on the arbitrary length m channel linear phase perfect reconstruction filter banks this correspondence extends the theory and lattice factorizations for m channel linear phase perfect reconstruction filter banks lpprfbs we deal with fir fbs with real valued filter coefficients in which all filters have the same arbitrary length l km beta 0 les beta m and same symmetry center in contrast to traditional constrained length profile l km first refined existence conditions on this larger class of fbs are given then lattice structures are developed for both odd and even channel fbs and their relationship with time domain lapped transforms is explained these structures are more general compared to conventional design methods and cover them as special cases furthermore we discuss how to structurally impose the regularity onto the lattice structure to ensure the smoothness of the basis function which is very desirable in high performance image compression finally these lattice structures are proven to be minimal in terms of the number of delay elements used in implementation and to completely span the class of lpprfbs with length l les 2m and the whole class of linear phase paraunitary filter banks lppufbs

on factorization of m channel paraunitary filterbanks we systematically investigate the factorization of causal finite impulse response fir paraunitary filterbanks with given filter length based on the singular value decomposition of the coefficient matrices of the polyphase representation a fundamental order one factorization form is first proposed for general paraunitary systems then we develop a new structure for the design and implementation of paraunitary system based on the decomposition of hermitian unitary matrices within this framework the linear phase filterbank and pairwise mirror image symmetry filterbank are revisited their structures are special cases of the proposed general structures compared with the existing structures more efficient ones that only use approximately half the number of free parameters are derived the proposed structures are complete and minimal although the factorization theory with or without constraints is discussed in the framework of m channel filterbanks the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems

filters for distortion free two band multirate filter banks in this paper conditions are given for a two band multi rate filter bank to be alias free and to have a unity frequency response it is shown that the class of quadrature mirror filters qmf s that satisfies these conditions is quite limited a class of filters which does satisfy these conditions is given and a simple procedure for designing filters from this class is presented with an example

cosine modulated filterbanks based on extended gaussian functions a new family of cosine modulated filterbanks based on functions called extended gaussian functions egfs is obtained the design is particularly simple since it is mainly based on a closed form expression nearly perfect reconstruction cosine modulated filterbanks are obtained as well as guidelines to estimate the filterbank parameters this analytical design method can be used to produce with a controlled accuracy filterbanks with practically no upper limitations in the number of coefficients and subbands furthermore a slight modification of the prototype filter coefficients is sufficient to satisfy exactly the perfect reconstruction constraints an analysis of the time frequency localization of the discrete prototype filters also shows that under certain conditions egf prototypes are at less than 0 3 from the optimal upper bound

a general formulation of modulated filter banks this paper presents a general framework for maximally decimated modulated filter banks the theory covers the known classes of cosine modulation and relates them to complex modulated filter banks the prototype filters have arbitrary lengths and the overall delay of the filter bank is arbitrary within fundamental limits necessary and sufficient conditions for perfect reconstruction pr are derived using the polyphase representation it is shown that these pr conditions are identical for all types of modulation modulation based on the discrete cosine transform dct both dct iii dct iv and dct i dct ii and modulation based on the modified discrete fourier transform mdft a quadratic constrained design method for prototype filters yielding pr with arbitrary length and system delay is derived and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation subchannelization

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

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 priori space time separated representation for the reduced order modeling of low reynolds number flows abstract reduced order models roms in fluid dynamics are nowadays mostly developed by performing a projection of the navier stokes equations onto a low dimensional space basis this basis is usually obtained through proper orthogonal decomposition pod which remains one the most efficient techniques to compress precomputed data the main drawback of a posteriori pod based roms is however their lacks of reliability as their parameters are varied preventing their direct uses within optimization algorithms the goal of the present article is to obtain an a priori low dimensional space time separated representation of the fluid fields without precomputed data the approach is based on the use of space time proper generalized decomposition pgd definitions which are successfully applied in several fields but whose uses in fluid dynamics remain scarce their applications to the navier stokes equations are indeed not straightforward due to the pressure velocity coupling the divergence free constraint and the non linear convective term the roms are built here from a space time weak formulation of the chorin temam prediction correction scheme more particularly a priori space time separated representations are obtained by applying the galerkin based progressive pgd definition the minimax pgd definition is moreover experimented on a linear stokes simplified case the related algorithms are explicitly given and illustrated on a transient lid driven cavity flow it is shown that the a priori space time separated representations converge to the full model solution as the decomposition order increases the ability of the resulting rom to learn iteratively from its own error is highlighted the progressive pgd algorithm can be used to effectively enrich incomplete pod and pgd precomputed space bases such as those obtained with different parameter values this may allow to ensure the accuracy of a rom as the parameter is varied which is of crucial interest for optimization problems

an efficient algorithm for the design of weighted minimax m channel cosine modulated filter banks this correspondence presents an efficient algorithm for the design of m channel cosine modulated filter banks our algorithm needs only a few iterations to obtain a weighted minimax solution and provides flexible control of the ripples in the filter s stopband the overall filter bank transfer function and the aliasing components

a systematic technique for designing linear phase fir prototype filters for perfect reconstruction cosine modulated and modified dft filterbanks this paper describes a systematic technique for designing prototype filters for generating perfect reconstruction pr orthogonal cosine modulated and modified discrete fourier transform filterbanks in the proposed design scheme the stopband energy of the prototype filter is minimized and the basic unknowns are the angles of a special lattice structure used for implementing the prototype filter so that the pr property is automatically satisfied independent of the angle values this selection of the unknowns makes the overall optimization problem unconstrained due to the fact that there are several local optima the design is performed in multiple steps in order to arrive at least at a very good suboptimal solution first for the given number of channels the length of the channel filters and the stopband edge of the prototype filter the corresponding two channel filterbank is designed based on the preoptimized data then after knowing the angles for the optimized two channel case the prototype filter for the desired filterbank is generated by gradually increasing the number of channels and by properly using the result of the previous step as a start up solution for the present step the main benefit of the proposed design technique is that it enables one to effectively design prototype filters for filterbanks with very high order analysis and synthesis filters

