measurability of optimal transportation and convergence rate for landau type interacting particle systems in this paper we consider nonlinear diffusion processes driven by space time white noises which have an interpretation in terms of partial differential equations for a specific choice of coefficients they correspond to the landau equation arising in kinetic theory the main goal of the paper is to construct an easily simulable diffusive interacting particle system converging towards this nonlinear process and to obtain an explicit pathwise rate this requires to find a significant coupling between finitely many brownian motions and the infinite dimensional white noise process the key idea will be to construct the right brownian motions by pushing forward the white noise processes through the brenier map realizing the optimal transport between the law of the nonlinear process and the empirical measure of independent copies of it a crucial problem will then be to establish the joint measurability of this optimal transport map with respect to the space variable and the parameter time randomness that makes the marginals vary to overcome this point we shall prove a general measurability result for the mass transportation problem and for the supports of the optimal transfer plans in the sense of set valued mappings this will allow us to construct the coupling and to obtain explicit convergence rates

adaptive multiple subtraction with wavelet based complex unary wiener filters abstractadaptive subtraction is a key element in predictive multiple suppression methods it minimizes misalignments and amplitude differences between modeled and actual multiples and thus reduces multiple contamination in the data set after subtraction due to the high crosscorrelation between their waveforms the main challenge resides in attenuating multiples without distorting primaries as they overlap on a wide frequency range we split this wide band problem into a set of more tractable narrow band filter designs using a 1d complex wavelet frame this decomposition enables a single pass adaptive subtraction via complex single sample unary wiener filters consistently estimated on overlapping windows in a complex wavelet transformed domain each unary filter compensates for amplitude differences within its frequency support and can correct small and large misalignment errors through phase and integer delay corrections this approach greatly simplifies the matching filter estimation and despit

adaptive filtering in subbands with critical sampling analysis experiments and application to acoustic echo cancellation an exact analysis of the critically subsampled two band modelization scheme is given and it is demonstrated that adaptive cross filters between the subbands are necessary for modelization with small output errors it is shown that perfect reconstruction filter banks can yield exact modelization these results are extended to the critically subsampled multiband schemes and important computational savings are seen to be achieved by using good quality filter banks the problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived the authors give a detailed analysis of the computational complexity of all the discussed schemes and experimentally verify the theoretical results that are obtained the adaptive behavior of the subband schemes that were tested is discussed

convergence analysis of alias free subband adaptive filters based on a frequency domain technique convergence analysis of alias free subband adaptive filters sadfs is presented based on a frequency domain technique where instead of analyzing the adaptive algorithms in the time domain the averaging method and the ordinary differential equation ode method are applied to the frequency domain expressions of the adaptive algorithms converted by the discrete fourier transform as an alias free sadf algorithm the sadf proposed by pradhan and reddy is known in this paper this technique is first applied to the pradhan s sadf the stability of the pradhan s sadf is verified in the frequency domain and a simple formula to evaluate the mean square error mse of the algorithm is theoretically derived by using a slight modification the technique can be applied to the two band delayless subband adaptive filter dlsadf with the hadamard transform the stability condition and the mse of the dlsadf with the hadamard transform are also obtained simulation results of both algorithms show the validity of the theoretical results

valuation of stock loans with regime switching this paper is concerned with stock loan valuation in which the underlying stock price is dictated by geometric brownian motion with regime switching the stock loan pricing is quite different from that for standard american options because the associated variational inequalities may have infinitely many solutions in addition the optimal stopping time equals infinity with positive probability variational inequalities are used to establish values of stock loans and reasonable values of critical parameters such as loan sizes loan rates and service fees in terms of certain algebraic equations numerical examples are included to illustrate the results

adaptive nonlinear system identification in the short time fourier transform domain in this paper we introduce an adaptive algorithm for nonlinear system identification in the short time fourier transform stft domain the adaptive scheme consists of a parallel combination of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we adaptively update the model parameters using the least mean square lms algorithm and derive explicit expressions for the transient and steady state mean square error mse in frequency bins for white gaussian inputs we show that estimation of the nonlinear component improves the mse performance only when the power ratio of nonlinear to linear components is relatively high furthermore as the number of crossband filters increases a lower steady state mse may be obtained at the expense of slower convergence experimental results support the theoretical derivations

