Manuel D Ortigueira

Abstract: In this paper, the classic Levy identication method is reviewed and reformulated using a complex representation. This new formulation is able to solve the well known bias of the classic method at low frequencies. The formulation is generic, addressing both integer order and fractional order transfer functions. A new algorithm based on a stacked matrix and its pseudo-inverse is proposed to accommodate the data over a wide range of frequencies. Several simulation results are presented, together with a real system identication. This system is the Archimedes Wave Swing, a prototype of a device to convert the energy of sea waves into electricity.

Abstract: The definition and simulation of fractional Brownian motion is considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.

Abstract: The Empirical Mode Decomposition (EMD) is reviewed and some questions related to its effective performance are discussed. Its interpretation in terms of AM/FM modulation is done. Solutions for its drawbacks are proposed. Numerical simulations are carried out to empirically evaluate the proposed modified EMD

Abstract: Fractional central differences and derivatives are studied in this paper. These are generalisations to real orders of the ordinary positive even and odd integer orders differences and derivatives and also coincide with the well known Riesz potentials. A study for coherence is done by applying the definitions to functions with Fourier transform. Some properties of these derivatives are presented and some particular cases studied.

Abstract: A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

Abstract: In this paper the modeling of Fractional Linear Systems through ARMA models is addressed. To perform this study a new recursive algorithm for Impulse Response ARMA modelling is presenting. This is a general algorithm that allows the recursive construction of ARMA models from the Impulse Response sequence. This algorithm does not need an exact order specification, since it gives some insights into correct orders. It is applied to modelling Fractional Linear Systems described by fractional powers of the backward difference and the bilinear transformations. The analysis of the results leads us to propose suitable models for those systems.

Abstract: Based on two methods recently proposed � the �Ranging Criterion� and the �Generators Ranging Criterion� � new (quasi-orthogonal) even BCH-derived sequences are generated which are very attractive for synchronous or quasi-synchronous CDMA systems. Numerical results show that the new family of BCH-derived sequences can contain a higher number of quasi-orthogonal sequences with lower correlation values and higher processing gains than the spreading sequences typically used in the third generation of mobile communications system, UMTS or in the recent LAS-CDMA technology. It is shown that the even BCH-derived sequences are easily generated by a linear shift register generator, allowing the construction of systems with receiver structures of low complexity as compared with those of quasi-synchronous systems using low correlation zone sequences, as for instance the LAS CDMA system.

Abstract: In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal equations that allow us to obtain the ARMA parameters. This new LS is then applied to the same examples as in [1] and [11] so performance comparisons can be drawn. Simulation results show that both magnitude frequency responses are essentially identical. Concerning the modeling stability, both algorithms present similar limitations, although for different ARMA model orders.

Abstract: The relation showing that the Grünwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of pseudo-function appear naturally without the need for a rejection of any infinite part. From the regularised derivative, new formulations are deduced and specialised first for the real functions and afterwards for functions with Laplace Transforms obtaining the definitions proposed by Liouville. With these tools suitable definitions of fractional linear systems are obtained.

Abstract: Fractional centred differences and derivatives definitions are proposed generalising to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalisations of the Cauchy integral derivative. To compute this integral, a special two straight line path was used. With this the referred integrals lead to the well known Riesz potential operators and their inverses that emerge as true fractional centred derivatives, but that can be computed through summations similar to the well known Grünwald-Letnikov derivatives

