Orthonormal FBs With Rational Sampling Factors and Oversampled DFT-Modulated FBs: A Connection and Filter Design

Methods widely used to design filters for uniformly sampled filter banks (FBs) are not applicable for FBs with rational sampling factors and oversampled discrete Fourier transform (DFT)-modulated FBs. In this paper, we show that the filter design problem (with regularity factors/vanishing moments) for these two types of FBs is the same. Following this, we propose two finite-impulse-response (FIR) filter design methods for these FBs. The first method describes a parameterization of FBs with a single regularity factor/vanishing moment. The second method, which can be used to design FBs with an arbitrary number of regularity factors/vanishing moments, uses results from frame theory. We also describe how to modify this method so as to obtain linear phase filters. Finally, we discuss and provide a motivation for iterated DFT-modulated FBs.     

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.     

一种设计近似完全重构非均匀余弦调制滤波器组的新算法

该文提出了一种设计近似完全重构非均匀余弦调制滤波器组的新算法。针对现有合并算法中非均匀滤波器组性能无法直接控制优化的缺点,新算法把非均匀滤波器组的设计问题归纳为一个关于原型滤波器的无约束优化问题,其中目标函数是非均匀滤波器组传递失真与原型滤波器阻带能量的加权和,最后利用线性迭代算法求解该优化问题。理论分析和数值实验表明,新算法获得的非均匀余弦调制滤波器组比现有算法设计的滤波器组整体性能更佳。     

Oversampled cosine-modulated filter banks with arbitrary systemdelay

Design methods for perfect reconstruction (PR) oversampled cosine-modulated filter banks with integer oversampling factors and arbitrary delay are presented. The system delay, which is an important parameter in real-time applications, can be chosen independently of the prototype lengths. Oversampling gives us additional freedom in the filter design process, which can be exploited to find FIR PR prototypes for oversampled filter banks with much higher stopband attenuations than for critically subsampled filter banks. It is shown that for a given analysis prototype, the PR synthesis prototype is not unique. The complete set of solutions is discussed in terms of the nullspace of a matrix operator. For example, oversampling allows the design of PR filter banks having unidentical prototypes (of equal and unequal lengths) for the analysis and synthesis stage. Examples demonstrate the increased design freedom due to oversampling. Finally, it is shown that PR prototypes being designed for the oversampled case can also serve as almost-PR prototypes for critically subsampled cosine-modulated pseudo QMF banks     

Design of M‐Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M‐channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop‐band attenuation, which is also taken care of in the proposed algorithm.     

16-channel oversampled analog-to-digital converter

Oversampled analog-to-digital conversion has been demonstrated to be an effective technique for high resolution analog-to-digital (A/D) conversion that is tolerant to process imperfections. The area and power budget of conventionally designed oversampled analog-to-digital converters has precluded their application from areas where a large number of low frequency signals need to be converted simultaneously. A new oversampled A/D design methodology is proposed to cut the area and power budget per channel of an oversampled analog-to-digital converter. The design and implementation of a 16-channel oversampled analog-to-digital converter is presented which can be used as the core of the multichannel data acquisition system. The prototype achieved 80 dB of signal-to-noise-plus-distortion over 1 kHz, -80 dB of crosstalk and used less than 20 mW of power excluding clock generation     

Design of 2D oversampled linear phase DFT modulated filter banks via modified Newton's method

In this paper, the structure of the 2D oversampled DFT modulated filter banks is analyzed and a spatial-domain condition of a filter bank without transfer function distortion is derived. Based upon the spatial-domain condition, a modified Newton's method is presented for fast design of 2D oversampled linear phase (LP) DFT modulated filter banks with nearly perfect reconstruction (NPR). We formulate the design problem into an unconstrained optimization with a fourth-order objective function, which is the weighted sum of the transfer function distortion of the filter bank and the stopband energy of the prototype filter (PF). The optimization is solved by the modified Newton's method, where each of iterations updates the PF by a set of linear equations. It is proved that the iteration process fast converges to a stationary point of the objective function. Compared with the existing methods, the new method is fast in computation and can design 2D filter banks with a large number of subbands.     

