Dopplerlet变换及其匹配收敛性分析

介绍了一种以伸缩、时移和频移后的加窗Doppler信号为基函数的时频信号表示Dopplerlet变换,证明了基于Dopplerlet基函数的自适应匹配投影塔形分解算法是收敛的,而且分解过程中所得残差信号的能量按指数律衰减。实验结果表明了以Dopplerlet为基函数的自适应匹配投影塔形分解法能更紧凑地表示自然界中的一类Doppler信号。     

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992)     

在不同噪声背景下Dopplerlet变换在信号恢复中的应用

在不提供信号与噪声统计特性的前提下,用自适应匹配投影塔形分解算法实现的Dopplerlet变换,能有效地去除信号中的噪声和干扰.文中给出了信号恢复的原理以及不同特性噪声背景下的算例结果.     

基于子空间的三阶多项式相位信号快速稀疏分解算法

针对稀疏分解冗余字典中原子数量庞大的缺点,该文提出一种三阶多项式相位信号的快速稀疏分解算法。该算法根据三阶多项式相位信号的特点,把原有信号变换成两个子空间信号,并根据这两个子空间信号构建相应的冗余字典,然后采用正交匹配追踪法来完成其稀疏分解,最后利用稀疏分解原理完成原有信号的稀疏分解。该算法把原有信号变换成两个不同子空间信号,构建了两个不同的冗余字典,对比采用一个冗余字典库,这种采用两个冗余字典的算法大大减少了原子数量,并且通过快速傅里叶变换,在一个冗余字典进行稀疏分解时,同时找到另一个冗余字典中的最匹配的原子。因此该算法通过减少原子数量和采用快速傅里叶变换大大加快了稀疏分解速度。实验结果表明,相比于采用Gabor原子构建的冗余字典,采用匹配追踪算法与遗传算法及最近提出的基于调制相关划分的快速稀疏分解,它的稀疏分解速度更快,并且具有更好的收敛性。     

关于信号tu(t)的傅里叶变换的探讨

傅里叶变换是“信号与线性系统”课程中一个非常重要的教学内容,是理解信号频域特性和进行线性系统频域分析的基础。课程中对于一些不满足绝对可积条件的信号,通过引入广义函数获得了它们的傅里叶变换。斜坡信号tu(t)不是绝对可积的信号,虽然一些文献中给出了它的傅里叶变换表达式,但对于该信号的傅里叶变换是否存在的问题却存在不同观点。论文对斜坡信号傅里叶变换的求解方法进行了研究,指出了常见的错误方法,并对斜坡信号的频率特性给出了一种观点。     

Walsh Spectral Estimates with Applications to the Classification of EEG Signals

A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions is presented. The Walsh power spectrum is examined from the point of view of its statistical properties, especially as it relates to spectral resolution. Features, selected from the spectrum of sleep EEG data are compared to corresponding Fourier features. Each feature set is used to classify the data using a minimum-distance clustering algorithm. The results show that the Walsh spectral features classify the data in much the same way as the Fourier spectral features. This provides sufficient justification for usage ofWalsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.     

A General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly

Examining the frequency content of signals is critical in many applications, from neuroscience to astronomy. Many techniques have been proposed to accomplish this. One of these, the S-transform, provides simultaneous time and frequency information similar to the wavelet transform, but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements. It has shown promise in many medical imaging applications but has high computational requirements. This paper presents a general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier, and S- transforms. A discrete, nonredundant formulation of this transform, as well as algorithms for calculating the forward and inverse transforms are also developed. These utilize efficient sampling of the time-frequency plane and have the same computational complexity as the fast Fourier transform. When configured appropriately, this new algorithm samples the continuous S-transform spectrum efficiently and nonredundantly, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm. The new and efficient algorithms make practical many existing signal and image processing techniques, both in biomedical and other applications.     

Multichannel transforms for signal/image processing

This paper presents a novel approach to the Fourier analysis of multichannel time series. Orthogonal matrix functions are introduced and are used in the definition of multichannel Fourier series of continuous-time periodic multichannel functions. Orthogonal transforms are proposed for discrete-time multichannel signals as well. It is proven that the orthogonal matrix functions are related to unitary transforms (e.g., discrete Hartley transform (DHT), Walsh-Hadamard transform), which are used for single-channel signal transformations. The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT. Therefore, fast algorithms for their computation can be easily constructed. Simulations on the use of discrete multichannel transforms on color image compression have also been performed.     

基于免疫克隆与核匹配追踪的快速图像目标识别

为了避免核匹配追踪通过贪婪算法在基函数字典中寻找一组基函数的线性组合来逼近目标函数的计算量大的缺陷,本文利用免疫克隆选择算法全局最优和局部快速收敛的特性,加快对核匹配追踪算法每次的匹配过程进行优化,提出了一种免疫克隆核匹配追踪图像目标识别算法,该算法有效降低了核匹配追踪算法的计算量,对UCI数据集和遥感图像进行的仿真实验结果表明,相比标准核匹配追踪,该算法保持相当识别率情况下可以明显缩短一次匹配追踪的时间,尤其当字典规模较大时效果更为明显;同基于遗传算法优化相比,本文方法目标识别速度快,精度高。     

基于频域分析的图像匹配定位算法的研究

首先对基于频域的抗旋转匹配算法和相关函数傅里叶变换匹配算法做了研究和分析,然后在相关函数傅里叶变换匹配算法的基础上,研究讨论了基于快速傅里叶变换和积分图的匹配定位算法,从而证明了基于频域相关技术做图像匹配具有相关峰尖锐突出、精度高、抗噪、对局部灰度变化不敏感等优点。     

