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     

基于快速MVR-CORDIC算法的格型IIR滤波器

文章提出一种基于MVR-CORDIC算法的格型IIR滤波器结构。采用MVR-CORDIC算法来改进格型IIR滤波器结构中的Givens旋转模块,使改进的滤波器在SQNR性能不变的情况下,比采用常规CORDIC算法的格型IIR滤波器节省约70%的面积,速度提高60%左右,改进后的格型IIR滤波器更适合于高速实时信号处理领域。     

A new algorithm for linear-phase paraunitary filter banks with pairwise mirror-image frequency responses

Subband filter banks have attracted much attention during the past few years. In this paper, an efficient design algorithm, which leads to linear-phase paraunitary filter banks with pairwise mirror-image frequency responses, is revisited and further studied. New lattice structures are presented to extend the algorithm to the case where the number (M) of channels is odd. Design examples of filter banks with 3 and 5 channels are presented.     

Adaptive Nonseparable Wavelet Transform via Lifting and its Application to Content-Based Image Retrieval

We present in this paper a novel way to adapt a multidimensional wavelet filter bank, based on the nonseparable lifting scheme framework, to any specific problem. It allows the design of filter banks with a desired number of degrees of freedom, while controlling the number of vanishing moments of the primal wavelet (mathtilde N? moments) and of the dual wavelet ( N? moments). The prediction and update filters, in the lifting scheme based filter banks, are defined as Neville filters of order mathtilde N? and N? , respectively. However, in order to introduce some degrees of freedom in the design, these filters are not defined as the simplest Neville filters. The proposed method is convenient: the same algorithm is used whatever the dimensionality of the signal, and whatever the lattice used. The method is applied to content-based image retrieval (CBIR): an image signature is derived from this new adaptive nonseparable wavelet transform. The method is evaluated on four image databases and compared to a similar CBIR system, based on an adaptive separable wavelet transform. The mean precision at five of the nonseparable wavelet based system is notably higher on three out of the four databases, and comparable on the other one. The proposed method also compares favorably with the dual-tree complex wavelet transform, an overcomplete nonseparable wavelet transform.     

Construction of Two-Dimensional Paraunitary Filter Banks Over Fields of Characteristic Two and Their Connections to Error-Control Coding

Filter banks over finite fields have found applications in digital signal processing and error-control coding. One method to design a filter bank is to factor its polyphase matrix into the product of elementary building blocks that are fully parameterized. It has been shown that this factorization is always possible for one-dimensional (1-D) paraunitary filter banks. In this paper, we focus on two-channel two-dimensional (2-D) paraunitary filter banks that are defined over fields of characteristic two. We generalize the 1-D factorization method to this case. Our approach is based on representing a bivariate finite-impulse-response paraunitary matrix as a polynomial in one variable whose coefficients are matrices over the ring of polynomials in the other variable. To perform the factorization, we extend the definition of paraunitariness to the ring of polynomials. We also define two new building blocks in the ring setting. Using these elementary building blocks, we can construct FIR two-channel 2-D paraunitary filter banks over fields of characteristic two. We also present the connection between these 2-D filter banks and 2-D error-correcting codes. We use the synthesis bank of a 2-D filter bank over the finite field to design 2-D lattice-cyclic codes that are able to correct rectangular erasure bursts. The analysis bank of the corresponding 2-D filter bank is used to construct the parity check matrix. The lattice-cyclic property of these codes provides very efficient decoding of erasure bursts for these codes.      

