Filterbänke mit Überabtastung

Oversampled filter banks offer more design freedom, better numerical stability, and less sensitivity to quantization noise as compared to critically sampled filter banks. These advantages come at the cost of increased computational complexity. Therefore, oversampled modulated filter banks allowing a particularly efficient implementation are of practical interest. Furthermore, in certain applications (such as image coding) it is important to have linear phase filters in all channels of the filter bank. In this paper we discuss oversampled filter banks with emphasis on cosine-modulated filter banks and linear phase filters. We establish a relation of oversampled filter banks with redundant signal expansions. We also perform an analysis of the numerical sensitivity of oversampled filter banks. The increased design freedom in oversampled filter banks is demonstrated both theoretically and by means of simulation examples. Finally, we present a unified theory of cosine-modulated filter banks.     

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.     

两带自适应FIR线性相位双正交滤波器组设计

自适应滤波器组设计是多速率滤波器组理论和应用的一个重要方面。由于其频率响应更好匹配于输入信号的统计特性,这类滤波器组可获得更大的子带编码增益。该文研究了两带自适应FIR线性相位双正交滤波器组的设计问题,给出了设计算法,特别是通过最优IIR双正交滤波器组确定初始点(初始滤波器组)的方法。仿真结果表明,得到的滤波器组的子带编码增益远远超过了最优的IIR正交滤波器组,与已有的设计结果比较,编码增益明显提高。     

On the study of four-parallelogram filter banks

The most commonly used 2-D filter banks are separable filter banks, which can be obtained by cascading two 1-D filter banks in the form of a tree. The supports of the analysis and synthesis filters in the separable systems are unions of four rectangles. The natural nonseparable generalization of such supports are those that are unions of four parallelograms. We study four parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of four parallelograms. For a given a decimation matrix, there could be more than one possible configuration (the collection of passbands of the analysis filters). Various types of configuration are constructed for four-parallelogram filter banks. Conditions on the configurations are derived such that good design of analysis and synthesis filters are possible. We see that there is only one category of these filter banks. The configurations of four-parallelogram filter banks in this category can always be achieved by designing filter banks of low design cost     

Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

THEORY AND DESIGN OF UNIFORM FILTER BANKS USING ALL-PASS FILTERS

In this paper,the theory of uniform filter banks using all-pass tilters is furtherdeveloped.A new structure of two stage filter banks using all-pass filter is proposed,The pre-stage is half-band filter with period,the post-stage is two sets of band-pass filter banks.Thepre-stage filter stop-band just controls the don't-care-band of the post-stage filter banks usingall-pass polyphase,so as to realize a continuous stop-band property Moreover,a method ofsynthesizing filter bank is derived,which eliminates aliasing and amplitude distortions of theanalysis/synthesis system Finally,an example is given.     

Multirate filter banks with block sampling

Multirate filter banks with block sampling were recently studied by Khansari and Leon-Garcia (1993). In this paper, we want to systematically study multirate filter banks with block sampling by studying general vector filter banks where the input signals and transfer functions in conventional multirate filter banks are replaced by vector signals and transfer matrices, respectively. We show that multirate filter banks with block sampling studied by Khansari and Leon-Garcia are special vector filter banks where the transfer matrices are pseudocirculant. We present some fundamental properties for the basic building blocks, such as Noble identities, interchangeability of down/up sampling, polyphase representations of M-channel vector filter banks, and multirate filter banks with block sampling. We then present necessary and sufficient conditions for the alias-free property, finite impulse response (FIR) systems with FIR inverses, paraunitariness, and lattice structures for paraunitary vector filter banks. We also present a necessary and sufficient condition for paraunitary multirate filter banks with block sampling. As an application of this theory, we present all possible perfect reconstruction delay chain systems with block sampling. We also show some examples that are not paraunitary for conventional multirate filter banks but are paraunitary for multirate filter banks with proper block sampling. In this paper, we also present a connection between vector filter banks and vector transforms studied by Li. Vector filter banks also play important roles in multiwavelet transforms and vector subband coding     

Order statistic filter banks

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian. We introduce the nonlinear class of order statistic (OS) filter banks that exploit the spectral characteristics of the input signal as well as its rank-ordering structure. The attained subband signals provide frequency and rank information in a localized time interval. OS filter banks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. OS filter banks are formed using traditional linear filter banks as fundamental building blocks. It is shown that OS filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former. To illustrate the properties of OS filter banks, we develop simulations showing that the learning characteristics of the LMS algorithm, which are used to optimize the weight taps of OS filters, can be significantly improved by performing the adaptation in the OS subband domain.     

Symmetric delay factorization: generalized framework forparaunitary filter banks

The symmetric delay factorization (SDF) was introduced to synthesize linear-phase paraunitary filter banks (LPPUFBs) with uniform order (i.e., filter length equal to NM for arbitrary N) and real-valued coefficients. The SDF presents the advantage of decomposing the polyphase transfer matrix (PTM) into only orthogonal matrices, even at the boundary of finite-duration signals, simplifying significantly the design of time-bounded filter banks (TBFBs) or of time-varying filter banks (TVFBs). However, the symmetric delay factorization applies only to LPPUFBs. On the other hand, lattice structures, as well as finite-size lattice structures, are proposed for classes of nonlinear-phase paraunitary filter banks, as the modulated lapped transform (MLT) and the extended tapped transform (ELT). This paper describes a new minimal and complete symmetric delay factorization valid for a larger class of paraunitary filter banks, encompassing paraunitary cosine modulated filter banks, with nonlinear phase basis functions, as well as for a set of LPPUFBs including the linear-phase lapped orthogonal transforms (LOTs) and the generalized tapped orthogonal transforms (GenLOTs). The derivations for filter banks with even and odd numbers of channels are formulated in a unified form. This approach opens new perspectives in the design of time-varying filter banks used for image and video compression, especially in the framework of region or object-based coding     