Abstract: In this paper a new class of Pseudo Noise Even Balanced (PN-EB) binary spreading sequences is derived from existing classical odd-length families of maximum length sequences, such as those proposed by Gold, by appending or inserting one extra zero element (chip) to the original sequences. The incentive to generate large families of PN-EB spreading sequences is motivated by analysing the spreading effect of these sequences from a natural sampling point of view. From this analysis, a new definition for PG is established, from which it becomes clear that very high Processing Gains (PGs) can be achieved in band-limited Direct Sequence Spread Spectrum (DSSS) applications by using spreading sequences with zero mean, given that certain conditions regarding spectral aliasing are met. To obtain large families of even balanced (i.e., equal number of ones and zeros) sequences, two design criteria are proposed, namely the Ranging Criterion (RC) and the Generating Ranging Criterion (GRC). PN-EB sequences in the polynomial range 3�n�6 are derived using these criteria, and it is shown that they exhibit secondary auto-correlation and cross-correlation peaks comparable to the sequences they are derived from. The methods proposed not only facilitate the generation of large numbers of new PN-EB spreading sequences required for CDMA applications, but simultaneously offer high processing gains and good despreading characteristics in multi-user SS scenarios with bandlimited noise and interference spectra. Simulation results are presented to confirm the respective claims made.

Abstract: Despite the great advances in the theory and applications of fractional calculus, some topics remain unclear making a systematic use difficult. In this paper the fractional differintegration definition problem is studied from a systems point of view. Both local (Grünwald-Letnikov) and global (convolutional) definitions are considered. It is shown that the Cauchy formulation should be adopted since it is coherent with usual practice in signal processing and control applications.

Abstract: Two new formulae for representing the Beta function in integral format are presented. They enlarge the argument domains for the inclusion of negative values. The proofs are based on the Mellin Transform.

Abstract: A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.

Abstract: A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.

Abstract: A new definition of a symmetric fractional B-spline is presented. This generalises the usual integer order B-spline, that becomes a special case of the new one.

Abstract: The initial condition problem for fractional linear system initialisation is studied in this paper. It is based on the generalised initial value theorem. The new approach involves functions belonging to the space of Laplace transformable distributions verifying the Watson-Doetsch lemma. The fractional derivatives of these functions are independent of the derivative definition. This class includes the most important functions appearing in computing the Impulse Response of continuous-time fractional linear systems.

Abstract: A generalisation of the linear prediction for fractional steps is reviewed, widening well-known concepts and results. This prediction is used to derive a causal interpolation algorithm. A reconstruction algorithm for the situation where averages are observed is also presented. Scale conversion of discrete-time signals is studied taking as base the fractional discrete-time system theory. Some simulation results to illustrate the behaviour of the algorithms will be presented. A new algorithm for performing the zoom transform is also described.

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Abstract: In this paper, we study the aperiodic comb signal from the point of view of the Fourier Transform. The comb is very important in the theory of ideal sampling. The knowledge of its properties is crucial for the establishment of suitable interpolation schemes. Here, we present sufficient conditions so that the Fourier Transform of an aperiodic comb is an aperiodic comb. We use this result to propose: 1) an alternative approach to the definition of an almost periodic signal and its anharmonic Fourier series; 2) a generalisation of the Shannon-Whittakker sampling/reconstruction for the irregular sampling case. Application of this theory to Pulse Duration Modulation and Pulse Position Modulation is also presented.

Abstract: In this paper, the class of continuous-time linear systems is enlarged with the inclusion of the fractional linear systems. These are systems described by fractional differential equations. It is shown how to compute the impulse, step, and frequency responses from the transfer function. The theory is supported by definitions of fractional derivative and integral, generalisations of the usual. An introduction to fractal signals as outputs of fractional differintegrators is also done. It is shown how to define a stationary fractal.

Abstract: In this paper, the class of discrete linear systems is enlarged with the inclusion of the discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how to compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be considered as having fractional poles or zeros. The concept of fractional differaccumulation is treated generalising the notions of fractal and �1/f noise�, and introducing two kinds of fractional differaccumulated stochastic processes: hyperbolic, resulting from fractional accumulation - similar to the continuous-time case - and parabolic noises resulting from fractional differencing.

Abstract: Proponemos un sistema para la comunicación sobre líneas de la energia eléctrica usando DS/BPSK con un régimen binario de 300 bits/s. La señal de ensanchado tiene una secuencia máxima de longitud 7 como código de �chip�, repetida 30 veces para cada dígito binario del código de la información BPSK. La sincronización entre la señal del receptor y la secuéncia PN localmente generada es obtenida por un nuevo acercamiento basado en un filtro adaptado.

