] can be regarded as bandpass memory- less nonlinearities [21] ([15] considers MC-CDMA signals and [12], [17], [18] consider OFDM signals). [19], [20] consider quantization effects on OFDM signals, i.e., the **nonlinear** devices can be regarded as I-Q memoryless nonlinearities.

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Basic peculiarities of **nonlinear** Kalman **filtering** algorithm applied to processing of interferometric signals are considered. Analytical estimates determining statistical characteristics of **signal** values prediction errors were obtained and analysis of errors histograms taking into account variations of different parameters of interferometric **signal** was carried out. Modeling of the **signal** prediction procedure with known fixed parameters and variable parameters of **signal** **in** the algorithm of **nonlinear** Kalman **filtering** was performed. Numerical estimates of prediction errors for interferometric **signal** values were obtained by formation and analysis of the errors histograms under the influence of additive noise and random variations of amplitude and frequency of interferometric **signal**. **Nonlinear** Kalman filter is shown to provide processing of signals with randomly variable parameters, however, it does not take into account directly the linearization error of harmonic function representing interferometric **signal** that is a **filtering** error source. The main drawback of the linear prediction consists **in** non-Gaussian statistics of prediction errors including cases of random deviations of **signal** amplitude and/or frequency. When implementing stochastic **filtering** of interferometric signals, it is reasonable to use prediction procedures based on local statistics of a **signal** and its parameters taken into account.

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Abstract. The asymptotic behavior of a **nonlinear** continuous time ﬁltering problem is studied when the variance of the observation noise tends to 0. We suppose that the **signal** is a two-dimensional process from which only one of the components is noisy and that a one-dimensional function of this **signal**, depending only on the unnoisy component, is observed **in** a low noise channel. An approximate ﬁlter is considered **in** order to solve this problem. Under some detectability assumptions, we prove that the ﬁltering error converges to 0, and an upper bound for the convergence rate is given. The eﬃciency of the approximate ﬁlter is compared with the eﬃciency of the optimal ﬁlter, and the order of magnitude of the error between the two ﬁlters, as the observation noise vanishes, is obtained.

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The extraction of parameters from a noisy electrocardiogram (**ECG**) remains an important task for the biomedical engineering community. The **ECG** is the representation of the potential difference between different points on a body surface that originate from the electrical activity of human heart and it’s considered as a nonstationary **signal**. Time- frequency transforms as Discrete Wavelet Transform (DWT) and Wavelet Packet Transform (WPT) are usually known as very useful **in** non-stationary signal’s analysis due to their multiresolution capabilities. Wavelet Transform (WT) based **filtering** is now a common practice for denoising of signals having multiresolution characteristics such as the **ECG** **signal** [8], [2], [3].

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A promising class of **nonlinear** **signal** processing schemes for reducing the envelope fluctuations (and, inherently, the PMEPR) of DS-CDMA signals was proposed **in** [8]. These schemes combine a **nonlinear** operation **in** the time-domain, followed by a linear, frequency-domain **filtering** operation to reduce significantly the PMEPR of the transmitted signals, while maintaining the spectral occupation of the corresponding conventional DS-CDMA signals. However, the performance degradation due to the **nonlinear** distortion effects on the transmitted signals can be relatively high, especially when a low PMEPR is intended and/or different powers are assigned to different spreading codes.

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Gustavo Pratas Norte | Mestrado Integrado em Medicina | Universidade da Beira Interior 19 doentes triados com DT foi de 14 minutos (P25-75 6,0-38,0) e dos doentes com EAMCST associado a DT foi de 6,5 minutos (P25–75 3,0-14,0), sendo que apenas 41,2% dos doentes com DT e 48,2% dos doentes com EAMCST associado a DT fizeram o **ECG** até aos 10 minutos. Num estudo realizado por Diercks, Kirk(8), apenas 30,8% dos doentes que foram admitidos no serviço de urgência com DT e 40,9% dos doentes com EAMCST associado a DT realizaram o **ECG** em menos de 10 minutos. Estas diferenças indicam um incumprimento dos tempo-alvo para **ECG** preconizados no protocolo interno de VVC do CHCB, assim como nas guidelines internacionais e nacionais(4-6). Para a melhoria destes indicadores, deve investir-se na triagem da DT para aumentar o número de doentes que realizam **ECG** e que o fazem num tempo inferior a 10 minutos.

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An important tool for the heart disease diagnosis is the analysis of electrocardiogram (**ECG**) signals, since the non-invasive nature and simplicity of the **ECG** exam. According to the application, **ECG** data analysis consists of steps such as preprocessing, segmentation, feature extraction and classification aiming to detect cardiac arrhythmias (i.e., cardiac rhythm abnormalities). Aiming to made a fast and accurate car- diac arrhythmia **signal** classification process, we apply and analyze a recent and robust supervised graph- based pattern recognition technique, the optimum-path forest (OPF) classifier. To the best of our knowl- edge, it is the first time that OPF classifier is used to the **ECG** heartbeat **signal** classification task. We then compare the performance (**in** terms of training and testing time, accuracy, specificity, and sensitivity) of the OPF classifier to the ones of other three well-known expert system classifiers, i.e., support vector machine (SVM), Bayesian and multilayer artificial neural network (MLP), using features extracted from six main approaches considered **in** literature for **ECG** arrhythmia analysis. **In** our experiments, we use the MIT-BIH Arrhythmia Database and the evaluation protocol recommended by The Association for the Advancement of Medical Instrumentation. A discussion on the obtained results shows that OPF classifier presents a robust performance, i.e., there is no need for parameter setup, as well as a high accuracy at an extremely low computational cost. Moreover, **in** average, the OPF classifier yielded greater perfor- mance than the MLP and SVM classifiers **in** terms of classification time and accuracy, and to produce quite similar performance to the Bayesian classifier, showing to be a promising technique for **ECG** **signal** analysis.