Framing pyramids

Burt and Adelson (1983) introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filters is a tight frame, and thus, the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform. In more general cases, we propose an efficient filterbank (FB) for the reconstruction of the LP using projection that leads to a proved improvement over the usual method in the presence of noise. Setting up the LP as an oversampled FB, we offer a complete parameterization of all synthesis FBs that provide perfect reconstruction for the LP. Finally, we consider the situation where the LP scheme is iterated and derive the continuous-domain frames associated with the LP.     

Incomplete sampling series and the recovery of missing samples fromoversampled band-limited signals

It is well known that a band-limited oversampled signal is completely determined even if an arbitrary finite number of samples is lost. It is shown that an alternative simple proof of this fact carries over to generalized sampling expansions. More precisely, it is shown that any finite number of missing samples can be recovered from the remaining ones, in the case of generalized Kramer sampling expansions, if an appropriate oversampling constraint is satisfied. The recovery can be accomplished either iteratively or noniteratively     

On simple oversampled A/D conversion in L2(R)

The accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval τ and on the bit rate R are characteristics fundamental to A/D conversion but not completely understood. These characteristics are studied for oversampled A/D conversion of band-limited signals in L² (R). We show that the digital sequence obtained in the process of oversampled A/D conversion describes the corresponding analog signal with an error which tends to zero as τ² in energy, provided that the quantization threshold crossings of the signal constitute a sequence of stable sampling in the respective space of band-limited functions. Further, we show that the sequence of quantized samples can be represented in a manner which requires only a logarithmic increase in the bit rate with the sampling frequency, R=O(|logτ|), and hence that the error of oversampled A/D conversion actually exhibits an exponential decay in the bit rate as the sampling interval tends to zero     

Design of 2-D FIR filters by nonuniform frequency sampling

A method for the frequency-sampling design of two-dimensional FIR filters with nonuniformly spaced samples is presented. By imposing some mild constraints on sample location in the 2-D frequency plane, the method always provides a unique design solution. Important characteristics of the method are design flexibility through the use of nonuniform samples and computational efficiency. This method is compared with the uniform sampling, inverse discrete Fourier transform (DFT) approach and also with a general method for filter design called arbitrary sampling. The method presented is shown to require much less computation than the arbitrary sampling approach, which may lead to possible degenerate cases where there is no unique solution for the filter. The method proposed does not lead to such degeneracies and possesses more flexibility than the uniform sampling method. Examples are given in order to compare the new method with the uniform sampling method     

A simple method to build oversampled filter banks and tight frames.

This paper presents conditions under which the sampling lattice for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of common knowledge that removing up/downsampling will not lose perfect reconstruction. The results provide a simple way of building oversampled filter banks. If the original filter banks are orthogonal, these oversampled banks construct tight frames of l2 (Z(n)) when iterated. As an example, a quincunx lattice is used to replace the rectangular one of the standard wavelet transform. This replacement leads to a tight frame that has a higher sampling in both time and frequency. The frame transform is nearly shift invariant and has intermediate scales. An application of the transform to image fusion is also presented.     

Oversampled linear-phase perfect reconstruction filterbanks: theory, lattice structure and parameterization

The paper presents the theory, lattice structure, and parameterization for a general class of P-channel oversampled linear-phase perfect reconstruction filterbanks (OLPPRFBs) - systems with sampling factor M (P/spl ges/M) and filter length of L=KM (K/spl ges/1) each. For these OLPPRFBs, the necessary existence conditions on the number of symmetric filters, n/sub /spl beta//, and antisymmetric filters, n/sub /spl alpha//, (i.e., symmetry polarity) are first investigated. VLSI-friendly lattice structures are then developed for two types of OLPPRFBs, type I system (n/sub /spl beta//=n/sub /spl alpha//) and type II system (n/sub /spl beta///spl ne/n/sub /spl alpha//). The completeness and minimality of each type of lattice are also analyzed. Compared with existing work, the proposed lattices are the most general and efficient ones for OLPPRFBs. Besides, through the lattice structures, the sufficiency of the existence conditions is also verified. Next, lifting-based structures are proposed to parameterize a left invertible matrix and all of its left inverses, which leads to unconstrained optimization as well as robust implementation of OLPPRFBs. Finally, several design examples are presented to confirm the validity of the theory and demonstrate the versatility of synthesis filterbanks in the oversampled system.     

