Symmetric extension methods for M-channel linear-phaseperfect-reconstruction filter banks

The symmetric extension method has been shown to he an efficient way for subband processing of finite-length sequences. This paper presents an extension of this method to general linear-phase perfect-reconstruction filter banks. We derive constraints on the length and symmetry polarity of the permissible filter banks and propose a new design algorithm. In the algorithm, different symmetric sequences are formulated in a unified form based on the circular-symmetry framework. The length constraints in symmetrically extending the input sequence and windowing the subband sequences are investigated. The effect of shifting the input sequence is included. When the algorithm is applied to equal-length filter banks, we explicitly show that symmetric extension methods can always be constructed to replace the circular convolution approach     

Low delay FIR filter banks: design and evaluation

The subject of this paper is the design of low and minimum delay, exact reconstruction analysis-synthesis systems based on filter banks. It presents a time domain approach to the problem of designing FIR filter banks with adjustable reconstruction delays. It is shown that using a time domain formulation for the analysis-synthesis systems, the system delay can be considered to be relatively independent of the length of the analysis and synthesis filters. After a summary of the time domain analysis and design framework, the design of low and minimum delay systems is considered in detail. Several design examples are provided in the paper to demonstrate the performance of the design algorithm     

New framework for modulated perfect reconstruction filter banks

A new formulation for the analysis and design of modulated filter banks is introduced. The formulation provides a broad range of design flexibility within a compact framework and allows for the design of a variety of computationally efficient modulated filter banks with different numbers of bands and virtually arbitrary lengths. A unique feature of the formulation is that it provides explicit control of the input-to-output system delay in conjunction with perfect reconstruction. Design examples are given to illustrate the methodology     

Theory and factorization for a class of structurally regular biorthogonal filter banks

Regularity is a fundamental and desirable property of wavelets and perfect reconstruction filter banks (PRFBs). Among others, it dictates the smoothness of the wavelet basis and the rate of decay of the wavelet coefficients. This paper considers how regularity of a desired degree can be structurally imposed onto biorthogonal filter banks (BOFBs) so that they can be designed with exact regularity and fast convergence via unconstrained optimization. The considered design space is a useful class of M-channel causal finite-impulse response (FIR) BOFBs (having anticausal FIR inverses) that are characterized by the dyadic-based structure W(z)=I-UV/sup /spl dagger//+z/sup -1/UV/sup /spl dagger// for which U and V are M/spl times//spl gamma/ parameter matrices satisfying V/sup /spl dagger//U=I/sub /spl gamma//, 1/spl les//spl gamma//spl les/M, for any M/spl ges/2. Structural conditions for regularity are derived, where the Householder transform is found convenient. As a special case, a class of regular linear-phase BOFBs is considered by further imposing linear phase (LP) on the dyadic-based structure. In this way, an alternative and simplified parameterization of the biorthogonal linear-phase filter banks (GLBTs) is obtained, and the general theory of structural regularity is shown to simplify significantly. Regular BOFBs are designed according to the proposed theory and are evaluated using a transform-based image codec. They are found to provide better objective performance and improved perceptual quality of the decompressed images. Specifically, the blocking artifacts are reduced, and texture details are better preserved. For fingerprint images, the proposed biorthogonal transform codec outperforms the FBI scheme by 1-1.6 dB in PSNR.     

Generalized block-lifting factorization of M-channel biorthogonal filter banks for lossy-to-lossless image coding

Generalized block-lifting factorization of M-channel (M > 2) biorthogonal filter banks (BOFBs) for lossy-to-lossless image coding is presented in this paper. Since the proposed block-lifting structure is more general than the conventional lifting factorizations and does NOT require many restrictions such as paraunitary, number of channels, and McMillan degree in each building block unlike the conventional lifting factorizations, its coding gain is higher than that of the previous methods. Several proposed BOFBs are designed and applied to image coding. Comparing the results with conventional lossy-to-lossless image coding structures, including the 5/3- and 9/7-tap discrete wavelet transforms in JPEG 2000 and a 4 × 8 hierarchical lapped biorthogonal transform in JPEG XR, the proposed BOFBs achieve better result in both objective measure and perceptual visual quality for the images with a lot of high-frequency components.     