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

perfect reconstruction fir filter banks some properties and factorizations perfect reconstruction finite impulse response fir filter banks are analyzed both in the z transform and time domains showing the alternatives between designs in the two domains various classes of perfect reconstruction schemes are indicated and relations between previously known systems are given windowed modulated filter banks with low computational complexity and perfect reconstruction are shown new factorizations of polyphase filter matrices leading in particular to linear phase filters are given the computational complexity and the architecture of the new structures are indicated

modeling and identification of nonlinear systems in the short time fourier transform domain in this paper we introduce a novel approach for improved nonlinear system identification in the short time fourier transform stft domain we first derive explicit representations of discrete time volterra filters in the stft domain based on these representations approximate nonlinear stft models which consist of parallel combinations of linear and nonlinear components are developed the linear components are represented by cross band filters between subbands while the nonlinear components are modeled by multiplicative cross terms we consider the identification of quadratically nonlinear systems and show that a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time domain volterra model particularly when long memory systems are considered experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach

orthonormal and biorthonormal filter banks as convolvers and convolutional coding gain convolution theorems for filter bank transformers are introduced both uniform and nonuniform decimation ratios are considered and orthonormal as well as biorthonormal cases are addressed all the theorems are such that the original convolution reduces to a sum of shorter decoupled convolutions in the subbands that is there is no need to have cross convolution between subbands for the orthonormal case expressions for optimal bit allocation and the optimized coding gain are derived the contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum with one of the convolved sequences taken to be the unit pulse function e coding gain expressions reduce to those for traditional subband and transform coding the filter bank convolver has about the same computational complexity as a traditional convolver if the analysis bank has small complexity compared to the convolution itself

joint alignment of multiple point sets with batch and incremental expectation maximization this paper addresses the problem of registering multiple point sets solutions to this problem are often approximated by repeatedly solving for pairwise registration which results in an uneven treatment of the sets forming a pair a model set and a data set the main drawback of this strategy is that the model set may contain noise and outliers which negatively affects the estimation of the registration parameters in contrast the proposed formulation treats all the point sets on an equal footing indeed all the points are drawn from a central gaussian mixture hence the registration is cast into a clustering problem we formally derive batch and incremental em algorithms that robustly estimate both the gmm parameters and the rotations and translations that optimally align the sets moreover the mixture s means play the role of the registered set of points while the variances provide rich information about the contribution of each component to the alignment we thoroughly test the proposed algorithms on simulated data and on challenging real data collected with range sensors we compare them with several state of the art algorithms and we show their potential for surface reconstruction from depth data

a primal dual proximal algorithm for sparse template based adaptive filtering application to seismic multiple removal unveiling meaningful geophysical information from seismic data requires to deal with both random and structured noises as their amplitude may be greater than signals of interest primaries additional prior information is especially important in performing efficient signal separation we address here the problem of multiple reflections caused by wave field bouncing between layers since only approximate models of these phenomena are available we propose a flexible framework for time varying adaptive filtering of seismic signals using sparse representations based on inaccurate templates we recast the joint estimation of adaptive filters and primaries in a new convex variational formulation this approach allows us to incorporate plausible knowledge about noise statistics data sparsity and slow filter variation in parsimony promoting wavelet frames the designed primal dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters the approach demonstrates significantly good performance in low signal to noise ratio conditions both for simulated and real field data

a certain class of diffusion processes associated with nonlinear parabolic equations we introduce a martingale problem to associate diffusion processes with a kind of nonlinear parabolic equation then we show the existence and uniqueness theorems for solutions to the martingale problem

a new delayless subband adaptive filter structure adaptive subband techniques have been developed to reduce complexity and slow convergence problems of the traditional fullband high order adaptive filters some of the disadvantages often encountered in most of the proposed architectures are the effect of aliasing associated with the multirate structure which is a source of error in the modeling of the unknown system and the delay introduced in the signal path we present a new delayless maximally decimated structure where the optimal subband filters are related to the wideband system in a closed form they make use of a special dft analysis filterbank where the polyphase components of the prototype filter represent fractional delays so that there is no need for adaptive cross filters and the unknown system can modeled perfectly in a closed loop scheme we interpret the proposed structure as a special case of a block adaptive filter with lower computational complexity than the conventional fullband lms algorithm some computer simulations are presented in order to verify the good features of the proposed structure

