The Experts below are selected from a list of 2031 Experts worldwide ranked by ideXlab platform
Senior Member - One of the best experts on this subject based on the ideXlab platform.
-
Signal Reconstruction From Two Close Fractional Fourier Power Spectra
2016Co-Authors: Tatiana Alieva, Mj Martin Bastiaans, Senior MemberAbstract:Abstract—Based on the definition of the instantaneous fre-quency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the Squared Modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It per-mits us to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios (SNRs) higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applica-tions of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured. Index Terms—Fractional Fourier transform, phase reconstruc-tion, time–frequency signal analysis, Wigner distribution. I
Norbert Henze - One of the best experts on this subject based on the ideXlab platform.
-
a characterization and a class of omnibus tests for the exponential distribution based on the empirical characteristic function
Journal of Mathematical Sciences, 2010Co-Authors: Norbert Henze, Simos G MeintanisAbstract:The characteristic function φ(t) of an exponentially distributed random variable is characterized by having its Squared Modulus identically equal to the real part of φ(t). We study the behavior of a class of consistent tests for exponentiality based on a weighted integral involving the empirical counterparts of these quantities, corresponding to suitably rescaled data. Bibliography: 25 titles.
-
goodness of fit tests for the inverse gaussian distribution based on the empirical laplace transform
Annals of the Institute of Statistical Mathematics, 2002Co-Authors: Norbert Henze, Bernhard KlarAbstract:This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the Squared Modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to the first nonzero component of Neyman's smooth test for the inverse Gaussian distribution. The tests, when implemented via the parametric bootstrap, maintain a nominal level of significance very closely. A large-scale simulation study shows that the new tests compare favorably with classical goodness-of-fit tests for the inverse Gaussian distribution, based on the empirical distribution function.
-
theory methods weighted integral test statistics and components of smooth tests of fit
Australian & New Zealand Journal of Statistics, 2000Co-Authors: Ludwig Baringhaus, Nora Gürtler, Norbert HenzeAbstract:This paper considers families of statistics for testing the goodness-of-fit of various parametric models such as the normal, exponential or Poisson. Each family consists of weighted integrals over the Squared Modulus of some measure of deviation from the parametric model, expressed by means of an empirical transform of the data. Letting the rate of decay of the weight function tend to infinity, each test statistic, after a suitable rescaling, approaches a limit that is closely connected to the first non-zero component of Neyman's smooth test for the parametric model.
-
Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function
Annals of the Institute of Statistical Mathematics, 2000Co-Authors: Nora Gürtler, Norbert HenzeAbstract:Let X _1,..., X _ n be independent observations on a random variable X . This paper considers a class of omnibus procedures for testing the hypothesis that the unknown distribution of X belongs to the family of Cauchy laws. The test statistics are weighted integrals of the Squared Modulus of the difference between the empirical characteristic function of the suitably standardized data and the characteristic function of the standard Cauchy distribution. A large-scale simulation study shows that the new tests compare favorably with the classical goodness-of-fit tests for the Cauchy distribution, based on the empirical distribution function. For small sample sizes and short-tailed alternatives, the uniformly most powerful invariant test of Cauchy versus normal beats all other tests under discussion.
-
a new approach to the bhep tests for multivariate normality
Journal of Multivariate Analysis, 1997Co-Authors: Norbert Henze, Thorsten WagnerAbstract:LetX1, ?, Xnbe i.i.d. randomd-vectors,d?1, with sample meanXand sample covariance matrixS. For testing the hypothesisHdthat the law ofX1is some nondegenerate normal distribution, there is a whole class of practicable affine invariant and universally consistent tests. These procedures are based on weighted integrals of the Squared Modulus of the difference between the empirical characteristic function of the scaled residualsYj=S?1/2(Xj?X) and its almost sure pointwise limit exp(??t?2/2) underHd. The test statistics have an alternative interpretation in terms ofL2-distances between a nonparametric kernel density estimator and the parametric density estimator underHd, applied toY1, ?, Yn. By working in the Frechet space of continuous functions on Rd, we obtain a new representation of the limiting null distributions of the test statistics and show that the tests have asymptotic power against sequences of contiguous alternatives converging toHdat the raten?1/2, independent ofd.
H. Schamel - One of the best experts on this subject based on the ideXlab platform.
-
Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation
EDP Sciences, 2002Co-Authors: R. Fedele, H. SchamelAbstract:An investigation to deepen the connection between the family of nonlinear Schrödinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schrödinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the Squared Modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schrödinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable $x-u_0 s$ (s being a time-like variable). This novel method in solving the nonlinear Schrödinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented
-
Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation
'Springer Science and Business Media LLC', 2002Co-Authors: R. Fedele, H. SchamelAbstract:An investigation to deepen the connection between the family of nonlinear Schrödinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schrödinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the Squared Modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schrödinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x - u0s (s being a time-like variable). This novel method in solving the nonlinear Schrödinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented
Tatiana Alieva - One of the best experts on this subject based on the ideXlab platform.
-
Signal Reconstruction From Two Close Fractional Fourier Power Spectra
2016Co-Authors: Tatiana Alieva, Mj Martin Bastiaans, Senior MemberAbstract:Abstract—Based on the definition of the instantaneous fre-quency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the Squared Modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It per-mits us to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios (SNRs) higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applica-tions of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured. Index Terms—Fractional Fourier transform, phase reconstruc-tion, time–frequency signal analysis, Wigner distribution. I
-
Signal reconstruction from two close fractional Fourier power spectra
SPIE milestone series, 2006Co-Authors: Tatiana Alieva, Mj Martin Bastiaans, Ljubisa StankovicAbstract:Based on the definition of the instantaneous fre quency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the Squared Modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It per mits us to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios (SNRs) higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applica tions of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured.
Patrick Flandrin - One of the best experts on this subject based on the ideXlab platform.
-
time scale energy distributions a general class extending wavelet transforms
IEEE Transactions on Signal Processing, 1992Co-Authors: Olivier Rioul, Patrick FlandrinAbstract:The theory of a new general class of signal energy representations depending on time and scale is developed. Time-scale analysis has been introduced recently as a powerful tool through linear representations called (continuous) wavelet transforms (WTs), a concept for which an exhaustive bilinear generalization is given. Although time scale is presented as an alternative method to time frequency, strong links relating the two are emphasized, thus combining both descriptions into a unified perspective. The authors provide a full characterization of the new class: the result is expressed as an affine smoothing of the Wigner-Ville distribution, on which interesting properties may be further imposed through proper choices of the smoothing function parameters. Not only do specific choices allow recovery of known definitions, but they also provide, via separable smoothing, a continuous transition from Wigner-Ville to either spectrograms or scalograms (Squared Modulus of the WT). This property makes time-scale representations a very flexible tool for nonstationary signal analysis. >