On the design of FIR analysis-synthesis filter banks with highcomputational efficiency

Presents an effective design algorithm for analysis-synthesis filter banks with computationally efficient structures. Although a wide variety of implementation structures can be accommodated, the focus of the paper is on cosine modulated filter banks. The design procedure is based on a time domain formulation of analysis-synthesis filter banks in which each individual channel filter is constrained to be a cosine modulated versions of a baseband filter. The resulting filter banks are very efficient in terms of computational requirements and are relatively easy to design. A unique feature of this approach is that relatively low reconstruction delays can be imposed on the system. A discussion of the associated computational properties of the designed systems and some design examples are included     

A group theoretic approach to multidimensional filter banks: theoryand applications

In this paper, we provide a new method for analyzing multidimensional filter banks. This method enables us to solve various open problems in multidimensional filter bank characterization and design. The essential element in this new approach is the redefinition of polyphase components. It will be shown that a rich set of mathematical tools, in particular algebraic group theory, will become available for use in the analysis of filter banks. We demonstrate the elegance and power of the tool set by employing it for the characterization of multidimensional filter banks and applying it to two open problems. The first problem is concerned with the development of a general method to design multichannel (⩾2), multidimensional filter banks using transformations, while the second problem is concerned with the derivation of general restrictions on group delays in linear phase filter banks. The treatment of these problems is only an illustration of the power of the tool set of algebraic group theory, employed for the first time in the context of multidimensional filter banks     

基于提升方法的滤波器组因子分解

讨论了FIR滤波器组的分解.2通道完全重构FIR 子波变换分解可为有限步的提升步骤,使用Laurent多项式的辗转相除法给出了这种分解的一个代数方法的证明;证明了二通道子波变换的分解定理不能平行推广到2M通道滤波器组.提出使用M-通道滤波器组构造2M-通道滤波器组,它由多相矩阵的分块化和提升方法实现,这种方法易于构造非线性滤波器组,如整数变换.     

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.     

一种最优去噪线性相位滤波器组的FPGA实现

格型结构是一种可以快速高效设计过采样线性相位完全重建滤波器组的方法。一旦分析滤波器组设定后,对应的综合滤波器结构也就确定,但综合滤波器组参数却有很大的灵活性,从中可以找出具有最优去噪效果的综合滤波器组,构成一个完整的滤波器组。对于求解出的具有最优去噪效果的过采样线性相位完全重构滤波器组,文中用DSP Builder在FPGA上予以实现,并用modelsim进行功能仿真。     

滤波器组在相干激光测风雷达信号处理中的应用

首先简要介绍了相干激光测风雷达和数字滤波器组的工作原理,然后重点分析了余弦调制滤波器组。余弦调制滤波器组具有实现简单、占用资源少等特点。信号通过滤波器组后可分解成若干个窄带子信号,目标的多普勒频率将落入其中一个子带信号中,针对这一子信号进行处理可获得较高的信噪比。利用Matlab设计出了8通道余弦调制滤波器组,然后对回波信号进行处理,从仿真结果和实测信号处理结果可以看出:该方法可以判断并抽取出多普勒频率所在的子带信号。     

Time-varying analysis-synthesis systems based on filter banks andpost filtering

Perfect reconstruction (PR) time-varying analysis-synthesis filter banks are those in which the filters are allowed to change from one set of PR filter banks to another as the input signal is being processed. Such systems have the property that, in the absence of coding, they faithfully reconstruct every sample of the input. Various methods have been reported for the time-varying filter bank design; all of them, however, utilize structures for conventional PR filter banks. These conventional structures that have been applied in the past result in different limitations in each method. This paper introduces a new structure for exactly reconstructing time-varying analysis-synthesis filter banks. This structure consists of the conventional filter bank followed by a time-varying post filter. The new method requires neither the redesign of the analysis sections nor the use of any intermediate analysis filters during transition periods. It provides a simple and elegant procedure for designing time-varying filter banks without the disadvantages of the previous methods     

From differential equations to the construction of new wavelet-like bases

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the Green's function of L. It is shown that these can be used to specify a sequence of embedded spline spaces that admit a hierarchical exponential B-spline representation. The corresponding B-splines are entirely specified by their poles and zeros; they are compactly supported, have an explicit analytical form, and generate multiresolution Riesz bases. Moreover, they satisfy generalized refinement equations with a scale-dependent filter and lead to a representation that is dense in L/sub 2/. This allows us to specify a corresponding family of semi-orthogonal exponential spline wavelets, which provides a major extension of earlier polynomial spline constructions. These wavelets are completely characterized, and it is proven that they satisfy the following remarkable properties: 1) they are orthogonal across scales and generate Riesz bases at each resolution level; 2) they yield unconditional bases of L/sub 2/-either compactly supported (B-spline-type) or with exponential decay (orthogonal or dual-type); 3) they have N vanishing exponential moments, where N is the order of the differential operator; 4) they behave like multiresolution versions of the operator L from which they are derived; and 5) their order of approximation is (N-M), where N and M give the number of poles and zeros, respectively. Last but not least, the new wavelet-like decompositions are as computationally efficient as the classical ones. They are computed using an adapted version of Mallat's filter bank algorithm, where the filters depend on the decomposition level.     

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.