inherent decorrelating and least perturbation properties of the normalized subband adaptive filter this correspondence describes and analyzes a class of subband adaptive filters safs that stems from various approaches of applying subband and multirate techniques in adaptive filtering this class of safs called the normalized saf nsaf has a unique weight control mechanism whereby subband error signals are used to adapt a fullband tap weight vector in this correspondence we elaborate on the inherent decorrelating properties of the nsaf which manifest themselves in different forms as integral elements of the weight control mechanism we also show that the nsaf possesses some least perturbation properties that are also found in the normalized least mean square nlms and affine projection ap algorithms

spectral analysis of subband adaptive digital filters subband adaptive digital filters at stationary points are analyzed in the frequency domain approximate expressions for the optimal subband filters are presented and then a spectral representation of the error variance is derived these are expressed in the frequency domain and hence enable us to see the aliasing effects in subband adaptive filtering

nonuniform subband adaptive filtering with critical sampling adaptive subband structures have been proposed with the objective of increasing the convergence speed and or reducing the computational complexity of conventional adaptive algorithms mainly for applications that require a large number of adaptive coefficients in this paper we present a nonuniform subband structure with critical sampling which is capable of modeling an arbitrary finite impulse response fir system with reduced aliasing a least mean square lms type adaptation algorithm with normalized step sizes which works at the lowest downsampling rate and minimizes the average of the subband squared errors is derived for the proposed structure a convergence analysis of the adaptation algorithm is presented from which its convergence rate and steady state mean square error can be estimated

wavelet transform domain adaptive fir filtering this paper presents and studies two new wavelet transform domain least mean square lms algorithms the algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity the procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation the first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process it then computes the cholesky factor of that matrix and uses its inverse to whiten the input the complexity of this first approach is o n log sup 2 n in contrast the second approach computes a sparse estimate of the cholesky factor of the wavelet domain correlation matrix of the input process directly this second approach has a computational complexity of o n log n floating point operations however it requires a more complex bookkeeping procedure both algorithms have a convergence rate that is faster than that of time domain lms and discrete fourier transform dft or discrete cosine transform dct based lms procedures the paper compares the two procedures and analyzes their mean and mean square performance

optimal variable step size for the lms newton algorithm with application to subband adaptive filtering an efficient approach for the computation of the optimum convergence factor for the lms least mean square newton algorithm applied to a transversal fir structure is proposed the approach leads to a variable step size algorithm that results in a dramatic reduction in convergence time the algorithm is evaluated in system identification applications where two alternative implementations of the adaptive filter are considered the conventional transversal fir realization and adaptive filtering in subbands

an equalization algorithm for wavelet packet based modulation schemes a considerable amount of attention has been given in the literature to the use of wavelets for modulation and equalization in this correspondence we present an equalization algorithm for a wavelet packet based modulation scheme a nonideal channel can be divided into a set of bands where each band can be approximated as a simple attenuation and delay channel wavelet packets being narrowband and orthonormal are a natural choice for realizing such bands thus if the data sequence is used to modulate a set of wavelet packets the equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets if the wavelet packets do not overlap in the frequency domain and possibly a change of sign in the decoded symbols the attenuation affects the snr at the output of the demodulator which in turn affects the correct decoding of the transmitted symbols a minimum square variance algorithm for adaptively choosing the delay has been proposed the algorithm uses the statistics of the received sequence to pick the appropriate delay simulations have been conducted to study the performance of the equalization algorithm and compare it with that of dft based dmt scheme

a competitive mean squared error approach to beamforming we treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of array observations conventional beamforming methods typically aim at maximizing the signal to interference plus noise ratio sinr however this does not guarantee a small mean squared error mse so that on average the resulting signal estimate can be far from the true signal here we consider strategies that attempt to minimize the mse between the estimated and unknown signal waveforms the methods we suggest all maximize the sinr but at the same time are designed to have good mse performance since the mse depends on the signal power which is unknown we develop competitive beamforming approaches that minimize a robust mse measure two design strategies are proposed minimax mse and minimax regret we demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods over a wide range of signal to noise ratio snr values finally we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal

a new method for low rank transform domain adaptive filtering this paper introduces a least squares matrix based framework for adaptive filtering that includes normalized least mean squares nlms affine projection ap and recursive least squares rls as special cases we then introduce a method for extracting a low rank underdetermined solution from an overdetermined or a high rank underdetermined least squares problem using a part of a unitary transformation we show how to create optimal low rank transformations within this framework for obtaining computationally competitive versions of our approach we use the discrete fourier transform dft we convert the complex valued dft based solution into a real solution the most significant bottleneck in the optimal version of the algorithm lies in having to calculate the full length transform domain error vector we overcome this difficulty by using a statistical approach involving the transform of the signal rather than that of the error to estimate the best low rank transform at each iteration we also employ an innovative mixed domain approach in which we jointly solve time and frequency domain equations this allows us to achieve very good performance using a transform order that is lower than the length of the filter thus we are able to achieve very fast convergence at low complexity using the acoustic echo cancellation problem we show that our algorithm performs better than nlms and ap and competes well with ftf rls for low snr conditions the algorithm lies in between affine projection and ftf rls both in terms of its complexity and its performance

propagation of chaos for the landau equation with moderately soft potentials we consider the 3d landau equation for moderately soft potentials 2 0 2 0 with the usual notation as well as a stochastic system of nn particles approximating it we first establish some strong weak stability estimates for the landau equation which are fully satisfactory only when 1 0 1 0 we next prove under some appropriate conditions on the initial data the so called propagation of molecular chaos that is that the empirical measure of the particle system converges to the unique solution of the landau equation the main difficulty is the presence of a singularity in the equation when 1 0 1 0 the strong weak uniqueness estimate allows us to use a coupling argument and to obtain a rate of convergence when 2 1 2 1 we use the classical martingale method introduced by mckean to control the singularity we have to take advantage of the regularity provided by the entropy dissipation unfortunately this dissipation is too weak for some very rare aligned configurations we thus introduce a perturbed system with an additional noise show the propagation of chaos for this system and finally prove that the additional noise is almost never used in the limit n n

steady state performance limitations of subband adaptive filters nonperfect filterbanks used for subband adaptive filtering saf are known to impose limitations on the steady state performance of such systems in this paper we quantify the minimum mean square error mmse and the accuracy with which the overall saf system can model an unknown system that it is set to identify first in case of mmse limits the error is evaluated based on a power spectral density description of aliased signal components which is accessible via a source model for the subband signals that we derive approximations of the mmse can be embedded in a signal to alias ratio sar which is a factor by which the error power can be reduced by adaptive filtering with simplifications sar only depends on the filterbanks second in case of modeling we link the accuracy of the saf system to the filterbank mismatch in perfect reconstruction when using modulated filterbanks both error limits mmse and inaccuracy can be linked to the prototype we explicitly derive this for generalized dft modulated filterbanks and demonstrate the validity of the analytical error limits and their approximations for a number of examples whereby the analytically predicted limits of error quantities compare favorably with simulations

adaptive filtering in subbands using a weighted criterion transform domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence thus improving the convergence rate however a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input output delay as small as possible thus imposing short transforms this dilemma has been alleviated by the so called short block transform domain algorithms but is still apparent this paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms e g critically subsampled lossless perfect reconstruction filter banks thus allowing better tradeoffs between algorithm improvement arithmetic complexity and input output delay the method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm this method leads to improvements in the convergence rate compared with both lms and classical frequency domain algorithms

a functional analysis approach to subband system approximation and identification the subband system identification method consists of identifying a linear system in the time frequency domain this technique can be also used to approximate a linear system in the same domain in both cases it has the advantage of having a very high numerical efficiency however analyzing such a technique is not trivial and the best setup for subband system approximation and identification is not clear in this paper we propose a functional analysis setting to the analysis of the subband technique which leads us to some results on both subband system approximation and identification concerning system approximation we provide an analytical expression to calculate the optimal subband approximation of a given full band system when the quality of the approximation is measured by the power of the output error signal assuming a white input signal we also provide a tight approximation error bound for a given subband configuration which applies in the case where the unknown system to be approximated is known to be the finite impulse response fir of a given order concerning system identification we provide a novel identification strategy that consists of identifying a low quality subband model and use it to build the required model for either subband or delayless reconstruction this identification strategy reduces the computational complexity of the identification process and yields significantly smaller asymptotic residual errors when compared with the existing methods