Design of two-channel IIR filter banks with arbitrary group delay

The nonlinear optimisation problem that results from considering the design of a two-channel nonuniform division filter bank is solved. This is through a frequency sampling and iterative approximation technique to find the tap coefficients and the reflection coefficients for the numerator and the denominator of the IIR analysis filters. An efficient stabilisation procedure ensures that the reflection coefficients lie in (-1,1). Simulation examples are provided for illustration     

基于多项式分解理论的低时延完全重构两通道滤波器组的设计

Euclid多项式分解算法可以用于滤波器组的设计,该文首先讨论了Euclid分解算法与低时延两通道完全重构的滤波器组设计理论,推导出可实现分解的条件,并从理论上加以证明,由于Euclid分解算法具有非唯一性,该文提出了一种新的算法以确定唯一的分解,并将这种算法用于具有低时延特性的两通道全重构滤波器组的设计,最后,通过给出的基于分解方法的设计例子,说明该方法是有效的。     

Modulated filter banks with arbitrary system delay: efficientimplementations and the time-varying case

We present a new method for the design and implementation of modulated filter banks with perfect reconstruction. It is based on the decomposition of the analysis and synthesis polyphase matrices into a product of two different types of simple matrices, replacing the polyphase filtering part in a modulated filter bank. Special consideration is given to cosine-modulated as well as time-varying filter banks. The new structure provides several advantages. First of all, it allows an easy control of the input-output system delay, which can be chosen in single steps of input sampling rate, independent of the filter length. This property can be used in audio coding applications to reduce pre-echoes. Second, it results in a structure that is nearly twice as efficient as performing the polyphase filtering directly. Perfect reconstruction is a structurally inherent feature of the new formulation, even for nonlinear operations or time-varying coefficients. Hence, the structure is especially suited for the design of time-varying filter banks where both the number of bands as well as the prototype filters can be changed while maintaining perfect reconstruction and critical sampling. Further, a proof of effective completeness is given, and the design of equal magnitude-response analysis and synthesis filter banks is described. Filter design can be performed by nonconstrained optimization of the matrix coefficients according to a given cost function. Design and audio-coding application examples are given to show the performance of the new filter bank     

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.     

CORDIC-lifting factorization of paraunitary filter banks based on the quaternionic multipliers for lossless image coding

Quaternions have offered a new paradigm to the signal processing community: to operate directly in a multidimensional domain. We have recently introduced the quaternionic approach to the design and implementation of paraunitary filter banks: four- and eight-channel linear-phase paraunitary filter banks, including those with pairwise-mirror-image symmetric frequency responses. The hypercomplex number theory is utilized to derive novel lattice structures in which quaternion multipliers replace Givens (planar) rotations. Unlike the conventional algorithms, the proposed computational schemes maintain losslessness regardless of their coefficient quantization. Moreover, the one regularity conditions can be expressed directly in terms of the quaternion lattice coefficients and thus easily satisfied even in finite-precision arithmetic. In this paper, a novel approach to realizing CORDIC-lifting factorization of paraunitary filter banks is presented, which is based on the embedding of the CORDIC algorithm inside the lifting scheme. Lifting allows for making multiplications invertible. The 2D CORDIC engine using sparse iterations and asynchronous pipeline processor architecture based on the embedded CORDIC engine as stage of processor is reported. Also it is necessary to notice, that the quaternion multiplier lifting scheme based on the 2D CORDIC algorithm is the structural decision for the lossless digital signal processing. This approach applies to very practical filter banks, which are essential for image processing, and addresses interesting theoretical questions.     

A simplified lattice factorization for linear-phase paraunitary filter banks with pairwise mirror image frequency responses

In this paper, by extending our previous work on general linear-phase paraunitary filter banks even-channel (LPPUFBs), we develop a new structure for LPPUFBs with the pairwise mirror image (PMI) frequency responses, which is a simplified version of the lattice proposed by Nguyen et al. Our simplification is achieved through trivial matrix manipulations and the cosine-sine (C-S) decomposition of a general orthogonal matrix. The resulting new structure covers the same class of PMI-LPPUFBs as the original lattice, while substantially reducing the number of free parameters involved in the nonlinear optimization. A design example is presented to demonstrate the effectiveness of the new structure.     

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.     

