1-D and 2-D signals parallel processing in mixed formats

Paper presents general methods of processing one- and two-dimensional signals that are based on functional transform of signal using corresponding transformation functions, for example, Hilbert transform in DFT, wavelet transform, etc. Fast parallel algorithms for such functional transforms in complete (PCM-PCM) and mixed (∇PCM-PCM or DM-PCM) formats are suggested. The latter ones are obtained using the proven theorems. In real-time scale and assuming the use of the same element base the suggested algorithms provide wider bandwidth of processed signals compared to those based on FFT. Their ability to provide results faster increases even more when substituting multiplication by shift operations. Examples of using the developed methods in parallel calculations structures are presented.     

Exact sampling results for some classes of parametric nonbandlimited 2-D signals

We present sampling results for certain classes of two-dimensional (2-D) signals that are not bandlimited but have a parametric representation with a finite number of degrees of freedom. While there are many such parametric signals, it is often difficult to propose practical sampling schemes; therefore, we will concentrate on those classes for which we are able to give exact sampling algorithms and reconstruction formulas. We analyze in detail a set of 2-D Diracs and extend the results to more complex objects such as lines and polygons. Unlike most multidimensional sampling schemes, the methods we propose perfectly reconstruct such signals from a finite number of samples in the noiseless case. Some of the techniques we use are already encountered in the context of harmonic retrieval and error correction coding. In particular, singular value decomposition (SVD)-based methods and the annihilating filter approach are both explored as inherent parts of the developed algorithms. Potentials and limitations of the algorithms in the noisy case are also pointed out. Applications of our results can be found in astronomical signal processing, image processing, and in some classes of identification problems.     

Anisotropic 2-D and 3-D averaging of fMRI signals

A novel method for denoising functional magnetic resonance imaging temporal signals is presented in this note. The method is based on progressively enhancing the temporal signal by means of adaptive anisotropic spatial averaging. This average is based on a new metric for comparing temporal signals corresponding to active fMRI regions. Examples are presented both for simulated and real two and three-dimensional data. The software implementing the proposed technique is publicly available for the research community.     

Wavelet-based noise removal for biomechanical signals: a comparative study

The purpose of this paper is to present wavelet-based noise removal (WBNR) techniques to remove noise from biomechanical acceleration signals obtained from numerical differentiation of displacement data. Manual and semiautomatic methods were used to determine thresholds for both orthogonal and biorthogonal filters. This study also compares the performance of WBNR approaches with four automatic conventional noise removal techniques used in biomechanics. The conclusion of this work is that WBNR techniques are very effective in removing noise from differentiated signals with sharp transients while leaving these transients intact. For biomechanical signals with certain characteristics, WBNR techniques perform better than conventional methods, as indicated by quantitative merit measures.     

CAS-CAS transform for 2-D signals: A few applications

A few applications of a separable Hartley-like (CAS-CAS) transform in two-dimensional (2-D) signal processing is presented. The applications discussed include (i) the interpolation of signals, (ii) the computation of Hilbert transform, and (iii) the complex cepstrum computation. The computational advantage of the proposed methods over the algorithms using 2-D FFT are discussed.     

Model based phase unwrapping of 2-D signals

A parametric model and a corresponding parameter estimation algorithm for unwrapping 2-D phase functions are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model fitting, the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise, as well as to local errors. In its first step, the algorithm fits a 2-D polynomial model to the observed phase. The estimated phase is then. Used as a reference information that directs the actual phase unwrapping process. The phase of each sample of the observed field is unwrapped by increasing (decreasing) it by the multiple of 2π, which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate. In practical applications, the entire phase function cannot be approximated by a single 2-D polynomial model. Hence, the observed field is segmented, and each segment is fit with its own model. Once the phase model of the observed field has been estimated, we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model field     