mean square deviation analysis of multiband structured subband adaptive filter algorithm a multiband structured subband adaptive filter msaf algorithm was introduced to achieve a fast convergence rate for the correlated input signal the convergence analysis of the adaptive filter algorithm is an important concept because it provides a guideline to design the adaptive filter however the convergence analysis of the msaf algorithm has not been researched as extensively as that of the normalized least mean square algorithm therefore it needs to be researched in this paper we present a new approach to the mean square deviation msd analysis of the msaf algorithm by using the persistently exciting input and the practical assumption that the stopband attenuation of the prototype filter is high unlike the previous analysis the proposed analysis is possible to be applied to the long length adaptive filter such as the acoustic echo cancellation the proposed analysis is also applied to a non stationary model with a random walk of the optimal weight vector the simulation results match with the theoretical results in both the transient state and steady state msd

polyphase networks block digital filtering lptv systems and alias free qmf banks a unified approach based on pseudocirculants the relationship between block digital filtering and quadrature mirror filter qmf banks is explored necessary and sufficient conditions for alias cancellation in qmf banks are expressed in terms of an associated matrix derived from the polyphase components of the analysis and synthesis filters these conditions called the pseudocirculant conditions make it possible to unite qmf banks with the framework of block digital filtering directly absence of amplitude distortion in an alias free qmf bank translates into the losslessness property of the pseudocirculant matrix involved

extended lapped transforms properties applications and fast algorithms the family of lapped orthogonal transforms is extended to include basis functions of arbitrary length within this new family the extended lapped transform elt is introduced as a generalization of the previously reported modulated lapped transform mlt design techniques and fast algorithms for the elt are presented as well as examples that demonstrate the good performance of the elt in signal coding applications therefore the elt is a promising substitute for traditional block transforms in transform coding systems and also a good substitute for less efficient filter banks in subband coding systems

a fast exact least mean square adaptive algorithm a general block formulation of the least mean square lms algorithm for adaptive filtering is presented this formulation has an exact equivalence with the original lms algorithm hence it retains its convergence properties while allowing a reduction in arithmetic complexity even for very small block lengths working with small block lengths is interesting from an implementation point of view large blocks result in large memory and large system delay and allows a significant reduction in the number of operations tradeoffs between a number of operations and a convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm hence the usual block lms appears as a special case which explains its convergence behavior according to the type of input signal correlated or uncorrelated

on the perfect reconstruction problem in n band multirate maximally decimated fir filter banks the problem of finding n k filters of an n band maximally decimated fir analysis filter bank given k filters so that fir perfect reconstruction can be achieved is considered the perfect reconstruction condition is expressed as a requirement of unimodularity of the polyphase analysis filter matrix based on the theory of euclidean division for matrix polynomials the conditions the given transfer functions must satisfy are given and a complete parameterization of the solution is obtained this approach provides an interesting alternative to the method of the complementary filter in the case of n 2 k n 1 where the latter leads to a system of nonlinear equations moreover it yields the polyphase synthesis filter matrix as a byproduct as an application a complete characterization of all paraunitary matrices with fixed first row is derived the problem of appropriately choosing the parameters characterizing the complementary filters to lead to filters of practical useful frequency responses is studied and analytical solutions for k n 1 are given it is demonstrated through an example that the complementary filters found via euclid s algorithm are not necessarily linear phase even if the given filters are the problem of obtaining linear phase solutions of given orders is investigated for the general case n spl ges 2 k spl les n 1 and systematic ways are developed to compute such solutions in the k n 1 and k 1 cases it is also shown that the resulting synthesis filters are linear phase design examples illustrating the theory are presented

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

a recursive method for the approximation of lti systems using subband processing using the subband technique an lti system can be implemented by the composition of an analysis filterbank followed by a transfer matrix subband model and a synthesis filterbank the advantage of this approach is that it offers a good tradeoff between latency and computational complexity in this paper we propose an optimization method for approximating an lti system using the subband technique the proposed method includes optimal allocation of parameters from different fir entries of the subband model while keeping constant the total number of parameters for a better utilization of the available coefficients the optimization is done in a weighted least squares sense considering either linear or logarithmic amplitude scale simulation results demonstrate the advantages of the proposed method when compared with classical implementation approaches using pole zero transfer functions or segmented fft algorithms