过采样广义调制滤波器组在B3G移动通信系统中的实现

本文在GMC-TDD-xDMA系统背景下从广义多载波并行传输的基本原理出发,讨论广义多载波调制解调的数字实现,得到多载波调制解调的广义DFT调制滤波器组实现结构,并给出了一种普遍适用的滤波器组快速实现方法.解决了DFT调制滤波器组在GMC-TDD-xDMA系统中运用时存在的问题.     

Symmetric alpha-stable filter theory

Symmetric α-stable (SαS) processes are used to model infinite-variance impulsive noise. In general, Wiener filter theory is not meaningful in (SαS) environments because the expectations may be unbounded. To develop a theory for linear finite impulse response systems with independent identically distributed (SαS) inputs, we propose median orthogonality as a linear filter criterion, derive a generalized Wiener-Hopf solution equation, and show a sufficient condition for a filter to achieve the criterion. For non-Gaussian (SαS) densities, zero-forcing least-mean-squares is the only well-known filter that satisfies the criterion, but others can be designed. We present a second algorithm and simulations showing that both converge to the generalized Wiener-Hopf solution     

滤波器组的多滤波器联合能量频谱感知算法

针对认知无线电系统,设计了一种基于滤波器组的多滤波器联合能量频谱感知算法.分析了算法的基本原理,给出了算法的流程,并以信噪比为参数说明了算法的优越性.仿真验证算法的检测概率与漏失概率,并对经典滤波器组的能量频谱感知算法的检测概率与漏失概率进行了比较,结果表明:本算法性能优于经典滤波器组能量频谱感知算法的性能.     

余弦调制滤波器组的原型滤波器设计

该文提出了一种近似重构的余弦调制滤波器组的原型滤波器设计方法。该方法将原型滤波器表示成A(z2)B(z)的形式(其中B(z)是最平坦FIR滤波器),通过优化低阶FIR滤波器A(z)的通带边缘频率,间接设计原型滤波器。文中给出的设计例子表明,该方法可获得很高阻带衰减的滤波器组。     

FIR principal component filter banks

Two-dimensional (2-D) principal component filter banks (PCFBs) of finite impulse response (FIR) are proposed. For 2-D signals, among all uniform paraunitary FIR analysis/synthesis filter banks, the FIR PCFBs have the most energy compaction and maximize the arithmetic mean to geometric mean ratio (AM/GM ratio) of subband variances, which is the theoretic coding gain (TCC) of the systems under proper assumptions. The theoretic proof and design techniques are provided. Several special cases are discussed. Experimental results show the potential power of the FIR PCFBs     

Time-varying filter banks and wavelets

Time-varying filter banks and wavelets are studied and a design procedure is presented. In the resulting analysis-synthesis structures, the analysis filters and the corresponding synthesis filters, the number of bands, and the decimation rates can be changed with time. Such structures can be considered as time-frequency overlapping block transforms. From this viewpoint, the tiling of the time-frequency plane and the corresponding basis functions are changed in time. The time-varying discrete wavelet transforms can be considered a special case of time-varying overlapping block transforms and are studied in detail. The formulation is based on the time domain formulation of time-varying analysis-synthesis structures. The design procedure can be used to design time-varying perfectly invertible transformations with a finite number of distinct analysis structures. For adaptive filter bank application, a least squares design method is also studied     

Wavelets and recursive filter banks

It is shown that infinite impulse response (IIR) filters lead to more general wavelets of infinite support than finite impulse response (FIR) filters. A complete constructive method that yields all orthogonal two channel filter banks, where the filters have rational transfer functions, is given, and it is shown how these can be used to generate orthonormal wavelet bases. A family of orthonormal wavelets that have a maximum number of disappearing moments is shown to be generated by the halfband Butterworth filters. When there is an odd number of zeros at π it is shown that closed forms for the filters are available without need for factorization. A still larger class of orthonormal wavelet bases having the same moment properties and containing the Daubechies and Butterworth filters as the limiting cases is presented. It is shown that it is possible to have both linear phase and orthogonality in the infinite impulse response case, and a constructive method is given. It is also shown how compactly supported bases may be orthogonalized, and bases for the spline function spaces are constructed     

Wavelets and filter banks: theory and design

The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetries