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Signal Processing, IEEE Transactions on

Issue 12 • Date Dec 1994

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Displaying Results 1 - 25 of 27
  • M-ary wavelet transform and formulation for perfect reconstruction in M-band filter bank

    Publication Year: 1994 , Page(s): 3508 - 3512
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design View full abstract»

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  • Efficient scheduling and instruction selection for programmable digital signal processors

    Publication Year: 1994 , Page(s): 3549 - 3552
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (308 KB)  

    We present an efficient method for optimized instruction selection and scheduling for programmable digital signal processors. Our approach uses artificial intelligence techniques to yield code that is comparable to that of hand-written assembly codes by DSP experts. Several examples which demonstrate the feasibility of the approach, targeted to the TMS32020/50 architecture, are presented View full abstract»

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  • Kalman-based estimator for DOA estimations

    Publication Year: 1994 , Page(s): 3543 - 3547
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    We introduce a new Kalman-based noise-subspace estimator combined with the Root-MUSIC for direction of-arrival (DOA) estimation of uncorrelated narrow-band plane waves impinging on an array of sensors. Without both a priori knowledge of the number of sources and the inflation method presented by Yang and Kaveh (1988), we show that the Kalman-based estimator can approximately estimate the complete noise subspace with small bias for high input signal-to-noise ratio (SNR) scenario. The proposed algorithm needs slightly more computation operations per adaptive cycle than Yang and Kaveh's LMS-based algorithm, but with much more rapid convergence. Simulations demonstrate the effectiveness of the proposed algorithm View full abstract»

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  • Detection and estimation using an adaptive rational function filter

    Publication Year: 1994 , Page(s): 3366 - 3376
    Cited by:  Papers (35)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (848 KB)  

    Proposes a new nonlinear adaptive filter structure based on rational functions. There are several advantages to the use of this filter. First, it is a universal approximator and a good extrapolator. Second, it ran be trained by a linear adaptive algorithm, which makes it suitable for real-time adaptive signal processing. Third, it has a best approximation for a specified function. To demonstrate its utility as a tool for solving adaptive signal processing problems, the authors apply the adaptive rational function filter to the problem of estimation and detection. The estimation problem pertains to the direction of arrival (DOA) estimation problem in array signal processing. For the detection problem, the authors consider the detection of a weak radar target (a small piece of ice) in an ocean environment View full abstract»

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  • ARMA system identification based on second-order cyclostationarity

    Publication Year: 1994 , Page(s): 3483 - 3494
    Cited by:  Papers (26)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (876 KB)  

    Previous work has presented novel techniques that exploit cyclostationarity for channel identification in data communication systems. The present authors investigate the identifiability of linear time-invariant (LTI) ARMA systems based on second-order cyclic statistics. They present a parametric and a nonparametric method. The parametric method directly identifies the zeros and poles of ARMA channels with a mixed phase. The nonparametric method estimates the channel phase based on the cyclic spectra alone. They analyze the phase estimation error of the nonparametric method for finite dimensional ARMA channels. For specific, finite dimensional ARMA channels, an improved method is given, which combines the parametric method with the nonparametric method. Computer simulation illustrates the effectiveness of the methods in identifying ARMA system impulse responses View full abstract»

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  • A Levinson-type algorithm for a class of non-Toeplitz systems with applications to multichannel IIR filtering

    Publication Year: 1994 , Page(s): 3309 - 3320
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (788 KB)  

    A very flexible Levinson-type recursion for a class of non-Toeplitz systems of linear equations is demonstrated. A complete solution is expressed as a linear combination of a partial solution and three auxiliary solutions. The class of systems possesses a special structure in that the coefficient matrices can be partitioned into four block Toeplitz submatrices. The number of multiplications and additions required to compute an n-dimensional solution is O(n2). The recursion is then applied to multichannel IIR filtering. Specifically, a lattice structure is established for linear minimum mean square error predictors having independently and arbitrarily specified numbers of poles and zeros. Next the recursion is used to develop a fast time and order recursive least-squares algorithm for ARX system identification. The novelty of the algorithm is that it can be used to efficiently determine parameter estimates of a family of ARX models View full abstract»

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  • Alternative proofs for “On unique localization of constrained-signal sources”

    Publication Year: 1994 , Page(s): 3547 - 3549
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (276 KB)  

