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.     

Nonlinear perfect reconstruction critically decimated filter banks

The authors introduce a new and non-trivial class of linear and nonlinear perfect reconstruction critically decimated filter banks. The filters consist of a simple cascaded architecture within the sub-sampled domain. The structures also allow filter banks which satisfy a stronger definition of critical decimation to be defined over module m integer arithmetic     

Two-dimensional perfect reconstruction FIR filter banks withtriangular supports

We present a theory and design of two-dimensional (2-D) perfect reconstruction (PR) filter banks (FBs) (PRFBs) in which the supports of the analysis and synthesis filters consist of two triangulars. The two-triangular FB can be realized by designing an appropriate 2-D complex prototype whose passband support is a triangle that is a half of a parallelepiped-shaped passband support defined by the sampling matrix. Then a complex prototype filter is modulated by the DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB satisfies the condition of permissibility. A necessary and sufficient condition for 2-D PRFBs is derived. Moreover, we present a design method of the 2-D PRFB that minimizes the cost function consisting of the frequency constraint and PR condition. Finally, a design example is presented to confirm the validity of the proposed method     

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     

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。     

Replacing resamplers in filter banks without losing perfect reconstruction

The condition under which the resamplers in a filter bank can be replaced without losing perfect reconstruction is presented. This is the generalisation of the common knowledge that removing resamplers and/or inserting unimodular resamplers do not destroy the perfect reconstruction of filter banks.     

Nonuniform perfect reconstruction filter banks over lattices withapplication to transmultiplexers

This paper presents a multidimensional multirate theory for signals defined over lattices. We extend the notion of the z transform and present linear periodically-shift-varying (LPSV) systems. We use this theory to study transmultiplexers for signals defined over arbitrary lattices (nonuniform or unequal-band case). We give dimensionality conditions for perfect reconstruction and determine the form of the solutions. Finally, we study tree-structured transmultiplexing systems. Such systems permit us to design nonuniform filter banks from uniform filter banks. Furthermore, their multistage implementation allows lower complexity     

Multidimensional perfect reconstruction filter banks: an approach of algebraic geometry

In image compression and some other applications, multidimensional filter banks are gaining their popularity due to the decrease in implementation cost. In this article, we study these filter banks from a viewpoint of algebraic geometry, where some insights are emerging. Familiar properties, such as perfect reconstruction and linear phase, appear differently when studied from this new angle. For the sake of practicability and a better understanding of problems, our focus in this work is further restricted to the filter banks that can achieve linear phase and perfect reconstruction properties. According to different symmetry nature, the filter banks are categorized into two types. Filters in a multidimensional filter bank represented by multivariate polynomials have common zeros that are different in nature from their 1D counterparts. In this work, the relation between the above-mentioned properties and various zeros is investigated. A criterion to test such filter banks is proposed and this criterion is also interpreted in resultant theory. Based on these results, as well as a proposed conjecture, a factorization of lifting scheme is presented for one type of these filter banks. For the other type of filter banks, we propose a method on perfect reconstruction completion.

The design of 2-D nonseparable directional perfect reconstruction filter banks

In this paper, we develop a directional 2-D nonseparable filter bank that can perfectly reconstruct the downsampled subband signals. The filter bank represents two powerful image and video processing tools: directional subband decomposition and perfect reconstruction. The directional filter banks consist of (1) the input signal and the subband signals modulation, (2) diamond shape prefilter, and (3) four different parallelogram shape prefilters. This paper addresses the design and implementation of a two-band filter bank that is proved to be able to provide perfect reconstruction of the downsampled subband signals. Finally, we use a conventional 1-D half-band filter as a prototype and then apply the McClellan transform for the specific 2-D diamond shape and parallelogram shape subfilters. This method is extremely simple in designing the analysis/synthesis subfilters for the filter bank.     

Filter banks allowing perfect reconstruction

Splitting a signal into N filtered channels subsampled by N is an important problem in digital signal processing. A fundamental property of such a system is that the original signal can be perfectly recovered from the subsampled channels. It is shown that this can always be done, and that FIR solutions exist. This is done by mapping the NM-dimensional nonlinear problem (where N is the number of channels and M the length of the FIR filters) into an M-dimensional linear problem. For N = 2, a general class of FIR solutions is derived, together with methods to find filters. The dual problem of mixing N signals into one channel upsampled by N is also addressed. Several applications are proposed. All results are obtained by looking at the N filter bank as a true N channel system, rather than N separate channels.     