Abstract: In this paper we present a recursive algorithm for factorization and inversion of matrices generated by adding dyads ( elementary or rank-one matrices ) as it happens in recursive array signal processing. The algorithm is valid for any recursively generated rectangular matrix and it has two parts: one valid for rank deficient and the other for full rank matrices. This later case is used to obtain a generalization of the Sherman-Morrison algorithm for the recursive inversion of the covariance matrix. The proposed algorithm is used also to obtain a new one to compute the inverse (pseudo-inverse) of any matrix, assumed to be formed by joining columns. In a similar way, it can be used to invert simultaneously two matrices, by considering their product.

Abstract: Se estudian las matrices elementales de rango 1 (diadas). Para estas matrices se presentan fórmulas para su factorizacion, inversion, descomposition en valores própios y valores singulares. Estos resultados son aplicados en análisis recursivo de qualquiera que sea la matriz, siempre que se descomponga en una suma de matrices de rango 1.

Abstract: The problem of ARMA modeling is focused in this paper. It is shown how to compute the ARMA parameters from a finite set of consecutive reflection coefficients in a completely recursive way. The algorithm consists on simple recursions for both the AR and MA parameters and it generalizes in a unifying framework other existing AR and MA algorithms.

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Abstract: Two important questions in array signal processing are adressed in this paper: the data matrix vs autocorrelation matrix alternative and the recursive implementation of subspace DOA methods. The discussion of the first question is done in face of the proposed class of recursive algorithms. These new algorithms are easily implementable and have a high degree of parallelism, suitable for on-line implementations. Algorithms for recursive implementation of the eigendecomposition (ED) of the autocorrelation matrix and SVD of the data matrix are described. The ED/SVD trade-off is discussed.

Abstract: Abstract. A new ARMA estimation algorithm is proposed. It is based on a fundamental relationship which shows that the AR polynomial of an ARMA(N, M) model belongs to the linear space spanned by the forward and backward linear predictors. This relationship allows us to construct an equivalent linear system with two inputs and the same output of the ARMA system. The inputs of this new system are the forward and backward linear prediction errors. As in this case the inputs and output are known, a least-squares identification algorithm is used to obtain the parameters of the system. These parameters define three polynomials. One of them is the AR polynomial. The other two converge asymptotically to the MA polynomial and to zero. Simple recursions are available to perform such a limiting operation.

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Abstract: The Empirical Mode Decomposition is a technique to decompose a given signal into a set of elemental signals called Intrinsic Mode Functions. The Empirical Mode Decomposition is the base of the so-called �Hilbert-Huang Transform� that comprises also a Hilbert Spectral Analysis and an instantaneous frequency computation. A modified improved algorithm for the Empirical Mode Decomposition is described. Its interpretation in terms of AM/FM modulation is done. Numerical simulations are carried out to empirically evaluate the algorithm.

Abstract: Generalised Fractional centred differences and derivatives are studied in this chapter. These generalise to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are presented. The limit computation inside the integrals leads to generalisations of the Cauchy derivative. Their computations using a special path lead to the well known Riesz potentials. A study for coherence is done by applying the definitions to functions with Fourier transform. The existence of inverse Riesz potentials is also studied.

Abstract: The initial condition problem for fractional linear system initialisation is restudied in this paper. A general formulation similar to the integer order is presented. The Riemann-Liouville and Caputo initial conditions are interpreted in terms of the general scheme.

Abstract: The initial condition problem for fractional linear system initialisation is restudied in this paper. A formulation generalizing the integer order approach is presented. This is based on a fractional jump formula and it does not depend of any transform. It is also valid for the time variant case. The Riemann-Liouville and Caputo initial conditions are interpreted in terms of the general scheme.

Abstract: In this paper we propose a procedure for the design of closed-loop controllers able to simultaneously satisfy multiple specifications. The procedure is based on the solution of a multi objective control problem. A particle swarm optimisation algorithm is used to minimise an objective function. A fractional controller is designed according to the propose approach.

Abstract: Two formulations of the quantum fractional derivative are presented here: the analogue to the common Grünwald-Letnikov derivatives and their integral formulations. The Mellin transforms of these derivative formulations will be used to solve the Euler-Cauchy differential equation.

Abstract: New derivative formulations analogue to the common Grünwald-Letnikov derivatives will be presented defining the quantum fractional derivative. The Mellin transform of this derivative will be used to obtain two integral formulations similar to the usual Liouville derivatives.

Abstract: The Empirical Mode Decomposition (EMD) is a technique to decompose a given signal into a set of elemental signals called Intrinsic Mode Functions (IMF). Each IMF is an AM/FM modulated signal, but it is not a true mode, understood as an impulse response of a second order linear system. In this paper we show how to obtain a set of mode functions from the set of IMF.

Abstract: The time-varying microstructure of sleep EEG spindles may have clinical significance in dementia studies. In this work, the sleep spindle is modeled as an AM-FM signal and parameterized in terms of six parameters, three quantifying the instantaneous envelope (IE) and three quantifying the instantaneous frequency (IF) of the spindle model. The IE and IF waveforms of sleep spindles from patients with dementia and normal controls were estimated using the time-frequency technique of Complex Demodulation (CD). Sinusoidal curve-fitting using a matching pursuit (MP) approach was applied to the IE and IF waveforms for the estimation of the six model parameters. Specific differences were found in sleep spindle instantaneous frequency dynamics between spindles from dementia subjects and spindles from controls.

Abstract: A reinterpretation of the classic definition of fractional Brownian motion leads to a new definition involving a fractional noise obtained as a fractional derivative of white noise. To obtain this fractional noise, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. For these derivatives the autocorrelation functions of the corresponding fractional noises have the same representations. The obtained results are used to define and propose a new simulation procedure.

Abstract: An alternative to the common Grünwald-Letnikov and Liouville derivatives will be presented: the quantum fractional derivative. A Grünwald-Letnikov like formulation called will be presented and its relation with the Mellin transform used to obtain two integral formulations similar to the usual Liouville derivatives.

Abstract: In this paper, the classic Levy identication method is reviewed and reformulated using a complex representation. This new formulation is able to solve the well known bias of the classic method at low frequencies. The formulation is generic, addressing both integer order and fractional order transfer functions. A new algorithm based on a stacked matrix and its pseudo-inverse is proposed to accommodate the data over a wide range of frequencies. Several simulation results are presented, together with a real system identication. This system is the Archimedes Wave Swing, a prototype of a device to convert the energy of sea waves into electricity.

Abstract: The initial condition problem for fractional linear system initialisation is restudied in this paper. It is shown that it does not depend on the derivative definition or on the use of any transform but on the structure of the system at hand. A general formulation similar to the integer order is presented.

Abstract: Fractional central differences and derivatives are proposed in this paper. The positive even and odd integer orders differences and derivatives are generalised to real orders, obtaining two new different types of differences and derivatives. For each type, suitable integral formulation is obtained. Their computations of the integrals lead to generalisations of the well known Riesz potentials. A study for coherence is done by applying the definitions to functions with Fourier transform.

Abstract: The problem of the definition of a fractional derivative suitable for stationary stochastic processes is faced in this paper. To do it two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied and it is shown that the proposed formulation leads to Mandelbrot�s definition.

Abstract: Parameter estimation for an assumed sleep EEG spindle model (AM-FM signal) is performed by using four time-frequency analysis methods. Results from simulated as well as from real data are presented. In simulated data, the Hilbert Transform-based method has the lowest average percentage error but produces considerable signal distortion. The Complex Demodulation and the Matching Pursuit-based methods have error rates below 10%, but the Matching Pursuit-based method produces considerable signal distortion as well. The Wavelet Transform-based method has the poorest performance. In real data, all methods produce reasonable parameter values. However, the Hilbert Transform and the Matching Pursuit-based methods may not be applicable for sleep spindles shorter than about 0.8 sec. Matching Pursuit-based curve fitting is utilized as part of the parameter estimation process.

