linearly coupled shaft torsional and blade bending vibrations in multi stage rotor blade systems abstract in an attempt towards the understanding of coupling effects between shaft torsional and blade in plane bending vibrations in turbomachinery and other rotating bladed structures an idealized model is considered where the blades are represented by uniform euler bernouilli beams a synthetical multi frame and mixed consisting in a coalescence of finite element and galerkin methods approach is used to derive a linearized mathematical model for the system it is shown that the related eigenanalysis problem splits into two separate sub problems corresponding to two kinds of possible normal mode motions eigenanalyses are performed concerning single as well as multi stage rotor blade system examples parametric studies are presented on the variation of the eigenfrequencies with system parameters eigenvalue loci veering phenomena are shown to occur causing departure of the eigenvalues from those obtained through an uncoupled analysis mode shape examples are also presented

stabilization of a boussinesq system of kdv kdv type a family of boussinesq systems has recently been proposed by bona chen and saut in j l bona m chen j c saut boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media i derivation and linear theory j nonlinear sci 12 4 2002 283 318 to describe the two way propagation of small amplitude gravity waves on the surface of water in a canal in this paper we investigate the boundary stabilization of the boussinesq system of kdv kdv type posed on a bounded domain we design a two parameter family of feedback laws for which the solutions issuing from small data are globally defined and exponentially decreasing in the energy space

asymptotic behavior of boussinesq system of kdv kdv type abstract this work deals with the local rapid exponential stabilization for a boussinesq system of kdv kdv type introduced by j bona m chen and j c saut this is a model for the motion of small amplitude long waves on the surface of an ideal fluid here we will consider the boussinesq system of kdv kdv type posed on a finite domain with homogeneous dirichlet neumann boundary controls acting at the right end point of the interval our goal is to build suitable integral transformations to get a feedback control law that leads to the stabilization of the system more precisely we will prove that the solution of the closed loop system decays exponentially to zero in the l 2 0 l norm and the decay rate can be tuned to be as large as desired if the initial data is small enough

multiwindow time varying spectrum with instantaneous bandwidth and frequency constraints we build on cohen s work cohen and lee 1988 1989 cohen 1990 1995 on instantaneous bandwidth and frequency by extending it to a multiwindow framework for polynomial phase signals unlike the case with a single spectrogram which cohen considered our multiwindow framework allows one to obtain a time varying spectral estimate that simultaneously satisfies instantaneous bandwidth and frequency constraints we then develop a method utilizing this new multiwindow time varying spectral technique for estimating the instantaneous frequency of a signal the method is computationally simple asymptotically unbiased for noise free signals and provides a signal to noise ratio snr improvement of more than 3 db over other estimators including the cross polynomial wigner distribution method for quadratic and cubic fm signals

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

kernel decomposition of time frequency distributions bilinear time frequency distributions tfds offer improved time frequency resolution over linear representations but suffer from difficult interpretation higher implementation cost and the lack of associated low cost signal synthesis algorithms in the paper the authors introduce some new tools for the interpretation and quantitative comparison of high resolution tfds these tools are used in related work to define low cost high resolution tfds and to define linear low cost signal synthesis algorithms associated with high resolution tfds first each real valued tfd is associated with a self adjoint linear operator spl psi the spectral representation of spl psi expresses the tfd as a weighted sum of spectrograms sps it is shown that the sp decomposition and weyl correspondence do not yield useful interpretations for high resolution tfds due to the fact that spl psi is not positive

rapid exponential feedback stabilization with unbounded control operators we study the wellposedness and the main features of a class of feedback control systems the involved control system is composed of the generator of a strongly continuous group for the free part and of an unbounded control operator so that the results can be applied to boundary or point control problems for partial differential equations of hyperbolic or petrowski type the feedback operator is explicit and one can achieve an arbitrary large decay rate for the closed loop system these results are proved under a controllability assumption and the proofs rely on general results about the algebraic riccati equation associated with the linear quadratic regulator problem

