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.     

Results on the factorization of multidimensional matrices for paraunitary filterbanks over the complex field

This paper undertakes the study of multidimensional finite impulse response (FIR) filterbanks. One way to design a filterbank is to factorize its polyphase matrices in terms of elementary building blocks that are fully parameterized. Factorization of one-dimensional (1-D) paraunitary (PU) filterbanks has been successfully accomplished, but its generalization to the multidimensional case has been an open problem. In this paper, a complete factorization for multichannel, two-dimensional (2-D), FIR PU filterbanks is presented. This factorization is based on considering a two-variable FIR PU matrix as a polynomial in one variable whose coefficients are matrices with entries from the ring of polynomials in the other variable. This representation allows the polyphase matrix to be treated as a one-variable matrix polynomial. To perform the factorization, the definition of paraunitariness is generalized to the ring of polynomials. In addition, a new degree-one building block in the ring setting is defined. This results in a building block that generates all two-variable FIR PU matrices. A similar approach is taken for PU matrices with higher dimensions. However, only a first-level factorization is always possible in such cases. Further factorization depends on the structure of the factors obtained in the first level.     

On factorization of M-channel paraunitary filterbanks

We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementation of paraunitary system based on the decomposition of Hermitian unitary matrices. Within this framework, the linear-phase filterbank and pairwise mirror-image symmetry filterbank are revisited. Their structures are special cases of the proposed general structures. Compared with the existing structures, more efficient ones that only use approximately half the number of free parameters are derived. The proposed structures are complete and minimal. Although the factorization theory with or without constraints is discussed in the framework of M-channel filterbanks, the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems     

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.     

A note on the factorization of matrices occurring in Wiener-Hopf problems

Simple expressions for the Wiener-Hopf factors of a certain matrix considered by Daniele are given.     

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.     

On the factorization of Wiener-Hopf matrices in problems solvable with Hurd's method

A class of two simultaneous Wiener-Hopf equations is reduced to the factorization and the decomposition of scalar functions. In particular, it has been shown that the problems previously solved by the Hilbert-Hurd method lead to Wiener-Hopf systems that belong to this class.     

Spectral factorization of two-variable para-Hermitian polynomial matrices

This paper presents an algorithm for the so-called spectral factorization of two-variable para-Hermitian polynomial matrices which are nonnegative definite on thej axis, arising in the synthesis of two-dimensional (2-D)passive multiports, Wiener filtering of 2-D vector signals, and 2-D control systems design. First, this problem is considered in the scalar case, that is, the spectral factorization of polynomials is treated, where the decomposition of a two-variable nonnegative definite real polynomial in a sum of squares of polynomials in one of the two variables having rational coefficients in the other variable plays an important role (cf. Section 4). Second, by using these results, the matrix case can be accomplished, where in a first step the problem is reduced to the factorization of anunimodular para-Hermitian polynomial matrix which is nonnegative definite forp=j , and in a second step this simplified problem is solved by using so-called elementary row and column operations which are based on the Euclidian division algorithm. The matrices considered may be regular or singular and no restrictions are made concerning the coefficients of their polynomial entries; they may be either real or complex.     

A novel transformer-based mm-Wave frequency doubler with enhanced output symmetry

A novel transformer-based differential frequency doubler operating in mm-Wave range is presented in this paper. The differential output signal is generated by the second harmonic of the nonlinear push-push pairs. In order to enhance the symmetry of the high frequency differential output, a stacked transformer implemented by the top two metal layers in 90-nm CMOS process is used as the loads in the proposed frequency doubler. Simulation results show that the proposed circuit has achieved less than $1^{\circ }$ phase mismatch and 0.6-dB amplitude mismatch operating at 60-GHz.     

A NEW METHOD OF DECONVOLUTION IN THE FREQUENCY DOMAIN

A new deconvolution method has been presented in this paper. Like conventional Discrete Fourier Transform(DFT) method, it is also a frequency domain method. Since there are only DFT, IDFT and multiplication calculations in the new method, the singular problem appeared in the conventional DFT method can be avoid, and the deconvolution problem can always be solved with the new method. The relationship between the presented method and conventional DFT method is discussed. A numerical example is also presented to illustrate the new method.     

Routing in the frequency domain

The design of single transceiver based multi-channel multi-hop wireless mesh networks focuses on the trade-off between rapid neighbor synchronization and maximizing the usage of all available channels. Existing designs are confined to the MAC layer and scale poorly as the network grows in coverage and density. We recently proposed Dominion as a cross-layer architecture that includes both medium access control and routing. Dominion eliminates the need for neighbor synchronization at the MAC layer and pushes the intelligence up the network stack. At the MAC layer, a node switches channels according to a deterministic schedule which guarantees that a node converges with each of its neighbors periodically. At the network layer, the channel-hopping aware routing substrate routes traffic along the frequency domain, i.e., packets along a multi-hop route generally traverse via multiple channels. In this paper, we present the complete design, analysis and evaluation of Dominion and make four new contributions. Firstly, we extend Dominion to support goal-oriented routing: source nodes can locally choose to maximize throughput or minimize end-to-end latency without requiring any changes in the network. Secondly, we describe a technique that eliminates intra-flow interference. In absence of extrinsic interference, Dominion now allows network flows to maintain constant throughput and deterministic end-to-end latencies irrespective of distance. Thirdly, via theoretical modeling and analysis, we provide expected throughput and end-to-end latencies for network flows. Finally, via extensive QualNet simulations we show that Dominion achieves 1064% higher throughput than IEEE 802.11 while being 299% fairer.     