m channel compactly supported biorthogonal cosine modulated wavelet bases we generalize the theory of compactly supported biorthogonal two channel wavelet bases to m channel a sufficient condition for the m channel perfect reconstruction filter banks to construct m channel biorthogonal bases of compactly supported wavelets is derived it is shown that the construction of biorthogonal m channel wavelet bases is equivalent to the design of a m channel perfect reconstruction filter bank with some added regularity conditions a family of m channel biorthogonal wavelet bases based on the cosine modulated filter bank cmfb is proposed it has the advantages of simple design procedure efficient implementation and good filter quality a new method fur imposing the regularity on the cmfbs is also introduced and several design examples are given

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

dct based general structure for linear phase paraunitary filterbanks in this paper we present a general structure for linear phase paraunitary filterbanks lppufb via both time domain pre processing and frequency domain post processing of the discrete cosine transform dct the proposed structure not only covers existing frameworks with either pre processing or post processing of the dct but enables the design of dct based lppufb with both partial block overlapping and variable length filters as well some high performance and low complexity transforms can be obtained by fine tuning the structure parameters furthermore a dct oriented initialization method is developed to improve the convergence and to simplify the parameterization in the filterbank optimization process the application in image compression is demonstrated

efficient implementation of arbitrary length cosine modulated filter bank the fast implementation of arbitrary length cosine modulated filter bank is investigated by using the linear phase property of the prototype filter a more efficient implementation structure is obtained for the filter bank in the new implementation 2 spl times 2 lossless lattices are used instead of 2 spl times 1 ones in the traditional implementation with the number reduced by half

structures for m channel perfect reconstruction fir qmf banks which yield linear phase analysis filters the authors develop structures for fir finite impulse response perfect reconstruction qmf quadrature mirror filter banks which cover a subclass of systems that yield linear phase analysis filters for arbitrary m the parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect reconstruction property if there are m subbands then depending on whether the coefficients h sub k n of each analysis filter are symmetric or antisymmetric several combinations of filter banks are possible some of these permit perfect reconstruction and some do not for a given m the authors develop a formula for the number of combinations for a subclass of linear phase perfect reconstruction structures as an example they elaborate on a perfect reconstruction linear phase lattice structure for three channels the lattice structure is such that regardless of the parameter values the qmf bank enjoys the perfect reconstruction property while at the same time the analysis filters have linear phase a design example is presented along with tables of impulse response coefficients

cosine modulated fir filter banks satisfying perfect reconstruction the authors obtain a necessary and sufficient condition on the 2m m number of channels polyphase components of a linear phase prototype filter of length n 2 mm where m an arbitrary positive integer such that the polyphase component matrix of the modulated filter is lossless the losslessness of the polyphase component matrix in turn is sufficient to ensure that the analysis synthesis system satisfies perfect reconstruction pr using this result a novel design procedure is presented based on the two channel lossless lattice this enables the design of a large class of fir finite impulse response pr filter banks and includes the n 2m case it is shown that this approach requires fewer parameters to be optimized than in the pseudo qmf quadrature mirror filter designs and in the lossless lattice based pr qmf designs for equal length filters in the three designs this advantage becomes significant when designing long filters for large m the design procedure and its other advantages are described in detail design examples and comparisons are included

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

digital filter bank design quadratic constrained formulation formulate the filter bank design problem as an quadratic constrained least squares minimization problem the solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters the formulations of the perfect reconstruction cosine modulated filter bank of the near perfect reconstruction pseudo qmf bank and of the two channel biorthogonal linear phase filter bank are derived using the proposed approach compared with other design methods the proposed technique yields pr filter banks with much higher stopband attenuation the proposed technique can also be extended to design multidimensional filter banks

the theory and design of arbitrary length cosine modulated filter banks and wavelets satisfying perfect reconstruction it is well known that fir filter banks that satisfy the perfect reconstruction pr property can be obtained by cosine modulation of a linear phase prototype filter of length n 2mm where m is the number of channels in this paper we present a pr cosine modulated filter bank where the length of the prototype filter is arbitrary the design is formulated as a quadratic constrained least squares optimization problem where the optimized parameters are the prototype filter coefficients additional regularity conditions are imposed on the filter bank to obtain the cosine modulated orthonormal bases of compactly supported wavelets design examples are given

stabilization analysis for discrete time systems with time delay the stabilization problem for a class of discrete time systems with time varying delay is investigated by constructing an augmented lyapunov function some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality lmi technique when norm bounded parameter uncertainties appear in the delayed discrete time system a delay dependent robust exponential stabilization criterion is also presented all of the criteria obtained in this paper are strict linear matrix inequality conditions which make the controller gain matrix can be solved directly three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results

subband coder design incorporating recursive quadrature filters and optimum adpcm coders this paper presents the results of an analytical and experimental study of the use of iir quadrature mirror filters and forward adapting adpcm with optimum quantizers for octave band subband coders for speech it is shown that the underlying analysis synthesis systems can be designed such that there is no interband aliasing distortion in the coded speech and such that the analysis synthesis transfer function has no frequency distortion or no phase distortion but not both the experimental study showed that subband coders based on a mixture of infinite impulse response iir and finite duration impulse response fir filters resulted in higher quality coding systems using fewer multiplies than for systems based on fir filters alone it was also found that a signal to noise ratio snr gain of about 4 db could be obtained using optimum quantizers for forward adapting adpcm coders over linear quantizers in backward adapting apcm codes but no perceptual quality gain was observed