rapid boundary stabilization of linear distributed systems we prove that under rather general assumptions an exactly controllable problem is uniformly stabilizable with arbitrarily prescribed decay rates our approach is direct and constructive and avoids many of the technical difficulties associated with the usual methods based on riccati equations we give several applications for the wave equation and for petrovsky systems

a centrosymmetric kernel decomposition for time frequency distribution computation time frequency distributions tfds are bilinear transforms of the signal and as such suffer from a high computational complexity previous work has shown that one can decompose any tfd in cohen s class into a weighted sum of spectrograms this is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of windows in this paper we introduce a mathematical framework for kernel decomposition such that the windows in the decomposition algorithm are not arbitrary and that the resulting decomposition provides a fast algorithm to compute tfds using the centrosymmetric structure of the time frequency kernels we introduce a decomposition algorithm such that any tfd associated with a bounded kernel can be written as a weighted sum of cross spectrograms the decomposition for several different discrete time kernels are given and the performance of the approximation algorithm is illustrated for different types of signals

toeplitz and hankel kernels for estimating time varying spectra of discrete time random processes for a nonstationary random process the dual time correlation function and the dual frequency loeve spectrum are complete theoretical descriptions of second order behavior that is each may be used to synthesize the random process itself according to the cramer loeve spectral representation when suitably transformed on one of its two variables each of these descriptions produces a time varying spectrum this spectrum is in fact the expected value of the rihaczek distribution in this paper we derive two large families of estimators for this spectrum one based on a diagonal toeplitz diagonal dtd factorization of smoothing kernels and the other based on a diagonal hankel diagonal dhd factorization the dtd factorization produces noncoherent averages of the time varying spectrogram and the dhd factorization produces coherent averages some of the dtd estimators may be called time varying power spectrum estimators and some of the dhd estimators may be called time varying wigner ville wv estimators the former may always be implemented as multiwindow spectrum estimators and in some casts they are true time variations on the blackman tukey rosenblatt grenander btgr spectrogram the latter are variations on the stankovic class of wv estimators

robust wigner distribution with application to the instantaneous frequency estimation the wigner distribution wd produces highly concentrated time frequency tf representation of nonstationary signals it may be used as an efficient signal analysis tool including the cases of frequency modulated signals corrupted with the gaussian noise in some applications a significant amount of impulse noise is present then the wd fails to produce satisfactory results the robust periodogram has been introduced for spectral estimation of this kind of noisy signals it can produce good concentration for pure harmonic signals however it is not so efficient in the cases of signals with rapidly varying frequency this is the motivation for introducing the robust wd it is a reliable tf representation tool for wide class of nonstationary signals corrupted with impulse noise this distribution produces good accuracy of the instantaneous frequency if estimation using the huber 1981 loss function a generalization of the wd is presented it includes both the standard and the robust wd as special cases this distribution can be used for tf analysis of signals corrupted with a mixture of impulse and gaussian noise the presented theory is illustrated on examples including applications on the if estimation and time varying filtering of signals corrupted with a mixture of the gaussian and impulse noise the case study analysis of the if estimators accuracy based on the standard and the robust wd forms is performed in order to improve the if estimation a median filter is applied on the obtained if estimate

transition kernels for bilinear time frequency distributions the author proposes a sequence of time frequency signal representations which offer a continuous transition from time smoothed pseudo wigner ville distributions pwvd to a specified class of positive representations this allows the selection of a representation which offers the desired tradeoff between the inherent localization properties of the pwvd and the lack of interference terms present in the class of positive representations a cause of some criticism of the method the sequence converges uniformly to the specified positive distribution