宽带分数延时滤波器的优化设计及FPGA实现

提出了一种可变分数延时宽带数字滤波器的优化设计方法,该方法首先采用内插的方法提高采样率,降低信号的归一化带,再采用Farrow结构来实现分数延时,通过抽取,恢复信号的初始采样率.其实现形式采用基于多相滤波的级联结构,使得内插和抽取相互抵消,降低滤波器的阶数,提高运算效率.采用基于FPGA的并行分布式算法,设计利用了器件的结构特点以及与器件特性独立的2种方法,在时域实现了高速、高阶的宽带分数延时滤波器,并在Altera Stratix FPGA上进行了仿真验证,最高工作频率分别为184 MHz和119 MHz.     

Coupled-mode theory for LP modes

A generalized definition of LP modes is introduced for an optical fiber with arbitrary refractive-index profile and arbitrary cross section, The orthogonality property of these LP modes has been considered. Based on a complete set of LP modes in a chosen reference fiber, a set of coupled-mode equations describing a practical fiber are established. Possible applications of these coupled-mode equations are demonstrated.     

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.     

大瞬时动态范围在数字中频接收机上的实现

在基于中频采样技术的数字中频接收机中，怎样在AD变换器位数受限的情况下实现较大的系统瞬时动态范围是系统设计中的一个重要问题。通过分析影响中频采样接收机瞬时动态范围的各种因素，文中给出了实现大瞬时动态的中频采样接收机的思路和方法。     

A Time-Based Bandpass ADC Using Time-Interleaved Voltage-Controlled Oscillators

In this paper, a bandpass analog-to-digital converter (ADC) based on time-interleaved oversampled ADC is introduced. Unlike previous delta–sigma bandpass ADCs that require accurate digital-to-analog converters and high-speed analog circuits, the proposed architecture provides bandpass function by time-interleaving first-order voltage-controlled-oscillator (VCO)-based ADCs. The use of VCO-based ADC has the advantage that its resolution is determined by the time resolution rather than the voltage resolution, thus making it attractive for future low-voltage CMOS processes. The performance of the proposed ADC is theoretically analyzed and simulated in ideal condition, as well as in nonideal condition, in the presence of nonlinearity, sampling clock jitter, and mismatch.      

On upsampling, downsampling, and rational sampling rate filterbanks

Solutions to the problem of design of rational sampling rate filter banks in one dimension has previosly been proposed. The ability to interchange the operations of upsampling, downsampling, and filtering plays an important role in these solutions. The present paper develops a complete theory for the analysis of arbitrary combinations of upsamplers, downsamplers and filters in multiple dimensions. Although some of the simpler results are well known, the more difficult results concerning swapping upsamplers and downsamplers and variations thereof are new. As an application of this theory, the authors obtain algebraic reductions of the general multidimensional rational sampling rate problem to a multidimensional uniform filter bank problem. However, issues concerning the design of the filters themselves are not addressed. In multiple dimensions, upsampling and downsampling operators are determined by integer matrices (as opposed to scalars in one dimension), and the noncommutativity of matrices makes the problem considerably more difficult. Cascades of upsamplers and downsamplers in one dimension are easy to analyze. The new results for the analysis of multidimensional upsampling and downsampling operators are derived using the Aryabhatta/Bezout identity over integer matrices as a fundamental tool. A number of new results in the theory of integer matrices that a relevant to the filter bank problem are also developed. Special cases of some of the results pertaining to the commutativity of upsamplers/downsamplers have been obtained in parallel by several authors     

A Generalized Oversampled Structure for Cosine-Modulated Transmultiplexers and Filter Banks

In this paper, a new structure, called the channel split-and-add method, for designing oversampled transmultiplexers and filter banks is presented. The proposed method is based on an initial design with an additional number of bands. The band number is then reduced to the desired value by the proper combination of adjacent and/or nonadjacent bands (subchannels). With the proposed approach it is always possible to perform the filtering tasks at the lowest data rate of the system. An example illustrates the design flexibility achieved with the proposed structure.