Use of co-occurrence matrices in the temporal domain

The concept of temporal co-occurrence matrices is introduced. The calculation and some of its features are described. Experimental results show that the temporal co-occurrence matrices can be applied to a wide range of interframe image processing, reducing the processing time involved.<>     

Texture classification with cross-covariance matrices in compressive measurement domain

Texture classification of images is an important problem in texture analysis, with the goal to assign an unknown sample image to one of a set of known texture classes. Many procedures have been proposed. However, traditional texture classification methods are often complicated and time-consuming. In addition, the whole original data set has to be known in advance. This paper presents a novel approach to texture classification that employs cross-covariance matrices in the compressive measurement domain. Since there is a linear relation between the cross-covariance matrix in the measurement domain and that in the transform domain, the characteristics of the original signals can be reflected through the sampling measurements. By abstracting the measurement-domain cross-covariance matrices of each image class, we build a texton dictionary composed of the cross-covariance vectors and then train each image class according to the texton dictionary. Through comparison with all the training results, test images are classified as the matching one. Experiments show that the texture classification method proposed in this paper has better accuracy, with only 14–50 % processing time than the existing methods.     

A method of digital filter synthesis in the frequency domain

In this letter, a new method of digital filter synthesis is presented. The transfer function of the resulting digital filter closely approximates the corresponding continuous transfer function of the correcting filter with steep transition regions.     

A transmit MIMO scheme with frequency domain pre-equalization for wireless frequency selective channels

In this paper, we introduce a transmit multiple-input multiple-output (MIMO) scheme with frequency domain pre-equalization for a multipath or frequency selective channel. In this scheme, MIMO processing in the frequency domain is performed at the transmitter or base station so that the receiver or mobile station only requires limited processing. This scheme provides high data rates and also inherits from the frequency domain equalization the property of relatively low complexity in severe multipath environments. The MIMO transmit processing is derived by minimizing the minimum mean square errors (MMSE), and expressions for the signal-to-interference-plus-noise ratio and error probability based on the Gaussian approximation of the interference term are provided. Some important associated issues, such as channel errors and computational complexity, are also investigated. Numerical simulations are also provided and these demonstrate the improved performance of our proposed scheme compared to other transmit MIMO schemes. In particular, they show that the proposed system can attain multipath or frequency diversity of the channel.     

Theory and lattice structure of complex paraunitary filterbankswith filters of (Hermitian-)symmetry/antisymmetry properties

The theory of the real-coefficient linear-phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex linear phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the linear-phase property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFB and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFB constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly     

A design method of multidimensional linear-phase paraunitary filterbanks with a lattice structure

A lattice structure of multidimensional (MD) linear-phase paraunitary filter banks (LPPUFBs) is proposed, which makes it possible to design such systems in a systematic manner. Our proposed structure can produce MD-LPPUFBs whose filters all have the region of support 𝒩(MΞ), where M and Ξ are the decimation and positive integer diagonal matrices, respectively, and 𝒩(N) denotes the set of integer vectors in the fundamental parallelepiped of a matrix N. It is shown that if 𝒩(M) is reflection invariant with respect to some center, then the reflection invariance of 𝒩(MΞ) is guaranteed. This fact is important in constructing MD linear-phase filter banks because the reflection invariance is necessary for any linear-phase filter. Since our proposed system structurally restricts both the paraunitary and linear-phase properties, an unconstrained optimization process can be used to design MD-LPPUFBs. Our proposed structure is developed for both an even and an odd number of channels and includes the conventional 1-D system as a special case. It is also shown to be minimal, and the no-DC-leakage condition is presented. Some design examples show the significance of our proposed structure for both the rectangular and nonrectangular decimation cases     

可变阶数语音编码模型的频域技术

为了进一步压缩比特率，在线性预测（LP）语音编码中使用了可变阶数方法。即根据当前语音帧的性质决定相应LP滤波器的阶数。但是，如果预测阶数太小，由于语音频谱的动态范围大，可能使LP分析不能够正确地匹配较高的共振峰。讨论了一个用于语音编码的频域技术，用以在浊音语音共振峰模型方面改善低阶数线性预测（LP）的性能。     

Burst measurements in the frequency domain

Methods for measuring the energy density spectrum of burst-like events have been categorized. Five methods that rely on measuring samples of the energy density spectrum are distinguished. A tutorial exposition of the principles underlying these methods is given. This work represents the second phase of a program by the IEEE Subcommittee on Methods of Measurement of Noise of the G-AE Standards Committee aimed at developing a unified approach to burst measurements, and is an adaptation of the Technical Report on Recommended Practices for Burst Measurements in the Frequency Domain, IEEE No. 265.     

Thresholding implemented in the frequency domain

Image processing procedures are usually carried out in the spatial domain where the images are acquired and presented/utilized. The linear nature of the Fourier transform allows only those operations that are linear to be mapped into the frequency domain. In contrast, nonlinear operations and manipulations cannot be realized directly in the frequency domain. One of these nonlinear operations is thresholding. When operating in the spatial domain to segment image contents into object and background, thresholding is simple and efficient. However, it has no obvious representation in the frequency domain and cannot be carried out there in a straightforward fashion. In this paper, a means to relax the rigid linear limitation of the Fourier transform was investigated. A novel approach was established to achieve spatial thresholding using only frequency domain operations. The spatial grayscale or scalar data set (two-dimensional (2-D) image or three-dimensional (3-D) volume) was expanded into a binary volume in hyperspace having one more dimension than the original data set. The extended dimension is the gray level of the original data. Manipulating only on that dimension produces the effect of thresholding.