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

spectral decomposition of time frequency distribution kernels this paper addresses the general problem of approximating a given time frequency distribution tfd in terms of other distributions with desired properties it relates the approximation of two time frequency distributions to their corresponding kernel approximation it is shown that the singular value decomposition svd of the time frequency t f kernels allows the expression of the time frequency distributions in terms of weighted sum of smoothed pseudo wigner ville distributions or modified periodograms which are the two basic nonparametric power distributions for stationary and nonstationary signals respectively the windows appearing in the decomposition take zero and or negative values and therefore are different than the time and lag windows commonly employed by these two distributions the centrosymmetry and the time support properties of the kernels along with the fast decay of the singular values lead to computational savings and allow for an efficient reduced rank kernel approximations

subspace analysis of spatial time frequency distribution matrices spatial time frequency distributions stfds have been previously introduced as the natural means to deal with source signals that are localizable in the time frequency domain previous work in the area has not provided the eigenanalysis of stfd matrices which is key to understanding their role in solving direction finding and blind source separation problems in multisensor array receivers the aim of this paper is to examine the eigenstructure of the stfd matrices we develop the analysis and statistical properties of the subspace estimates based on stfds for frequency modulated fm sources it is shown that improved estimates are achieved by constructing the subspaces from the time frequency signatures of the signal arrivals rather than from the data covariance matrices which are commonly used in conventional subspace estimation methods this improvement is evident in a low signal to noise ratio snr environment and in the cases of closely spaced sources the paper considers the music technique to demonstrate the advantages of stfds and uses it as grounds for comparison between time frequency and conventional subspace estimates

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

performance of quadratic time frequency distributions as instantaneous frequency estimators general performance analysis of the shift covariant class of quadratic time frequency distributions tfds as instantaneous frequency if estimators for an arbitrary frequency modulated fm signal is presented expressions for the estimation bias and variance are derived this class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear if however when the if is not a linear function of time then the estimate is biased cases of white stationary and white nonstationary additive noises are considered the well known results for the wigner distribution wd and linear fm signal and the spectrogram of signals whose if may be considered as a constant within the lag window are presented as special cases in addition we have derived the variance expression for the spectrogram of a linear fm signal that is quite simple but highly signal dependent this signal is considered in the cases of other commonly used distributions such as the born jordan and the choi williams distributions it has been shown that the reduced interference distributions outperform the wd but only in the case when the if is constant or its variations are small analysis is extended to the if estimation of signal components in the case of multicomponent signals all theoretical results are statistically confirmed

fast implementations of generalized discrete time frequency distributions cohen s class of time frequency distributions tfds have significant potential for the analysis of complex signals in order to evaluate the tfd of a signal using its samples discrete time tfds dtfds have been defined as the fourier transform of a smoothed discrete autocorrelation existing algorithms evaluate real valued dtfds using ffts of the conjugate symmetric autocorrelation although the computation required to smooth the autocorrelation is often greater than that for the fft there are no widely applicable fast algorithms for this part of the processing since the fft is relatively inexpensive downsampling is ineffective for reducing computation if the dtfd needs only to be evaluated at a few frequencies for each time instant the cost per time frequency sample can be extremely high the authors introduce two approaches for reducing the computation time of dtfds first they define approximations to real valued dtfds using spectrograms that admit fast space saving evaluations frequency downsampling reduces the computation time of these approximations next they define dtfds that admit fast evaluations over sparse sets of time frequency samples a single short time fourier transform is calculated in order for dtpd time frequency samples to be evaluated at an additional fixed cost per sample

minimum bias multiple taper spectral estimation two families of orthonormal tapers are proposed for multitaper spectral analysis minimum bias tapers and sinusoidal tapers spl upsisup k where spl upsisub nsup k spl radic 2 n 1 sin spl pi kn n 1 and n is the number of points the resulting sinusoidal multitaper spectral estimate is s spl circ f 1 2k n 1 spl sigmasub j 1sup k y f j 2n 2 y f j 2n 2 sup 2 where y f is the fourier transform of the stationary time series s f is the spectral density and k is the number of tapers for fixed j the sinusoidal tapers converge to the minimum bias tapers like 1 n since the sinusoidal tapers have analytic expressions no numerical eigenvalue decomposition is necessary both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth the bandwidth of the jth taper is simply 1 n centered about the frequencies spl plusmn j 2n 2 thus the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers the band limited spectral concentration spl intsub wsup w v f sup 2 df of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the slepian 1978 tapers in contrast the slepian tapers can have the local bias spl intsub 1 2 sup 1 2 f sup 2 v f sup 2 df much larger than of the minimum bias tapers and the sinusoidal tapers