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There is a body of literature **in** atmospheric science that considers cloud microphysical parameterizations as one of the main sources of error **in** operational climate and weather forecast models (e.g. Cantrell and Heymsfield, 2005; K¨archer and Koop, 2005). Microphysical processes deal with small spatial and temporal scales (smaller than a few cen- timeters and up to an hour) which are not directly resolved **in** global circulation models (GCMs). Therefore, the param- eterization of microphysical processes at scales resolved **in** GCMs (down to 100 kilometers and down to a few hours) is based on many assumptions which are currently not opti- mal at providing accurate descriptions of cloud microphysi- cal properties. Parameters characterizing microphysical pro- cesses are cloud particle phases, their main orientations, their habits as well as their size distributions. A better understand- ing of such small scale processes and their characterization at large scales are of great importance **in** order to improve mi- crophysical parameterizations. This can be achieved from the knowledge we gain from a proper use of cloud observation sensors (Shupe et al., 2008).

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The research of Prony **filtering** method performed **in** the simula- tion experiments allowed us to explore its features and clarify the range of problems, where the method can be used effectively. They show that if the real data (observations of the wave field) contains high-frequency components corresponding to seismic objects, then the Prony **filtering** allows us to identify them quite accurately. **In** this case the objects allocated **in** the wave field (for example, reflections from fixed horizon) can have rather good resolution **in** the temporal and spatial coordinates. During **filtering** process there can be changes **in** the shape of the extracted **signal** leading to its tension as well as to the appearance of additional sharp dis- tortions. At the same time, the methodological techniques devel- oped for determination of the optimal **filtering** parameters allow us to improve the accuracy of **signal** components extraction. Com- parison of the results of Prony and band-pass **filtering** demon- strates significant advantages of the first over the second **in** the separation and analysis of **signal** components with different fre- quencies. This provides a good opportunity for the method to de- termine the frequency sensitive effects and localization of regions with different damping/dispersion of seismic energy. The results

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The study protocol was **in** accordance with the principles of the Helsinki Declara- tion and was approved by the Ethics Com- mittee **in** Clinical Research of the Laranjeiras National Institute of Cardiology, Rio de Ja- neiro, RJ, Brazil, and all subjects provided written informed consent before enrollment. The study population was recruited from January to July 2004 and comprised 36 sub- jects divided into two groups: 18 trained long-distance runners (athletes) and 18 healthy untrained subjects (controls). The sample size used **in** the present study was calculated from numerical variables as de- scribed by Smith et al. (6) and Raineri et al. (10). From reference data, the sampling pro- cedure was based on the difference of the 40-µV terminal (LAS40, ms) of at least 10 ms, with values of α = 0.05 and ß = 0.1, on the vector magnitude, filtered by a 4-pole bi- directional bandpass Butterworth filter with cut-off frequencies at 40 and 250 Hz, and using XYZ Frank orthogonal leads. The sub- jects participating **in** the present study were slightly younger but had similar anthropo- metric characteristics and gender distribu- tion as those **in** the studies used as reference **in** the sampling procedure (6,10). Inclusion criteria were volunteers over 18 and less than 40 years old, **in** good mental and physi- cal health, without a previous history of cardiovascular disease or systemic arterial hypertension. Subjects less than 18 and more than 40 years old, with a previous history of diabetes mellitus, thyroid dysfunction or liver disease, alcohol consumers, or tobacco smok- ers, or those currently taking any medicine were excluded.

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multiphoton absorption and ionization, caused by fs-laser exposure, lead to free electron generation and photoreduction reactions. When kHz repetition rate laser is applied, such effects are observed **in** the absorption spectrum through color centers, defects and other induced electronic states. Then, this preferential light absorption gives rise to the plasmon band after the suitable annealing. On the other hand, metallic nanoparticles readily precipitate when thermal effects associated with high repletion rates are presents, and the SPR band is observed even without heat treatment. An detailed study about the ionic species and clusters of silver induced by femtosecond laser was recently reported. 53

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It is important to highlight that the cut size obtained during operation of the hydrocyclone results not only from the action of the centrifugal field but also from the solid material carried by the downward stream fluid. Therefore, for the purpose of comparison with other hydrocyclones, the cut size due exclusively to centrifugal separation should be defined. This definition corresponds to the so-called reduced cut size ( d ' 50 ), **in** which the flow-splitting effect (dead flux effect) is discounted (Svarovsky, 1984).

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