过采样精确重构余弦调制滤波器组的设计

本文首先推导出过采样滤波器组精确重构的条件,由于此时所需的约束条件数比临界采样时少,因而可以设计出频域衰减特性更好的滤波器用,然后提出了精确重构约束条件下原型概通江波器的一种新的设计方法,采用矢的二次型约束优化算法,该算法优化方便,收剑速度快,与其它方法相比,滤波器的阻带衰减大。     

Minimax design of two-channel nonuniform-division FIR filter banks

The paper deals with the minimax design of two-channel nonuniform-division filter (NDF) banks. Based on a linearisation scheme, the design problem is formulated as an optimisation problem with linear constraints. The authors present a method to design a two-channel NDF bank using a modified dual-affine scaling variant of Karmarkar's (1984) algorithm. This method provides the optimal results that the linear-phase FIR analysis and synthesis filters have equiripple stopband response and the resulting NDF bank also shows equiripple reconstruction error behaviour. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Design of Oversampled Interleaved DFT Modulated Filter Bank Using 2Block Gauss-Seidel Method

In this paper, we present several new properties of the recently introduced interleaved DFT modulated filter bank and an efficient algorithm for designing the filter bank. The periodicity and symmetry properties of the overall transfer function and aliasing transfer functions are stated. Then the design of the filter bank is formulated into a constrained optimization problem that jointly minimizes the overall distortion and aliasing distortion subject to fixed bounds on the stopband energy, transition-band energy, and passband flatness of the prototype filters. The constrained optimization problem is solved by the 2block Gauss-Seidel method, which alternatively optimizes the analysis PF pair and the synthesis PF pair. Since the overall distortion and aliasing distortion are jointly minimized, the proposed algorithm can lead to filter banks with small reconstruction error, even when the filter banks behave with a low redundancy ratio and short PFs. The convergence of the proposed algorithm is proved. Numerical examples and comparisons with the existing method are included to demonstrate the performance of the proposed algorithm.     

An efficient algorithm to design weighted minimax perfectreconstruction quadrature mirror filter banks

An efficient algorithm is presented to design lattice structure two-channel perfect reconstruction quadrature mirror filter (PR-QMF) banks. We formulate the filter bank design problem as an unconstrained weighted least squares problem with respect to the coefficients of the lattice structure. The proposed iterative algorithm optimizes the lattice coefficients and provides flexible control of the filters' stopband ripple profiles. Typically, only a few iterations of the algorithm are needed to obtain an optimal solution in the weighted minimax sense. We include a set of practical design rules for use with our algorithm. These rules allow very good estimation of important filter bank characteristics, such as the filter length and the number of signed digits for quantization of the lattice coefficients into canonic signed digit representation, to meet a given set of PR-QMF bank specifications     

Oversampled filter banks from extended perfect reconstruction filter banks

Oversampled filter banks are currently being proposed for robust transmission applications. In this paper, we completely characterize multidimensional doubly finite-impulse-response (FIR) filter banks, that is, oversampled filter banks whose dual is FIR. Then, we consider the problem of extending perfect reconstruction critically sampled multidimensional filter banks in order to obtain doubly FIR (DFIR) filter banks. As a result, very simple criteria for constructing DFIR filter banks as extensions of orthogonal filter banks are obtained. This paper also analyzes the problem of constructing totally FIR filter banks, i.e., DFIR filter banks that remain DFIR even when some channels are removed. It is shown that any totally FIR filter bank can be implemented as the cascade of a critically sampled DFIR filter bank whose number of channels is equal to the subsampling factor, a redundant finite-dimensional transform, and a suitable set of delays.     