CORDIC-based VLSI architectures for digital signal processing

The evolution of CORDIC, an iterative arithmetic computing algorithm capable of evaluating various elementary functions using a unified shift-and-add approach, and of CORDIC processors is reviewed. A method to utilize a CORDIC processor array to implement digital signal processing algorithms is presented. The approach is to reformulate existing DSP algorithms so that they are suitable for implementation with an array performing circular or hyperbolic rotation operations. Three categories of algorithm are surveyed: linear transformations, digital filters, and matrix-based DSP algorithms     

A Design of 2 L-Channel FIR Paraunitary Filter Banks with Complex Coefficients

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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     

Linear phase paraunitary filter bank with filters of differentlengths and its application in image compression

In this paper, the theory, structure, design, and implementation of a new class of linear-phase paraunitary filter banks (LPPUFBs) are investigated. The novel filter banks with filters of different lengths can be viewed as the generalized lapped orthogonal transforms (GenLOTs) with variable-length basis functions. Our main motivation is the application in block-transform-based image coding. Besides having all of the attractive properties of other lapped orthogonal transforms, the new transform takes advantage of its long, overlapping basis functions to represent smooth signals in order to reduce blocking artifacts, whereas it reserves short basis functions for high-frequency signal components like edges and texture, thereby limiting ringing artifacts. Two design methods are presented, each with its own set of advantages: the first is based on a direct lattice factorization, and the second enforces certain relationships between the lattice coefficients to obtain variable length filters. Various necessary conditions for the existence of meaningful solutions are derived and discussed in both cases. Finally, several design and image coding examples are presented to confirm the validity of the theory     

A Lifting Scheme of Symmetric-antisymmetric Multiwavelet Transform for Image Coding

A symmetric-antisymmetric (SA) multiwavelet lifting factorization of matrix filter banks is presented as an extension of Sweldens’ traditional scalar wavelet lifting scheme. A prefilter absorbed (PA) multiwavelet lifting factorization is also presented to reduce the redundant computations in prefiltering. Then an algorithm of multiwavelet lifting is designed and used for signal decomposition. The experimental results show this lifting scheme can achieve lower complexity while preserve high quality for image coding.     

Cosine-modulated FIR filter banks with linear phase and paraunitaryproperties

A new class of cosine-modulated FIR filter banks is proposed. The necessary and sufficient condition is given which ensures that the filter banks satisfy the paraunitary and linear phase properties simultaneously. The prototype filter can be designed by optimising its stopband energy on the two-channel lattice parameters, and the filter banks can be implemented efficiently using DCT and DST     

Fast pipelined CORDIC-based adaptive lattice predictor: algorithmsand architecture

The authors present a novel CORDIC-based adaptive algorithm and a pipelined architecture for unnormalised lattice prediction filter. Previously, they have presented a CORDIC-based adaptive lattice filtering (CALF) algorithm for normalised lattice filters which features a sign-sign direct (rotation) angle updating scheme (Hu and Liao, 1992). The authors consider a delayed CALF (DeCALF) algorithm in which the rotation angle is updated based on `delayed' prediction errors. In doing so, they are able to develop a fully pipelined implementation of DeCALF which achieves B-fold throughput rate increase where B is the number of CORDIC iterations (stages). This is accomplished at insignificant hardware overhead and minor parameter tracking performance degradation     

M-Channel Nonlinear Phase Filter Banks in Image Compression: Structure, Design, and Signal Extension

This paper describes a transform coding technique based on M-channel perfect reconstruction filter banks with a nonlinear phase. In contrast with linear-phase filter banks, the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform. We present new lattice structures of paraunitary and perfect reconstruction (biorthogonal) filter banks, which can be implemented with a lower computational complexity and/or represented by a few free parameters, through the decomposition of the lattice blocks and the displacement across the delay block. We further discuss a smooth extension method for nonlinear-phase filter banks to obtain a nonexpansive transform. The promise of our proposed approaches is demonstrated through several design examples, extended signals and compression results     

Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks.