    We provide simple proofs for the theorems in “On Unique Localization of Constrained-Signal Sources” by M. Wax (see ibid. vol.40, p.1542-1547, June 1992). The approach is based on the topological dimension of a set. All the possible observation matrices form the legitimate set. The observation matrices that can have nonunique solutions form the ambiguity set. The components of the legitimate and ambiguity set are random matrices. We find the conditions under which the dimensionality of the ambiguity set is smaller than the dimensionality of the legitimate set. In such a case, the probability of the ambiguity set is zero and with probability one, a unique solution can be found for the localization problem View full abstract»

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  • A simple scheme for adapting time-frequency representations

    Publication Year: 1994 , Page(s): 3530 - 3535
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (472 KB)  

    We propose a simple, efficient technique for continuously adapting time-frequency and time-scale representations over time. The procedure computes a short-time quality measure of the representation for a range of values of a free parameter and estimates the optimal parameter value maximizing the quality measure via interpolation View full abstract»

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  • Convergence properties of median and weighted median filters

    Publication Year: 1994 , Page(s): 3515 - 3518
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    It has been shown that assuming the first and last value carry-on appending strategy, a finite number of passes of the same median filter to an arbitrary signal of finite length results in a root signal that will be invariant to additional filtering passes. This so-called convergence property is reproven using an extremely simple approach. In addition, the well-known idempotent property (i.e., where convergence is achieved with only one filtering pass) of a recursive median filter is reproven similarly, and the convergence behavior of weighted median filters is studied View full abstract»

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  • A Bayesian approach to auto-calibration for parametric array signal processing

    Publication Year: 1994 , Page(s): 3495 - 3507
    Cited by:  Papers (53)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1020 KB)  

    A number of techniques for parametric (high-resolution) array signal processing have been proposed in the last few decades. With few exceptions, these algorithms require an exact characterization of the array, including knowledge of the sensor positions, sensor gain/phase response, mutual coupling, and receiver equipment effects. Unless all sensors are identical, this information must typically be obtained by experimental measurements (calibration). In practice, of course, all such information is inevitably subject to errors. Several different methods have been proposed for alleviating the inherent sensitivity of parametric methods to such modelling errors. The technique proposed in the present paper is related to the class of so-called auto-calibration procedures, but it is assumed that certain prior knowledge of the array response errors is available. This is a reasonable assumption in most applications, and it allows for more general perturbation models than does pure auto-calibration. The optimal maximum a posteriori (MAP) estimator for the problem at hand is formulated, and a computationally more attractive large-sample approximation is derived. The proposed technique is shown to be statistically efficient, and the achievable performance is illustrated by numerical evaluation and computer simulation View full abstract»

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  • Time-domain tests for Gaussianity and time-reversibility

    Publication Year: 1994 , Page(s): 3460 - 3472
    Cited by:  Papers (36)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1132 KB)  

    Statistical signal processing algorithms often rely upon Gaussianity and time-reversibility, two important notions related to the probability structure of stationary random signals and their symmetry. Parametric models obtained via second-order statistics (SOS) are appropriate when the available data is Gaussian and time-reversible. On the other hand, evidence of nonlinearity, non-Gaussianity, or time-irreversibility favors the use of higher-order statistics (HOS). In order to validate Gaussianity and time-reversibility, and quantify the tradeoffs between SOS and HOS, consistent, time-domain chi-squared statistical tests are developed. Exact asymptotic distributions are derived to estimate the power of the tests, including a covariance expression for fourth-order sample cumulants. A modification of existing linearity tests in the presence of additive Gaussian noise is discussed briefly. The novel Gaussianity statistic is computationally attractive, leads to a constant-false-alarm-rate test and is well suited for parametric modeling because it employs the minimal HOS lags which uniquely characterize ARMA processes. Simulations include comparisons with an existing frequency-domain approach and an application to real seismic data. Time-reversibility tests are also derived and their performance is analyzed both theoretically and experimentally View full abstract»

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  • A note on the error propagation analysis of recursive least squares algorithms

    Publication Year: 1994 , Page(s): 3523 - 3525
    Cited by:  Papers (1)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB)  

    The article comments on the error propagation analysis of recursive least squares algorithms presented by Ljung and Ljung (1985), Verhaegen (1989), and Haykin (1991). In particular, it corrects some incorrect statements about the error propagation given in the literature. It considers the problem of spatial adaptive filtering using the RLS minimization View full abstract»

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  • Statistics of tricoherence

    Publication Year: 1994 , Page(s): 3430 - 3440
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (896 KB)  