Modelling 1-D signals using Hermite basis functions

The paper discusses a method for estimating the Hermite coefficients of a discrete-time one-dimensional signal. To estimate the Hermite coefficients a solution based on Gaussian quadratures is used. The paper also looks at various least mean squared (LMS) estimation methods to estimate two further parameters which are incorporated into the orthonormal Hermite basis function; a spread term and a shift term. In addition, the effects of scaling, dilation and translates of a signal on its Hermite coefficients, spread and shift terms are presented. The paper concludes with a brief discussion on the potential application of the Hermite parameters as features for use in problems requiring shape discrimination within a one-dimensional signal. It also mentions those applications where this was found to be appropriate     

宽带线调信号脉内参数及二维角联合估计

针对具有时变阵列流型的宽带线性调频(WLFM)信号,建立瞬时波束空间阵列模型,实现多个WLFM信号瞬时频率和二维角联合估计;同时利用二维角估计值完成信号间瞬时频率的分离,并最终实现各个WLFM信号脉内参数(初始频率和调频斜率)估计.算法具有相干信号处理能力,且不需空间平滑或聚汇等预处理.仿真实验证明了算法的有效性.     

2-D and 1-D multipaired transforms: frequency-time type wavelets

A concept of multipaired unitary transforms is introduced. These kinds of transforms reveal the mathematical structure of Fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images. Considering paired transforms, we analyze simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one-dimensional (1-D) “signals”, that determine such splitting. The main properties of the orthogonal system of paired functions are described, and the matrix decompositions of the Fourier and Hadamard transforms via the paired transforms are given. The multiplicative complexity of the two-dimensional (2-D) 2^r×2^r-point discrete Fourier transform by the paired transforms is 4^r/2(r-7/3)+8/3-12 (r>3), which shows the maximum splitting of the 5-D Fourier transform into the number of the short 1-D Fourier transforms. The 2-D paired transforms are not separable and represent themselves as frequency-time type wavelets for which two parameters are united: frequency and time. The decomposition of the signal is performed in a way that is different from the traditional Haar system of functions     

Interpolation of 2-D signals from their isolated zeros

In this paper, interpolation formulas are derived for the recovery of a two-dimensional (2-D) bandlimited signal from its isolated zeros. Different constellations of zero locations are considered. The interpolation formulas, based on Lagrange interpolation, are given both in Cartesian and in polar coordinates.     

Design of 1-D and 2-D IIR eigenfilters

An effective method is proposed for the design of recursive digital filters in the time/spatial domain. The method is based on the computation of an eigenvalue and its corresponding eigenvector of an appropriate real symmetric and positive-definite matrix derived from the objective error function of the impulse response in the least-squares sense. The method can be used to design 1D IIR digital filters as well as 2D IIR digital filters. The method is easy and the performance is comparable to those of the existing methods. One of the main advantages of the proposed method is that the solution is obtained directly without the need for iteration     

New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality

In this part, a comparison between the different state-space models is presented. We discuss proper definitions of state, controllability and observability and their relations to minimality of 2-D systems. We also present new circuit realizations and 2-D digital filter hardware implementation of 2-D transfer functions.     

非圆信号快速高精度二维测向算法

针对窄带非圆信号,提出了一种基于共轭梯度迭代搜索的快速高精度二维来波方向估计算法。利用非圆信号椭圆协方差矩阵非零特性,将阵列接收数据矩阵共轭重排,增加了阵列自由度,扩展了阵列有效孔径,提高了多信号检测能力,改善了阵列测向性能。对扩展后的阵列接收数据利用共轭梯度迭代搜索方式求得信号子空间,避免了多次求解样本协方差矩阵及其特征分解过程,显著降低了运算复杂度。仿真实验验证了所提算法的有效性和实用性。     