Filter Bank Channelizers for Multi-Standard Software Defined Radio Receivers

The ability to support multiple channels of different communication standards, in the available bandwidth, is of importance in modern software defined radio (SDR) receivers. An SDR receiver typically employs a channelizer to extract multiple narrowband channels from the received wideband signal using digital filter banks. Since the filter bank channelizer is placed immediately after the analog-to-digital converter (ADC), it must operate at the highest sampling rate in the digital front-end of the receiver. Therefore, computationally efficient low complexity architectures are required for the implementation of the channelizer. The compatibility of the filter bank with different communication standards requires dynamic reconfigurability. The design and realization of dynamically reconfigurable, low complexity filter banks for SDR receivers is a challenging task. This paper reviews some of the existing digital filter bank designs and investigates the potential of these filter banks for channelization in multi-standard SDR receivers. We also review two low complexity, reconfigurable filter bank architectures for SDR channelizers based respectively on the frequency response masking technique and a novel coefficient decimation technique, proposed by us recently. These filter bank architectures outperform existing ones in terms of both dynamic reconfigurability and complexity.     

Adaptive McClellan transformations for quincunx filter banks

A technique is developed for the design of 2-D nonseparable two-channel filter banks for a quincunx sampling lattice, where the isopotentials of the frequency response can be optimized and adapted to the input signal's statistics. By employing known odd-length symmetric linear phase filter banks as the l-D prototype filters for 2-D filters parameterized by the McClellan transformation, conditions are derived such that the resulting 2-D two-channel filter bank retains the perfect-reconstruction or aliasing-free properties of the 1-D prototype two-channel filter bank. A particular two-parameter transformation function is developed that has sufficient flexibility to adapt its orientation in any direction and whose optimization involves a simple constrained least-squares problem in which the feasible set lies within a circle. The results have practical applications in many areas of image and video processing where multirate filter banks are used     

New technique for designing nearly orthogonal wavelet filter bankswith linear phase

A new technique based on nonlinear optimisation to design nearly orthogonal wavelet filter banks with linear phase is proposed. The main idea is to impose a certain number of zeros at z=-1 for a symmetric filter and make it satisfy the power complementary condition as accurately as possible. From this filter, a semi-orthogonal wavelet filter bank which is nearly orthogonal can be constructed. This semi-orthogonal filter bank can be approximately implemented using a filter bank consisting of only one prototype filter. The frequency selectivity can also be designed at the same time by using a weighted cost function     

General analysis of two-band QMF banks

The two-channel perfect-reconstruction quadrature-mirror-filter banks (PR QMF banks) are analyzed in detail by assuming arbitrary analysis and synthesis filters. Solutions where the filters are FIR or IIR correspond to the fact that a certain function is monomial or nonmonomial, respectively. For the monomial case, the design problem is formulated as a nonlinear constrained optimization problem. The formulation is quite robust and is able to design various two-channel filter banks such as orthogonal and biorthogonal, arbitrary delay, linear-phase filter banks, to name a few. Same formulation is used for causal and stable PR IIR filter bank solutions     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

Design of Biorthogonal Filter Banks Using a Multi-objective Genetic Algorithm for an Image Coding Scheme

In this paper, we present an optimization method based on a multi-objective Genetic Algorithm (GA) for the design of linear phase filter banks for an image coding scheme. To be effective, the filter banks should satisfy a number of desirable criteria related to such a scheme. Instead of imposing the entire PR condition as in conventional designs, we introduce flexibility in the design by relaxing the Perfect Reconstruction (PR) condition and defining a PR violation measure as an objective criterion to maintain near perfect reconstruction (N-PR) filter banks. Particularly in this work, the designed filter banks are near-orthogonal. This has been made possible by minimizing the deviation from the orthogonality in the optimization process. The optimization problem is formulated as a constrained multi-objective, and a modified Nondominated Sorting Genetic Algorithm NSGAII is proposed in this work to find the Pareto optimal solutions that achieve the best compromise between the different objective criteria. The experimental results show that the filter banks designed with the proposed method outperform significantly the 9/7 filter bank of JPEG2000 in most cases. Furthermore, the filter banks are near orthogonal. This is very helpful, especially where embedded coding is required.     