ergodic properties for multirate linear systems stochastic analysis of a multirate linear system typically requires the signals in the system to possess certain ergodic properties among them ergodicity in the mean and ergodicity in the correlation are the most commonly used ones we show that multirate operations and time variant linear filtering can destroy these ergodic properties motivated by this fact we introduce the notions of strong ergodicity in the mean and strong ergodicity in the correlation we show that these properties are preserved under a number of operations namely downsampling upsampling addition and uniformly stable linear time variant filtering we also show that white random processes with uniformly bounded second moments are strongly ergodic in the mean and that mutually independent random processes with uniformly bounded fourth moments are jointly strongly ergodic in the correlation the main implication of these results is that if a multirate linear system is driven by white independent random processes with uniformly bounded second fourth moments then every signal in the system is strongly ergodic in the mean correlation and therefore ergodic in the mean correlation an application of these results is also discussed

polynomial transform implementation of digital filter banks this paper investigates the use of polynomial transforms for the implementation of uniform digital bandpass filter banks the technique is based upon a decomposition of the n bandpass filters into a set of real polyphase filters followed by a dct discrete cosine transform of size n the dct is converted into a dft discrete fourier transform of size n and the polyphase filters are evaluated by dft s this procedure yields a two dimensional dft which is computed by a polynomial transform and odd dft s we show that this technique reduces significantly the number of arithmetic operations when compared to conventional methods and yields a regular structure in which most of the computations are performed with fft type algorithms

fixed point error analysis of the normalized ladder algorithm an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification assuming rounding arithmetic a preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate the study therefore is directed to find a model for predicting the bias in the estimated reflection coefficients the analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients these errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one two main results are presented in the paper 1 a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived 2 a recursive relation for the average error arising from the finite precision arithmetic in the squared residuals is derived this relation illustrates how the errors made in one stage affect the errors in the succeeding stages simulations are performed to check the theoretical models the experimental results agree very closely with the theoretical predictions

asymptotic properties of subband identification the purpose of the paper is to study the asymptotic properties i e strong convergence and asymptotic convergence rate of the subband identification method in every subband and in the overall method the study of strong convergence aims to answer the question whether the best possible model is retrieved on the limit with probability one the study of the asymptotic convergence rate aims to give an expression that quantifies how fast the model approaches the best possible value as the number of samples goes to infinity to do this we need to generalize existing results for fullband identification in the process of doing so we come up with a new notion of ergodicity which we call strong ergodicity strongly ergodic signals not only satisfy the assumptions required for our analysis but also enjoy an interesting property which is that strong ergodicity is invariant under a number of transformations in particular the subband components of a strongly ergodic signal are guaranteed to be strongly ergodic therefore ergodic which is not true for an ergodic signal in general

delayless subband adaptive filtering using the hadamard transform in this correspondence an analysis of a delayless critically decimated subband adaptive filter structure is presented in this structure adaptive weights in each subband are computed by the lms algorithm and then transformed into those in fullband by the hadamard transform it is shown that a stationary point of the proposed algorithm corresponds to the fullband wiener filter some numerical results are also presented to show the performance of this scheme

undermodeling error quantification for quadratically nonlinear system identification in the short time fourier transform domain in this paper we introduce an estimation error analysis for quadratically nonlinear system identification in the short time fourier transform stft domain the identification scheme consists of a parallel connection of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we mainly concentrate on two types of undermodeling errors the first is caused by employing a purely linear model in the estimation process i e nonlinear undermodeling and the second is a consequence of restricting the number of estimated crossband filters in the linear component we derive analytical relations between the noise level nonlinearity strength and the obtainable mean square error mse in subbands we show that for low signal to noise ratio snr conditions a lower mse is achieved by allowing for nonlinear undermodeling and utilizing a purely linear model however as the snr increases the performance can be generally improved by incorporating a nonlinear component into the model we further show that as the snr increases a larger number of crossband filters should be estimated to attain a lower mse whether a linear or nonlinear model is employed experimental results support the theoretical derivations

running fir and iir filtering using multirate filter banks the computational complexity of running fir finite impulse response and iir infinite impulse response filtering using multirate filter banks is considered no restrictions are put on signal filter or block lengths it is shown how to map long running convolutions into smaller ones by using filter banks based on aperiodic convolution algorithms and short time fourier transforms with the proposed approach good tradeoffs among computational complexity system architecture and input output delay are achieved