Abstract: Integral representations for both direct and reverse fractional differences are presented. From these the fractional differintegration is readily obtained generalizing the Cauchy integral formula. Its shown that the Grünwald-Letnikov and generalized Cauchy differintegrations are equal.

Abstract: The Empirical Mode Decomposition (EMD) is reviewed and some questions relating to its effective performance are discussed. Algorithmic variations, including a new parabolic interpolation method are presented. Numerical simulations are carried out to empirically evaluate the modified EMD. The modified EMD is used to conduct an eeg analysis. The attained results support the modified EMD.

Abstract: Efficient R wave detection is a crucial preprocessing step of most of the ECG signal analysis . Likewis e, ECG delineation comprising P wave and QRS complex, is required for ECG processing, namely in High- Resolution Electrocardiography (HR-ECG). We have performed R wave detection using the Mexican Hat wavelet and achieved a sensibility Se=97.77 % and a positive prediction P+=99.46%. Our data is HR-ECG and the delineation process occurs in two steps: wavelet detection and application of the Task Force (Breithardt et al.) detection rules.

Abstract: Starting from the generalised Cauchy formula for the differintegration, new relations are obtained, namely a regularised version. From this, forward and backward differintegrations are deduced and specialised for the case of functions with Laplace Transform. As a by-products of the algorithm generalisations of the Euler Beta function are presented.

Abstract: Based on two recently proposed methods in the literature � the �Ranging Criterion� and the �Generators Ranging Criterion� � new (quasi-orthogonal) even BCH-derived sequences are generated, which are very attractive for (synchronous or quasi-synchronous) CDMA applications. These sequences can be easily generated by a linear shift register generator, adding one extra zero or by a cyclically read memory table. Simulation results showed that the new family of even BCH-derived sequences can contain a higher number of sequences with lower correlation values and higher processing gains than the spreading sequences typically used in the third generation of mobile communications system, UMTS.

Abstract: In this paper the modeling of Fractional Linear Systems through ARMA models is addressed. This study is performed by using a recursive algorithm for Impulse Response ARMA modelling leading us to propose suitable models for this problem

Abstract: Despite the great advances in the theory and applications of fractional calculus, some topics remain unclear making difficult its use in a systematic way. This paper studies the fractional differintegration definition problem from a systems point of view. Both local (Grünwald-Letnikov) and global (convolutional) definitions are considered. It is shown that the Cauchy formulation must be adopted since it is coherent with usual practice in signal processing and control applications..

Abstract: A CMOS analogue circuit for Gaussian noise generution as well as a novel circuitfor transforming Gaussian noise into uniform noise, hoth.designed/or operating with a supply voltoge o/ I . S K arepresented. Both circuits are optimizedfor U 0 . 3 5st~an - dord CMOS technology using an equation-based design methodology based on generic algorithms. Electrical simulations demonstrate that high noise amplinrdes together with reasonable hondwidths can be achieved with relatively low power dissipation. Potential applications include self-calihrution and on-chip self-testing of video-rate analogue-to-digital converters.

Abstract: New BCH-derived PN-EB (pseudo-noise even balanced) sequences suitable to be used in CDMA systems are presented in this paper. It is assumed a new definition for Processing Gain, which better accounts for the system performance regarding the narrow band noise rejection, and it is shown how to obtain high processing gain values, namely, by using zero mean spreading signals in channels with selective noise. The new sequences have low autocorrelation levels, exist in large numbers and can provide higher processing gain with selective noise.