On the perfect reconstruction problem in N-band multirate maximallydecimated FIR filter banks

The problem of finding N-K filters of an N-band maximally decimated FIR analysis filter bank, given K filters, so that FIR perfect reconstruction can be achieved, is considered. The perfect reconstruction condition is expressed as a requirement of unimodularity of the polyphase analysis filter matrix. Based on the theory of Euclidean division for matrix polynomials, the conditions the given transfer functions must satisfy are given, and a complete parameterization of the solution is obtained. This approach provides an interesting alternative to the method of the complementary filter in the case of N>2,K相似文献   

基于进行计算设计无法的完全重构两通道滤波器组

该文提出了一种设计无乘法完全重构的两通道滤波器组的方法。这种滤波器组在基于对提升模式结构改进的研究成果之上,提出了给定初始值的进化计算搜索设计方法。这种设计方法具有比用遗传算法快的特点。文中详细描述了此算法的过程,并给出了设计例子和结果。     

General design of nearly perfect polyphase filter banks

In a polyphase approach of filter banks with critical sampling, it is proposed to design and implement the elements of the synthesis section as approximations of the inverses of the elements in the analysis section. The conditions for such approximations to be valid are stated and a design procedure is described, along with the corresponding structure. The approach generalises theqmf method by adding more flexibility, since it relaxes the constraints on the analysis prototype filter specification and allows different complexities in both sections. The general approach can yield de-signs able to compete favourably withqmf and pseudo-QMF in many aspects.     

最小二乘与加权最小二乘空域矩阵滤波器设计

空域矩阵滤波器是一种新的信号处理技术,通过一个滤波矩阵与接收到的阵列数据相乘,可实现保留通带目标信号,抑制阻带干扰的目的.本文主要研究了最小二乘和加权最小二乘两类的空域矩阵滤波器.给出了空域滤波器设计基本原理,通过最优化问题得出了最优解.最小二乘空域矩阵滤波器是加权系数为1的加权加权最小二乘空域矩阵滤波器的特列.由加权最小二乘迭代仿真结果可以看出,迭代次数的增加使滤波器阻带响应极大值逐渐变小,可实现恒定阻带抑制效果,设计效率较高.     

Two-stage, least squares design of biorthogonal filter banks

A two-stage approach is employed for the design of a class of two-channel biorthogonal filter banks. The filter banks belong to the class HPFB (halfband pair filter bank) and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The design of the free parameters of the Bernstein polynomial is achieved through a least squares method. In the first stage, the analysis low-pass filter is designed and in the second stage, the synthesis lowpass filter is designed. With the two-stage approach, the design process is efficient and involves solving linear equations. The design technique allows filters with different characteristics to be designed easily.     

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     

A sequentially operated periodic FIR filter for perfect reconstruction

This paper presents a sequentially operated periodic FIR filter to perform the functions of multirate filter banks for perfect reconstruction. This filter consists of an analysis filter and a synthesis filter. Each of these filters has a single-input/single-output FIR filter with periodically time-varying coefficients and a sequentially operated multichannel sampling scheme. As a result, the proposed filter can offer considerable improvements in computation and implementation. For the design of the filter, we provide a necessary and sufficient condition for perfect reconstruction in terms of the blocked transfer matrices and give a design procedure.     

Nonuniform filter banks: a reconstruction and design theory

A general procedure for the design of analysis-synthesis systems based on nonuniform filter banks is described. The procedure is based on a time-domain analysis of nonuniform systems, which results in a set of conditions for the exact reconstruction of the input signal at the output. These conditions are used as part of a powerful iterative algorithm for designing finite impulse response (FIR) filter banks with an arbitrary nonuniform frequency resolution. This new framework permits the design of systems with arbitrary rational decimation rates in different bands. Systems based on maximally or nonmaximally decimated filter banks, on low and minimum delay systems, and on block decimators are also among the systems that can be designed using this method     

Perfect reconstruction versus MMSE filter banks in source coding

Classically, the filter banks (FBs) used in source coding schemes have been chosen to possess the perfect reconstruction (PR) property or to be maximally selective quadrature mirror filters (QMFs). This paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion, which, in the most general case, is the sum of two terms: a first one due to the non-PR property of the FB and the other being due to signal quantization in the subbands. The resulting filter banks are called minimum mean square error (MMSE) filter banks. Several quantization noise models are considered. First, under the classical white noise assumption, the optimal positive bit rate allocation in any filter bank (possibly nonorthogonal) is expressed analytically, and an efficient optimization method of the MMSE filter banks is derived. Then, it is shown that while in a PR FB, the improvement brought by an accurate noise model over the classical white noise one is noticeable, it is not the case for the MMSE FB. The optimization of the synthesis filters is also performed for two measures of the bit rate: the classical one, which is defined for uniform scalar quantization, and the order-one entropy measure. Finally, the comparison of rate-distortion curves (where the distortion is minimized for a given bit rate budget) enables us to quantify the SNR improvement brought by MMSE solutions