Iterative greedy algorithm for solving the FIR paraunitary approximation problem

In this paper, a method for approximating a multi-input multi-output (MIMO) transfer function by a causal finite-impulse response (FIR) paraunitary (PU) system in a weighted least-squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase-type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmultiplexers.     

A subband adaptive filter allowing maximally decimation

Conventional subband adaptive filters (ADF) using filter banks have shown degradation in performance because of the nonideal nature of filter banks. For this problem, the authors propose an alias free subband structure for adaptive filtering using polyphase frequency sampling filter (FSF) banks. As a preliminary, they make it clear that the conventional polyphase discrete Fourier transform (DFT) bank is equivalent to a class of the FSF bank. Then, they propose a new class of ADF using the FSF banks based on the frequency sampling theorem. As a result, the proposed technique enables subband adaptive filtering without the degradation effect of both the aliasing and cross terms, even if one chooses critical subsampling     

Bounds on error amplification in oversampled filter banks for robust transmission

This paper analyzes the problem of error amplification in frame-based coding schemes derived from oversampled filter banks. Oversampled filter banks are currently being proposed for robust transmission applications, since added redundancy can be used for error recovery in case of losses. Error amplification is determined by the lower bound of the subframe resulting after losses. Theoretical expressions are derived to characterize such lower bound for different loss statistics. Criteria are derived that can be useful for the design of oversampled filter banks in various applications. The analysis and some application examples demonstrate that filter bank performance strongly depends on how the coefficients are organized into packets.     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Partial spectrum reconstruction using digital filter banks

The problem of reconstructing a part of the spectrum is reduced to designing the filter bank to satisfy a set of conditions. For the case considered here, these conditions cannot be satisfied simultaneously, so perfect reconstruction is not possible. The necessary and sufficient conditions on the filters so that the resulting filter bank cancels most alias components are found. Such filter banks are called partial alias cancellation filter banks. The product of the polyphase transfer matrices of these filter banks must be a block pseudocirculant matrix. An algorithm design procedure is discussed, and examples are given to demonstrate the theory     

The analysis and design of two-dimensional nearly-orthogonal symmetric wavelet filter banks

The design and analysis of two-channel two-dimensional (2D) nonseparable nearly-orthogonal symmetric wavelet filter banks with quincunx decimation is studied. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter and minimize the deviation of the filter satisfying the orthogonal condition to obtain a nearly-orthogonal FIR filter bank. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. With this filter, a semi-orthogonal filter bank is constructed. Methods for analyzing the correlation of the semi-orthogonal filter banks are proposed. The integer translates of the wavelet and scaling function are nearly-orthogonal. The integer translates of the wavelet at different scale are completely orthogonal. The semi-orthogonal filter bank can be efficiently implemented using the corresponding nearly-orthogonal FIR filter bank.     

Design of Time–Frequency Localized Filter Banks: Transforming Non-convex Problem into Convex Via Semidefinite Relaxation Technique

We present a method for designing optimal biorthogonal wavelet filter banks (FBs). Joint time–frequency localization of the filters has been chosen as the optimality criterion. The design of filter banks has been cast as a constrained optimization problem. We design the filter either with the objective of minimizing its frequency spread (variance) subject to the constraint of prescribed time spread or with the objective of minimizing the time spread subject to the fixed frequency spread. The optimization problems considered are inherently non-convex quadratic constrained optimization problems. The non-convex optimization problems have been transformed into convex semidefinite programs (SDPs) employing the semidefinite relaxation technique. The regularity constraints have also been incorporated along with perfect reconstruction constraints in the optimization problem. In certain cases, the relaxed SDPs are found to be tight. The zero duality gap leads to the global optimal solutions. The design examples demonstrate that reasonably smooth wavelets can be designed from the proposed filter banks. The optimal filter banks have been compared with popular filter banks such as Cohen–Daubechies–Feauveau biorthogonal wavelet FBs, time–frequency optimized half-band pair FBs and maximally flat half-band pair FBs. The performance of optimal filter banks has been found better in terms of joint time–frequency localization.     

Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L/sub /spl infin// error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.