2-D direction finding of coherent signals VIA Temporo-Spatial processing

In most wireless communication systems, two-dimensional Directions-Of-Arrival (DOA) of multipath signals need to be found for spatial selective transmission. However, it is quite difficult to find their DOAs due to the coherent nature of multipath signals and considerable computations when performing 2-D searches. In this paper, a new algorithm to estimate 2-D DOA of multiple narrow-band signals is proposed. A DOA cyclic matrix is constructed whose eigenvalues and eigenvectors can be simultaneously used to extract 2-D DOA without 2-D searches. By exploiting the temporal property of cyclostationarity, the signal detection capability is significantly improved. Besides, based on the decorrelation model for mobile terminal signals, the algorithm can be effectively extended to the coherent case without spatial smoothing and the loss of array aperture. Simulation results are given to illustrate the performance of the new algorithm.     

Stability analysis of 1-D and 2-D fixed-point state-space digitalfilters using any combination of overflow and quantizationnonlinearities

A new criterion, together with its frequency-domain interpretation for the global asymptotic stability of zero-input one-dimensional (1-D) state-space digital filters under various combinations of overflow and quantization nonlinearities and for the situation where quantization occurs after summation only, is presented. A condition in closed form involving solely the parameters of the state transition matrix for the nonexistence of limit cycles in second-order digital filters is derived. Improved versions of some of the stability results due to Leclerc and Bauer (1994) are established. Finally, the approach is extended to two-dimensional (2-D) digital filters described by the Roesser and the Fornasini-Marchesini second local state-space models     

An estimation algorithm for 2-D polynomial phase signals.

We consider nonhomogeneous 2-D signals that can be represented by a constant modulus polynomial-phase model. A novel 2-D phase differencing operator is introduced and used to develop a computationally efficient estimation algorithm for the parameters of this model. The operation of the algorithm is illustrated using an example.     

线性调频信号2-D到达角估计的虚拟阵元法

通过原始数据的共轭重排构造了虚拟阵列，利用实际阵列与虚拟阵列的互Wigner-Ville分布建立了新的空间时频分布，并给出了基于子空间投影和L-阵列的线性调频信号2-D到达角估计算法。理论分析和仿真实验证明了算法的有效性。     

Galileo系统L1P与L1F信号间干扰的分析

在L1频段上,Galileo系统的授权服务信号L1P和开放服务信号L1F共用中心频点1 575.42 MHz,它们的功率谱部分重叠,相互之间存在干扰。通过仿真研究L1P和L1F信号间的干扰,对它们的干扰系数、载噪比衰减值进行了详细分析,找出了决定这两种信号间干扰大小的主要因素。仿真结果显示,L1P信号受到来自于L1F信号的最大干扰为0.002 dB,来自于CDMA干扰的最大值为0.26 dB;L1F受到来自于L1P信号的最大干扰几乎为0 dB,来自于CDMA干扰的最大值为0.604 dB。这表明,CDMA干扰是主要干扰源,L1P和L1F信号间的干扰可以忽略。这主要受益于L1P信号采用余弦相位的BOC调制,L1F信号采用CBOC调制,使这两个信号的功率谱重叠部分大大减少,从而干扰系数很小,大大减小了它们间的干扰。     

Scalability of 2-D wavelet transform algorithms: analytical and experimental results on MPPs

This paper studies the scalability of two-dimensional (2-D) discrete wavelet transform (DWT) algorithms on massively parallel processors (MPPs). The principal operation in the 2-D DWT is the filtering operation used to implement the filter banks of the 2-D subband decomposition. This filtering operation can be implemented as a convolution in the time domain or as a multiplication in the frequency domain. We demonstrate that there exist combinations of machine size, image size, and wavelet kernel size for which the time-domain algorithms outperform the frequency domain algorithms and vice-versa. We therefore demonstrate that a hybrid approach that combines time- and frequency-domain approaches can yield linear scalability for a broad range of problem and machine sizes. Furthermore, we show the effect of processor speed versus communication overhead and the use of separable versus nonseparable wavelets on the crossover points between the algorithm approaches.