mean square error analysis of nonuniform subband adaptive filters for system modeling nonuniform filterbanks have recently been proposed for subband adaptive filters safs however nonuniform safs have not yet been given a thorough performance analysis this paper gives a comprehensive mean square error mse analysis of system modeling nonuniform and degeneratively uniform safs after convergence for a specified filterbank using the equivalent polyphase representation suggested by ono et al minimum mse mmse estimates for the individual subband errors are presented with respect to a given filterbank for finite length fir infinite length causal iir and infinite noncausal adaptive filters using these subband mmse estimators an mmse estimator is derived for the overall fullband error finally the derived mmse estimators are verified by a numerical simulation the intent of this paper is not to compare nonuniform and uniform saf performance but merely to present a unified mathematical methodology to predict their mmses

stock loan with automatic termination clause cap and margin this paper works out fair values of the stock loan model with automatic termination clause cap and margin this stock loan is treated as a generalized perpetual american option with possibly negative interest rate and some constraints since it helps a bank to control the risk the banks charge lower service fees compared to stock loans without any constraints the automatic termination clause cap and margin are in fact a stop order set by the bank mathematically it is a kind of optimal stopping problem arising from the pricing of financial products which is first revealed we aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters this loan size interest rate cap margin and fee for providing such a service and quantity of this automatic termination clause and the relationships among these parameters as well as the optimal exercise times we present numerical results and make analysis about the model parameters and how they impact on value of stock loan

one and two level filter bank convolvers in a recent paper it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results in this paper we further generalize the result we also derive the statistical coding gain for the generalized subband convolver as an application we derive a novel low sensitivity structure for fir filters from the convolution theorem we define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation this gain serves as a figure of merit for the low sensitivity structure several numerical examples are included to demonstrate the usefulness of these ideas by using the generalized polyphase representation we show that the subband convolvers linear periodically time varying systems and digital block filtering can be viewed in a unified manner furthermore the scheme called ifir filtering is shown to be a special case of the convolver

efficient design of oversampled npr gdft filterbanks we propose a flexible efficient design technique for the prototype filter of an oversampled near perfect reconstruction npr generalized discrete fourier transform gdft filterbank such filterbanks have several desirable properties for subband processing systems that are sensitive to aliasing such as subband adaptive filters the design criteria for the prototype filter are explicit bounds derived herein on the aliased components in the subbands and the output the distortion induced by the filterbank and the imaged subband errors in the output it is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved the proposed design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter including the tradeoff between aliasing in the subbands and the distortion induced by the filterbank we calculate several examples of these tradeoffs and demonstrate that the proposed method can generate filters with significantly better performance than filters obtained using current design methods

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

blind adaptive constrained reduced rank parameter estimation based on constant modulus design for cdma interference suppression this paper proposes a multistage decomposition for blind adaptive parameter estimation in the krylov subspace with the code constrained constant modulus ccm design criterion based on constrained optimization of the constant modulus cost function and utilizing the lanczos algorithm and arnoldi like iterations a multistage decomposition is developed for blind parameter estimation a family of computationally efficient blind adaptive reduced rank stochastic gradient sg and recursive least squares rls type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods an analysis of the convergence properties of the method is carried out and convergence conditions for the reduced rank adaptive algorithms are established simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in ds cdma systems

equations de type de boltzmann spatialement homogenes we study the construction of a nonhomogeneous n valued markov process whose laws at fixed times evolve according to a boltzmann type equation spatially homogeneous we then consider the problem of the asymptotic propagation of chaos for a system of a large number of interacting particles

capped stock loans in this paper we study a kind of financial product stock loans in which there is a capped limit for the stock price when it exceeds a predetermined barrier loans with two types of cap are analyzed constant caps and caps with a constant growth rate we build the pricing models of the contracts by analyzing the form of the optimal stopping time and derive the formulas of the value functions we present the numerical results and make an analysis of fair values of related parameters a comparison between capped stock loans and uncapped ones is also given we find that capped loans have their own advantages such as more flexibility and lower cost