    Statistics of the estimates of tricoherence are obtained analytically for nonlinear harmonic random processes with known true tricoherence. Expressions are presented for the bias, variance, and probability distributions of estimates of tricoherence as functions of the true tricoherence and the number of realizations averaged in the estimates. The expressions are applicable to arbitrary higher order coherence and arbitrary degree of interaction between modes. Theoretical results are compared with those obtained from numerical simulations of nonlinear harmonic random processes. Estimation of true values of tricoherence given observed values is also discussed View full abstract»

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  • On-line identification of hidden Markov models via recursive prediction error techniques

    Publication Year: 1994 , Page(s): 3535 - 3539
    Cited by:  Papers (26)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (420 KB)  

    An on-line state and parameter identification scheme for hidden Markov models (HMMs) with states in a finite-discrete set is developed using recursive prediction error (RPE) techniques. The parameters of interest are the transition probabilities and discrete state values of a Markov chain. The noise density associated with the observations can also be estimated. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to show that the algorithms converge for a wide variety of initializations. In addition, an improved version of an earlier proposed scheme (the Recursive Kullback-Leibler (RKL) algorithm) is presented with a parameterization that ensures positivity of transition probability estimates View full abstract»

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  • Recovery of a sparse spike time series by L1 norm deconvolution

    Publication Year: 1994 , Page(s): 3353 - 3365
    Cited by:  Papers (16)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1044 KB)  

    An L1 norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in CANDU nuclear reactors. For each problem, parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor. This performance factor is based on a quantified analysis of the transitions in estimates of h as the damping parameter is varied over a wide range of possible values. It is shown that for the examined cases in which the true impulse response is a sparsely filled spike strain, the L1 norm provides significantly better results than the more commonly used L2 norm minimization schemes. These results are shown to be consistent with theoretical predictions View full abstract»

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  • On circularity

    Publication Year: 1994 , Page(s): 3473 - 3482
    Cited by:  Papers (168)  |  Patents (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (912 KB)  

    Circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors. However, this concept can be extended in various ways for nonnormal vectors. The first purpose of the paper is to introduce and compare some possible definitions of circularity. From these definitions, it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components. Therefore, the relationships between circularity and stationarity are analyzed in detail. Finally, the theory of linear mean square estimation for complex signals exhibits some connections with circularity, and it is shown that without this assumption, the estimation theory must be reformulated View full abstract»

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  • Harmonic retrieval in mixed Gaussian and non-Gaussian ARMA noises

    Publication Year: 1994 , Page(s): 3539 - 3543
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB)  

    The article proposes an approach to harmonic retrieval in mixed Gaussian and non-Gaussian ARMA noises. Under the assumption of asymmetrically distributed non-Gaussian noise, the approach consists of third-order cumulant-based AR modeling of the non-Gaussian ARMA noise, followed by filtering the noisy output data, followed by fourth-order cumulant-based harmonic retrieval. The effectiveness of this approach is demonstrated through standard simulation results View full abstract»

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  • Extending self-similarity for fractional Brownian motion

    Publication Year: 1994 , Page(s): 3526 - 3530
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    The fractional Brownian motion (fBm) model has proven to be valuable in modeling many natural processes because of its persistence for large time lags. However, the model is characterized by one single parameter that cannot distinguish between short- and long-term correlation effects. This article investigates the idea of extending self-similarity to create a correlation model that generalizes discrete fBm referred to as asymptotic fBm (afBm). Namely, afBm is parameterized by variables controlling short- and long-term correlation effects. It proposes a fast parameter estimation algorithm for afBm based on the Haar transform, and demonstrates the performance of this parameter estimation algorithm with numerical simulations View full abstract»

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  • Fast implementation of the continuous wavelet transform with integer scales

    Publication Year: 1994 , Page(s): 3519 - 3523
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (448 KB)  

    We describe a fast noniterative algorithm for the evaluation of continuous spline wavelet transforms at any integer scale m. In this approach, the input signal and the analyzing wavelet are both represented by polynomial splines. The algorithm uses a combination of moving sum and zero-padded filters, and its complexity per scale is O(N), where N is the signal length. The computation is exact, and the implementation is noniterative across scales. We also present examples of spline wavelets exhibiting properties that are desirable for either singularity detection (first and second derivative operators) or Gabor-like time-frequency signal analysis View full abstract»

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  • The cumulant theory of cyclostationary time-series. II. Development and applications

    Publication Year: 1994 , Page(s): 3409 - 3429
    Cited by:  Papers (61)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1656 KB)  