Abstract: A digital-domain self-calibration technique for video-rate pipeline A/D converters based on a white Gaussian noise input signal is presented. The implementation of the proposed algorithm requires simple digital circuitv. An application design example of the self-calibration of a IZb. 40 MUS CMOSpipeline ADC is shown to illustrate that the overall linearity of the ADC can be highly improved using this technique.

Abstract: The initial condition problem for fractional linear system initialisation is studied in this paper. A new approach that involves functions belonging to the space of Laplace transformable distributions is presented. It is based on the generalised initial value theorem and on reinterpretations of the most common differintegration definitions.

Abstract: Time-Frequency and Time-Scale distributions of sequential ST segments the High-Resolution Electrocardiogram, are represented using both the Morlet Wavelet based scalogram and the Zhao- Atlas-Marks representation. Resolution and representation readability, concerning the Ventricular Late Potentials are compared. The beat-tobeat variation of one VLP case is examined.

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Abstract: The fractional differintegration problem is treated from the Signal Processing point of view. A brief review of the Laplace transform approach to differintegration is done. The continuous-time/discrete-time system conversion is discussed and presented a Grünwald-Letnikov integration

Abstract: A generalisation of the linear prediction for fractional steps is reviewed, widening well-known concepts and results. This prediction is used to derive a causal interpolation algorithm. A reconstruction algorithm for the situation where averages are observed is also presented.

Abstract: Scale conversion of discrete-time signals are studied taking as base the fractional discrete-time system theory. Some simulation results to illustrate the behaviour of the algorithms will be presented. A new algorithm for performing the zoom transform is also described.

Abstract: Fractional linear systems are introduced as well as their Transfer Functions and Impulse Responses that are computed in a way to emphasise their main similarities and differences. Special attention is paid to the interconversions between continuous-time and discrete-time, by showing procedures and relating problems

Abstract: A generalisation of the linear prediction for fractional steps is presented, widening well-known concepts and results. This prediction is used to derive a causal interpolation algorithm useful in several applications.

Abstract: In this paper we will focus our special attention into the DS-SS communication systems with band limited noise channel and no aliasing, using special sequences which ones allowed to achieve a higher Processing Gain (PG). The new type of sequences are all PN even balanced sequences (PN-EB), which means they present the same number of �zeroes� and �ones�, and so, have zero mean. The number of available PN-EB sequences is very large, when compared with the number of TCH sequences and others with the same length. They perform a very good secondary peak level of auto-correlation function.

Abstract: The design of new sequence for high Processing Gain (PG) in DSSS systems with band limited noise channel and no aliasing, is shown. The PN-EB sequences present the same number of �zeroes� and �ones�, and zero mean. The number available is very large. All perform very good secondary peak level of autocorrelation.

Abstract: In this paper we will focus on the design of new sequences, to achieve a high Processing Gain in DSSS communication systems with band limited noise channel and no aliasing. This sequences are PN even balanced (PN-EB) sequences, which means they present the same number of �zeroes� and �ones�, and so, have zero mean. The number of PN-EB sequences available is very large, when compared with other sequences of the same length. All of them perform a very good secondary peak level of the autocorrelation function.

Abstract: In this paper a description of a MatLab implementation of a new ECG analysis system based on the use of archetypal analysis for the study and interpretation of ECG signals is presented. The archetypal analysis is described together with new algorithms for the study of the heart frequency variability. Some features of the system are described and some results presented.

Abstract: In this paper we deal with a frequency estimation problem using a zoom transform algorithm. In many a signal processing problems, it is of paramount importance the exact determination of the frequency of a signal. Some techniques derived from the FFT, just pad the signal with enough zeros in order to better sample its Discrete-Time Fourier Transform. Our approach, although FFT-based, does not rely on such method, using instead a �zoom� function built around the well-known sinc(.) function, resulting in an exact and deterministic method. Its analytic formulation is presented and illustrated with some simulation results over short-time based signals

Abstract: The fractional differintegration problem is treated from the Signal Processing point of view. A review of the Laplace Transform approach to differintegration is done. The initial condition problem for fractional linear system initialisation is also presented.