分数阶Fourier级数展开及相关性质研究

介绍了一种从分数阶Fourier变换（FRFT）思想导出的分数阶Fourier级数（FRFS）展开方法,可以看作为Fourier级数的进一步推广,在研究非平稳信号中有着重要的应用。分数阶Fourier级数以一组有限时域内的正交Chirp信号为基函数来逼近分析信号,与Fourier级数相比,在分析非平稳信号中具有更大的灵活性。文中给出了Chirp信号FRFS分解的解析表示,分析了FRFS展开系数的振荡特性;同时对不同参数下的FRFS收敛速度进行了研究和计算机仿真,对于工程实际中的计算具有较好的参考价值。     

Scale periodicity and its sampling theorem

The scalar transform is a new representation for signals, offering a perspective that is different from the Fourier transform. We introduce the notion of a scalar periodic function. These functions are then represented through the discrete scale series. We also define the notion of a strictly scale-limited signal. Analogous to the Shannon interpolation formula, we show that such signals can be exactly reconstructed from exponentially spaced samples of the signal in the time domain. As an interesting, practical application, we show how properties unique to the scale transform make it very useful in computing depth maps of a scene     

Sampling of Bandlimited Signals in Fractional Fourier Transform Domain

Fractional Fourier transformed bandlimited signals are shown to form a reproducing kernel Hilbert space. Basic properties of the kernel function are applied to the study of a sampling problem in the fractional Fourier transform (FRFT) domain. An orthogonal sampling basis for the class of bandlimited signals in the FRFT domain is then given. A nonuniform sampling theorem for bandlimited signals in the FRFT domain is also presented. Numerical experiments are given to demonstrate the effectiveness of the proposed nonuniform sampling theorem.     

A scheme for automatic computation of Fock-type integrals

The evaluation of Fock-type integrals-i.e., integrals that are formally the Fourier transform of a slowly varying factor comprising a quotient of terms containing Airy functions and their derivatives-is developed in a computationally efficient way. The integrals are evaluated by use of a simple extension of a Fourier quadrature method that is related to the discrete Fourier transform. The resulting quadrature is applicable to both surface-field and reflected-field Fock integrals for a lossy impedance surface. The computation is believed to be efficient enough to allow the use of these functions in field computations codes where the Fock integrals must be computed on an as-needed basis.     

Fast Complexified Quaternion Fourier Transform

In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BiQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs.     

Generalized instantaneous parameters and window matching in thetime-frequency plane

The concept of instantaneous parameters, which has previously been associated exclusively with 1-D measures like the instantaneous frequency and the group delay, are extended to the 2-D time-frequency plane. Such generalized instantaneous parameters are associated with the short-time Fourier transform. They may also be interpreted as local moments of certain time-frequency distributions. It is shown that these measures enable local signal behavior to be characterized in the time-frequency plane for nonstationary deterministic signals. The usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms. This is achieved through window matching in the time-frequency plane. An algorithm is provided that illustrates the performance of this window matching. Results based on simulated and real data are presented     

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     

分数阶傅里叶变换域上带通信号的采样定理

傅里叶变换和采样定理是信号处理领域的两大基本问题,采样定理研究了傅里叶变换域上带限信号的采样和重构理论.分数阶傅里叶变换(FRFT)是傅里叶变换的一种推广,与之相应的采样理论目前还不十分完备,所以有必要从FRFT域上重新研究采样定理.本文首先得到了均匀冲激串采样信号的FRFT,然后在此基础上导出了FRFT域上带通信号和低通信号的采样定理和重构公式.这些结果是经典理论的推广,将丰富分数阶傅里叶变换的理论体系.     

Content-based and perceptual bit-allocation using matching pursuits

When communicating at a very-low bit-rate, video coders are unable to preserve high visual quality for all images. A selection of key regions according to human viewing and understanding may therefore be useful: it allows extracting essential features and to code them with a high quality, while the remainder of the image is coarsely transmitted. Such an approach requires a signal decomposition allowing an adaptive spatial variant bit allocation. Matching pursuits (MP) explicitly select the information to be transmitted among a large and overcomplete set of functions and quantize it according to a fixed and constant step. For MP, bit allocation is equivalent to function selection. This makes matching pursuits well suited for spatial variant bit allocation, since functions matched to important objects can be chosen. In this paper, we first show the abilities of matching pursuits to allocate an available bit-budget according to a semantic understanding of the scene. This semantic information can be provided either automatically or interactively. Second, the possibility to incorporate perceptive criteria within the MP coding algorithm is investigated.     

Fourier spectral factor model for prediction of multidimensional signals

A prediction model for multidimensional weakly stationary signals positing fewer number of common dynamic unobserved factors than the number of measured signals is presented. The strategy involves decomposing the measured signals into two independent parts such that one of them is multidimensional idiosyncratic noise while the other is enforced to bear the dynamic covariances using an appropriately transformed lower dimensional factor. The autocovariance functions of the two components are estimated using a Fourier spectral factor model - Spector - by the principle of maximum likelihood. Using the asymptotic properties of discrete Fourier transform, an estimation method based on eigenvalue decomposition of the spectral density function is presented. The predictability using Spector is validated by vector autoregression on publicly available database of signals.