    For pt.I see ibid., vol.42, no.12, p.3387-3408 (1994). The development of the theory of nonlinear processing of cyclostationary time-series that is initiated in Part I is continued. A new type of cumulant for complex-valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time-series from real-valued to complex-valued time-series. The relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined. Formulas for the temporal and spectral cumulants of complex-valued pulse-amplitude-modulated time-series are derived. Estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed. The performance of these estimators is illustrated by several computer simulation examples for pulse-amplitude-modulated time-series. The theory is applied to the problems of weak-signal detection and interference-tolerant time-delay estimation View full abstract»

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  • Joint DOA estimation and phase calibration of linear equispaced (LES) arrays

    Publication Year: 1994 , Page(s): 3449 - 3459
    Cited by:  Papers (19)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (692 KB)  

    The important problem of self-calibration of phased arrays for unknown phase errors in conjunction with their use in high-resolution direction of arrival (DOA) estimation is addressed. The authors consider the canonical (and widely used) linear equispaced (LES) array with a constant but unknown phase response and develop an algorithm that does not require any a priori knowledge of the direction of arrival of a signal. Analytical results are presented regarding estimator performance that are verified by a representative body of simulations. In addition, estimator performance is compared with a constrained Cramer-Rao lower bound (CRLB) View full abstract»

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  • Evolution equations for continuous-scale morphological filtering

    Publication Year: 1994 , Page(s): 3377 - 3386
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (968 KB)  

    Multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks. Morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges. The authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings. These equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals. The nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of a nonlinear function of certain partial differential operators View full abstract»

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  • The cumulant theory of cyclostationary time-series. I. Foundation

    Publication Year: 1994 , Page(s): 3387 - 3408
    Cited by:  Papers (63)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1956 KB)  

    The problem of characterizing the sine-wave components in the output of a polynomial nonlinear system with a cyclostationary random time-series input is investigated. The concept of a pure nth-order sine wave is introduced, and it is shown that pure nth-order sine-wave strengths in the output time-series are given by scaled Fourier coefficients of the polyperiodic temporal cumulant of the input time-series. The higher order moments and cumulants of narrowband spectral components of time-series are defined and then idealized to the case of infinitesimal bandwidth. Such spectral moments and cumulants are shown to be characterized by the Fourier transforms of the temporal moments and cumulants of the time-series. It is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts. To put the contributions of the paper in perspective, a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided View full abstract»

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  • Investigating the nonlinear dynamics of cellular motion in the inner ear using the short-time Fourier and continuous wavelet transforms

    Publication Year: 1994 , Page(s): 3335 - 3352
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1692 KB)  

    The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are used to analyze the time course of cellular motion in the inner ear. The velocity responses of individual outer hair cells and Hensen's cells to sinusoidal and amplitude modulated (AM) acoustical signals applied at the ear canal display characteristics typical of nonlinear systems, including the generation of harmonic and half-harmonic components. The STFT proves to be valuable for following the time course of the frequency components generated using sinusoidal and ARM input signals. The CWT is also useful for analyzing these signals; however, it is generally not as effective as the STFT when octave-band-based CWT's are used. For the transient response, the spectrogram (which is the squared magnitude of the STFT) and the octave-band-based scalogram (which is the squared magnitude of the CWT) prove equally valuable, and the authors have used both to study the responses of these cells to step-onset tones of different frequencies. Such analyses reveal information about the preferred vibration frequencies of cells in the inner ear and are useful for deciding among alternative mathematical models of nonlinear cellular dynamics. A modified Duffing oscillator model yields results that bear some similarity to the data View full abstract»

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  • A fast algorithm for polyphase quadrature filters

    Publication Year: 1994 , Page(s): 3513 - 3515
    Cited by:  Papers (1)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    A fast algorithm for computing the polyphase quadrature filters (PQF), which are typically used in data reduction of audio and speech signals, enables the implementation of either a larger number of subbands or a better data reduction method, or both, in real-time applications. The algorithm, which was developed for use in a hidden channel approach, has been implemented on a Motorola 56001 (27 MHz), where the fast algorithm enables practical use of more than 32 subbands on audio signals. As the number of calculations for M subbands is reduced from approximately M2 to M log2(M), a 64-band analysis or synthesis filter requires only about 22% of the computation capacity compared with approximately 43470 with other algorithms View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Editor-in-Chief
Sergios Theodoridis
University of Athens