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

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

minimal positive solutions to some singular second order differential equations abstract the existence of a minimal c1 0 1 positive solution is established for some second order singular boundary value and initial value problems by new schemes which are related to x our nonlinearity may be singular at t 0 1 x 0 or x 0

on m channel linear phase fir filter banks and application in image compression this paper investigates the theory and structure of a large subclass of m channel linear phase perfect reconstruction fir filter banks systems with analysis and synthesis filters of length l sub i k sub i m spl beta where spl beta is an arbitrary integer 0 spl les spl beta m and k sub i is any positive integer for this subclass of systems we first investigate the necessary conditions for the existence of linear phase perfect reconstruction filter banks lpprfbs next we develop a complete and minimal factorization for all even channel linear phase paraunitary systems the most general lapped orthogonal transforms to date finally several design examples as well as comparisons with previous generalized lapped orthogonal transforms genlots in image compression are presented to confirm the validity of the theory

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

families of biorthogonal wavelets several families of biorthogonal wavelet bases are constructed with various properties in particular for a given filter fn of finite length 2n 1 a parametric family of dual filters fvn of length 2n 1 is constructed the parametric nature of the dual filters makes it possible to design the optimum dual filter fv0n corresponding to a fixed filter fn

linc a common theory of transform and subband coding a common theory of lapped orthogonal transforms lots and critically sampled filter banks called l into n coding linc is presented the theory includes a unified analysis of both coding methods and identity relations between the transform inverse transform analysis filter bank and synthesis filter bank a design procedure for linc analysis synthesis systems which satisfy the conditions for perfect reconstruction is developed the common linc theory is used to define an ideal linc system which is used together with the power spectral density of the input signal to calculate theoretical bounds for the coding gain a generalized overlapping block transform obt with time domain aliasing cancellation tdac is used to approximate the ideal linc a generalization of the obt includes multiple block overlap and additional windowing a recursive design procedure for windows of arbitrary lengths is presented the coding gain of the generalized obt is higher than that of the karhunen loeve transform klt and close to the theoretical bounds for linc in the case of image coding the generalized obt reduces the blocking effects when compared with the dct

second order boundary value problems of singular type abstract positive solutions are established for the singular second order boundary value problem formula singularities at i y 0 andy 0 ii y 0 but noty 0 and iii y 0 but noty 0 are discussed separately

subband coding of images using asymmetrical filter banks we address the problem of the choice of subband filters in the context of image coding the ringing effects that occur in subband based compression schemes are the major unpleasant distortions a new set of two band filter banks suitable for image coding applications is presented the basic properties of these filters are linear phase perfect reconstruction asymmetric length and maximum regularity the better overall performances compared to the classical qmf subband filters are explained the asymmetry of the filter lengths results in a better compaction of the energy especially in the highpass subbands moreover the quantization error is reduced due to the short lowpass synthesis filter the undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter the proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images which explains the better coding performance

subband decomposition of signals with generalized sampling the authors generalize down and up sampling operations by proposing block sampling perfect reconstruction conditions for two band subband coding with block sampling are derived by generalizing the sampling operation new degrees of freedom are introduced and as a result filter banks which were not previously possible become possible generalized down sampler introduces different aliasing components than that of the traditional down sampler this can be used to ease some the requirements of the filter bank design problem a constructive sampling method is proposed so that coprimeness of the transfer functions of the analysis filter banks is not only a necessary but also sufficient condition for perfect reconstruction the results are extended to the case where the filter banks are linear periodically time varying the multichannel case is analyzed and the relation between unimodular matrices and perfect reconstruction filter banks is discussed

reconstruction of signals after filtering and sampling rate reduction a wave digital filter wdf two port has two input and two output terminals by using these to appropriately connect a wdf to its transpose the filtering effect is fully compensated except for an all pass phase and this independently of any selectivity requirement this remains true if at the points of interconnection every second sample is reduced to zero provided that a certain condition easily to be satisfied exactly is fulfilled very efficient solutions are then possible the method is of interest e g for subband coding

singular differential equations with linear and nonlinear boundary conditions abstract existence results are established for the singular equation y f t y 0 where f is not a caratheodory function our nonlinearity f is allowed to change sign

positive solutions of nonlinear singular boundary value problem in abstract space by constructing a particular closed convex set and applying the monch fixed point theorem we study the existence of apositive solutions of singular boundary value problem x t f t x t t 0 1 x 0 x 1 in banach space singularities occuring at t 0 1 and x our method is completely distinct from what the former literatures used even if we discuss the above problem in scalar space

lagrange multiplier approaches to the design of two channel perfect reconstruction linear phase fir filter banks the authors present two approaches to the design of two channel perfect reconstruction linear phase finite impulse response fir filter banks both approaches analyze and design the impulse responses of the analysis filter bank directly the synthesis filter bank is then obtained by simply changing the signs of odd order coefficients in the analysis filter bank the approach deals with unequal length filter banks by designing the lower length filters first one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect reconstruction constraint equations the second approach generalizes the first and covers the design for all parts of linear phase perfect reconstruction constraint equations

intrinsic characterization of the variable separation in the hamilton jacobi equation the nonorthogonal separation of variables in the hamilton jacobi equation corresponding to a natural hamiltonian h 12gijpipj v with a metric tensor of any signature is intrinsically characterized by geometrical objects on the riemannian configuration manifold killing vectors killing tensors and killing webs comparisons with previous characterizations and some illustrative examples are given

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

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

new quadrature mirror filter structures this paper introduces new quadrature mirror filter qmf structures for the frequency domain analysis and synthesis of digital signals the conventional qmf technique is first extended to cover complex quadrature mirror filters cqmf in which a digital signal is split into n adjacent complex subbands where the real and imaginary parts are subsampled by 1 2n with respect to the original signal the computational complexity of qmf banks is then analyzed and a new scheme which reduces the computational complexity by about a factor of two over conventional qmf implementations is proposed finally the filter design tradeoffs are discussed and the microprogramed implementation of qmf banks is evaluated

perfect reconstruction iir digital filter banks supporting nonexpansive linear signal extensions in this paper perfect reconstruction polyphase infinite impulse response iir filter banks involving causal and anticausal inverses are examined for finite length signals first a novel and efficient nonexpansive perfect reconstruction algorithm based on the state space implementation is presented then the proposed method is extended to support linear signal extensions at the boundaries in a nonexpansive manner the powerfulness of the proposed algorithm is demonstrated with the image compression results

design of filter banks using transformation of variables new results the design problem of multirate filter banks can be divided into two parts the first part involves the issue of reconstruction errors the second part involves the issue of designing good quality subband filters there is a class of techniques that we refer to as transformation of variables which satisfactorily addresses the two parts of the design problem this class of filter banks is specified by its prototype filters and transformation kernel it is the flexibility and relative ease in designing the kernel that enables the technique to satisfactorily address the second part of the design problem we present two new methods of designing the kernel that will enhance the design techniques flexibility and effectiveness the first is the combination of the mcclellan transformation and rotation operators the second introduces and uses the concept of directional singular value decomposition svd

positive solutions of some second order nonlinear singular differential equations abstract with new schemes the existence of the positive solutions is proved to some second order nonlinear singular boundary value problems and initial value problems which have higher order singularities

m channel nonlinear phase filter banks in image compression structure design and signal extension this paper describes a transform coding technique based on m channel perfect reconstruction filter banks with a nonlinear phase in contrast with linear phase filter banks the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform we present new lattice structures of paraunitary and perfect reconstruction biorthogonal filter banks which can be implemented with a lower computational complexity and or represented by a few free parameters through the decomposition of the lattice blocks and the displacement across the delay block we further discuss a smooth extension method for nonlinear phase filter banks to obtain a nonexpansive transform the promise of our proposed approaches is demonstrated through several design examples extended signals and compression results

narrowband interference suppression using undecimated wavelet packets in direct sequence spread spectrum receivers a new algorithm for narrowband interference suppression in direct sequence spread spectrum ds ss communications is presented the algorithm combines the undecimated wavelet packet transform uwpt with frequency shifts to confine the interference energy in a subband that is subsequently eliminated computer simulation shows a robust performance that appears to be independent of the interference frequency

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

on solvability and unique solvability of two point singular boundary value problems abstract for the differential equation u f t u u where the function f a b r 2 r has nonintegrable singularities with respect to the time variable at t a and t b new unimprovable sufficient conditions of solvability and unique solvability of the boundary value problems u a 0 u b 0 and u a 0 u b 0 are established

positive solutions of nonlinear singular boundary value problems in abstract spaces by constructing a particular closed convex set and applying the monch fixed point theorem we study the existence of positive solutions of the singular boundary value problem x t f t x t t 0 1 x 0 x 1 in banach space singularities occurring at t 0 1 and x our method is completely distinct from what the former literature used even if we discuss the above problem in scalar space

nonuniform multirate filter banks analysis and design with an spl hscr sub spl infin performance measure a general multirate filter bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst case energy gain spl hscr sub spl infin norm of the error system between the multirate system and a pure time delay system using blocking and polyphase decomposition we associate with the multirate system an equivalent linear time invariant lti system whose transfer matrix can be computed by a simple procedure based on this lti system the optimal design problem can be reduced to one of spl hscr sub spl infin optimization which can be solved by ready made software in many cases for illustration optimal synthesis filters are designed for a two channel example and their properties are studied in detail

quadrature mirror filter design in the time domain a new technique for designing quadrature mirror filters is described the formulation carried out in the time domain is shown to result in an optimization problem requiring minimization of a quartic multinomial an iterative solution is suggested which involves computation of the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps our experiments show that convergence to the optimum tap weights is stable and the accuracy of the final solution is limited only by the accuracy of the eigenvalue eigenvector routine as in an earlier technique the user can specify the stop band frequency the relative weights of the passband ripple energy and the stopband residual energy and of course the number of filter taps

on bounds of shift variance in two channel multirate filter banks critically sampled multirate fir filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage we assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged we express these changes by a so called commutator we then derive a sharp upper bound for shift variance via the operator norm of the commutator which is independent of the input signal its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator leading to a matrix norm which depends on frequency this bound can be regarded as a worst case instance holding for all input signals for two channel fir filter banks with perfect reconstruction pr we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used moreover the framework allows to identify the signals for which the upper bound is almost reached as so called near maximizers of the frequency dependent matrix norm for unitary pr filter banks these near maximizers are shown to be narrow band signals to complement this worst case bound we derive an additional bound on shift variance for input signals with given amplitude spectra where we use wide band model spectra instead of narrow band signals like the operator norm this additional bound is based on the above frequency dependent matrix norm we provide results for various critically sampled two channel filter banks such as quadrature mirror filters pr conjugated quadrature filters wavelets and biorthogonal filters banks

existence and unboundedness of positive solutions for singular boundary value problems on half line by constructing a special cone and using cone compression and expansion fixed point theorem this paper presents some existence results of positive solutions of singular boundary value problem bvp for short on half line for a class of second order differential equations at the same time the boundedness and unboundedness of positive solutions for bvp are considered also

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

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

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed

existence of positive solutions for quasi linear differential equations suffic ient conditions for the existence of at least one positive solution for the following quasilinear differential equation op x i c t f x 0 are given where op u ulv 2u p 2 is a constant c e c r r f x 0 for x o f x 0 for x 0 the method used in this paper is the shooting method 2004 elsevier ltd all rights reserved