We characterize and design multidimensional (MD) orthogonal filter banks using special paraunitary matrices and the Cayley transform. Orthogonal filter banks are represented by paraunitary matrices in the polyphase domain. We define special paraunitary matrices as paraunitary matrices with unit determinant. We show that every paraunitary matrix can be characterized by a special paraunitary matrix and a phase factor. Therefore, the design of paraunitary matrices (and thus of orthogonal filter banks) becomes the design of special paraunitary matrices, which requires a smaller set of nonlinear equations. Moreover, we provide a complete characterization of special paraunitary matrices in the Cayley domain, which converts nonlinear constraints into linear constraints. Our method greatly simplifies the design of MD orthogonal filter banks and leads to complete characterizations of such filter banks.     

一种雷达信号处理机的软件设计

结合某雷达信号处理机研制项目,对该雷达信号处理机的脉冲压缩、动目标显示和动目标检测、恒虚警处理等软件进行设计。论文首先回顾了该处理机用到的几种雷达信号处理方法：线性调频信号的脉冲压缩、基于一次相消器和二次相消器的动目标显示、通过窄带多普勒滤波器组的动目标检测处理、恒虚警检测等方面的工作原理和实现方式。根据信号处理机硬件平台设计了相关的信号处理软件,并实现上述信号处理功能。     

无乘法的线性相位滤波器组的优化设计

提出了一种新的优化方法来设计系数为2的幂和(SOPOT)形式的线性相位完全重构(LPPR)滤波器组。其基本思想是将LPPR格型结构滤波器组中的格型系数直接表示成SOPOT形式，并将这些系数编码成个二进制码串，然后在一定的目标函数下利用遗传算法对这二进制码串进行优化。利用这种方法可以省去传统方法中首先设计无限精度系数的步骤，简化SOPOT型系数的LPPR滤波器组的设计过程。实验结果表明，该方法可以得到较好设计结果。     

A Block-Floating-Point-Based Realization of the Block LMS Algorithm

An efficient scheme is proposed for implementing the block LMS (BLMS) algorithm in a block-floating-point framework that permits processing of data over a wide dynamic range at a processor complexity and cost as low as that of a fixed-point processor. The proposed scheme adopts appropriate formats for representing the filter coefficients and the data. Using these and a new upper bound on the step size, update relations for the filter weight mantissas and exponent are developed, taking care so that neither overflow occurs, nor are quantities which are already very small multiplied directly. It is further shown how the mantissas of the filter coefficients and also the filter output can be evaluated faster by suitably modifying the approach of the fast BLMS algorithm.     

Multidimensional orthogonal filter bank characterization and design using the Cayley transform.

We present a complete characterization and design of orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension using the Cayley transform (CT). Traditional design methods for one-dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional (MD) spectral factorization theorem. In the polyphase domain, orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations. The CT establishes a one-to-one mapping between paraunitary matrices and para-skew-Hermitian matrices. In contrast to the paraunitary condition, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve. Based on this characterization, we propose efficient methods to design MD orthogonal filter banks and present new design results for both IIR and FIR cases.     

A Systematic Approach for Synthesizing VLSI Architectures of Lifting-Based Filter Banks and Transforms

The lifting scheme has become an important tool for designing filter banks and transforms of digital signal processing. Recently, the conventional lifting scheme that concerns the construction of 2-channel filter banks has been extended to $M$-channel filter banks $(M>2)$, bringing up the desirable properties of the lifting scheme to a broader range of applications. Many hand-crafted lifting-based VLSI architectures exist, which mostly concentrate on a single and specific target application having fixed data throughput and resource consumption. However, the reusability of such architectures is limited due to the lack of scalability. To overcome this issue, we present a design methodology for automatic synthesis of VLSI architectures suitable for arbitrary lifting-based $M$-channel filter banks and transforms. The proposed methodology enables high parameterizability in terms of data throughput, resource consumption, and arithmetic precision for the generated architectures. The concept of parameterizing design elements is important for modern system-on-chip design, since it features design space exploration and increases reusability. The proposed methodology is implemented as a high-level compilation tool that generates VLSI architectures at the register transfer level. We present results on the implementation of different architectures that were generated by our tool.