the design of uniformly and nonuniformly spaced pseudoquadrature mirror filters in the past quadrature mirror filters qmf s have been used to derive both uniformly and nonuniformly spaced filterbanks a pair of qmf s divides a signal into two equal bands which can be decimated at 2 1 and subsequently combined to reconstruct the original signal in order to derive filterbanks with more than two bands qmf s are combined in a binary tree structure pseudoquadrature mirror filters are similar to qmf s but can be designed to split a signal directly into any number of equally spaced bands thus generalizing the qmf concept in this paper the theory of pseudoquadrature mirror filters is reviewed these filters retain the desirable property that the channel signals from a uniformly spaced bank of m filters can be decimated by m 1 then interpolated and reassembled to reproduce the original signal an extension is made to the theory to allow a set of nonuniformly spaced filters to be derived from a uniformly spaced set and still retain all the desirable characteristics another extension to the theory is the derivation of a family of different sized filterbanks all derived from the same original prototype potential applications for the new filterbanks include improvements in subband coding of speech and music and analog scrambling of speech

a set of algorithms linking nlms and block rls algorithms this paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares nlms and the block recursive least squares brls algorithms all these algorithms use small block lengths thus allowing easy implementation and small input output delay it is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares lms algorithm while converging much faster a precise evaluation of the arithmetic complexity is provided and the adaptive behavior of the algorithm is analyzed simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the nlms algorithm the conclusions of the theoretical analysis are checked by simulations illustrating that even in the case where noise is added to the reference signal the proposed algorithm allows altogether a faster convergence and a lower residual error than the nlms algorithm finally a sample by sample version of this algorithm is outlined which is the link between the nlms and recursive least squares rls algorithms

local existence lower mass bounds and a new continuation criterion for the landau equation abstract we consider the spatially inhomogeneous landau equation with soft potentials first we establish the short time existence of solutions assuming the initial data has sufficient decay in the velocity variable and regularity no decay assumptions are made in the spatial variable next we show that the evolution instantaneously spreads mass throughout the domain the resulting lower bounds are sub gaussian which we show is optimal the proof of mass spreading is based on a stochastic process and makes essential use of nonlocality by combining this theorem with prior results we derive two important applications c smoothing even for initial data with vacuum regions and a continuation criterion the solution can be extended as long as the mass and energy densities stay bounded from above this is the weakest condition known to prevent blow up in particular it does not require a lower bound on the mass density or an upper bound on the entropy density

performance analysis for subband identification the so called subband identification method has been introduced recently as an alternative method for identification of finite impulse response systems with large tap sizes it is known that this method can be more numerically efficient than the classical system identification method however no results are available to quantify its advantages this paper offers a rigorous study of the performance of the subband method more precisely we aim to compare the performance of the subband identification method with the classical fullband identification method the comparison is done in terms of the asymptotic residual error asymptotic convergence rate and computational cost when the identification is carried out using the prediction error method and the optimization is done using the least squares method it is shown that by properly choosing the filterbanks the number of parameters in each subband the number of subbands and the downsampling factor the two identification methods can have compatible asymptotic residual errors and convergence rate however for applications where a high order model is required the subband method is more numerically efficient we study two types of subband identification schemes one using critical sampling and another one using oversampling the former is simpler to use and easier to understand whereas the latter involves more design problems but offers further computational savings

quadrature mirror filter design for an arbitrary number of equal bandwidth channels the two channel quadrature mirror filter structure of croisier and esteban may be extended to an arbitrary number of equal bandwidth channels given certain restrictions on the bandpass filters the most serious restriction is that the stopband attenuation of eacli band pass filter must be high for all frequencies outside twice the nominal 3 db bandwidth of the filter this restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise a key feature of our filter structure is that the number of multiplies adds and stored coefficients required for implementation is significantly less than those needed for the conventional qmf structure given the same number of channels fortran code for a 16 channel filter structure is listed as an example of efficient implementation

stock loan valuation based on the finite moment log stable process abstract the empirical test suggests that the log return series of stock price in us market reject the normal distribution and admit instead a subclass of the asymmetric distribution in this paper we investigate the stock loan problem under the assumption that the return of stock follows the finite moment log stable process fmls in this case the pricing model of stock loan can be described by a space fractional partial differential equation with time varying free boundary condition firstly a penalty term is introduced to change the original problem to be defined on a fixed domain and then a fully implicit difference scheme has been developed secondly based on the fully implicit scheme we prove that the stock loan value generated by the penalty method cannot fall below the value obtained when the stock loan is exercised early thirdly the numerical experiments are carried out to demonstrate differences of stock loan model under the fmls and the standard normal distribution optimal redemption strategy of stock loan has been achieved furthermore the impact of key parameters in our model on the stock loan evaluation are analyzed and some reasonable explanation are given