Frame analysis of the discrete Gabor-scheme

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this function. The frame bounds are calculated by means of the eigenvalues of the matrix-valued function, and the dual frame, which is used in calculation of the expansion coefficients, is expressed by means of the inverse matrix. DFT-based algorithms for computation of the expansion coefficients, and for the reconstruction of signals from these coefficients, are generalized for the case of oversampling of the Gabor space. The algorithms are implemented in an example of representation of a nonstationary signal     

Peak value estimation of bandlimited signals from their samples, noise enhancement, and a local characterization in the neighborhood of an extremum

The paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling. This problem has significant relevance to orthogonal frequency-division multiplexing (OFDM) signal processing and system design. In particular, an upper bound on the peak value is established given the peak value of the samples and the oversampling rate. Moreover, it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound. The proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum. A different analysis examines the effect of small errors in the samples. It is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal. Again, an upper bound is derived relating the peak error in the samples and the peak error in the signals. Furthermore, both problems are shown to be coupled and put in a unifying context. The bounds are compared and applied to problems concerning OFDM.     

Optical flow estimation using temporally oversampled video.

Recent advances in imaging sensor technology make high frame-rate video capture practical. As demonstrated in previous work, this capability can be used to enhance the performance of many image and video processing applications. The idea is to use the high frame-rate capability to temporally oversample the scene and, thus, to obtain more accurate information about scene motion and illumination. This information is then used to improve the performance of image and standard frame-rate video applications. This paper investigates the use of temporal oversampling to improve the accuracy of optical flow estimation (OFE). A method for obtaining high accuracy optical flow estimates at a conventional standard frame rate, e.g., 30 frames/s, by first capturing and processing a high frame-rate version of the video is presented. The method uses the Lucas-Kanade algorithm to obtain optical flow estimates at a high frame rate, which are then accumulated and refined to estimate the optical flow at the desired standard frame rate. The method demonstrates significant improvements in OFE accuracy both on synthetically generated video sequences and on a real video sequence captured using an experimental high-speed imaging system. It is then shown that a key benefit of using temporal oversampling to estimate optical flow is the reduction in motion aliasing. Using sinusoidal input sequences, the reduction in motion aliasing is identified and the desired minimum sampling rate as a function of the velocity and spatial bandwidth of the scene is determined. Using both synthetic and real video sequences, it is shown that temporal oversampling improves OFE accuracy by reducing motion aliasing not only for areas with large displacements but also for areas with small displacements and high spatial frequencies. The use of other OFE algorithms with temporally oversampled video is then discussed. In particular, the Haussecker algorithm is extended to work with high frame-rate sequences. This extension demonstrates yet another important benefit of temporal oversampling, which is improving OFE accuracy when brightness varies with time.     

Rapid gridding reconstruction with a minimal oversampling ratio

Reconstruction of magnetic resonance images from data not falling on a Cartesian grid is a Fourier inversion problem typically solved using convolution interpolation, also known as gridding. Gridding is simple and robust and has parameters, the grid oversampling ratio and the kernel width, that can be used to trade accuracy for computational memory and time reductions. We have found that significant reductions in computation memory and time can be obtained while maintaining high accuracy by using a minimal oversampling ratio, from 1.125 to 1.375, instead of the typically employed grid oversampling ratio of two. When using a minimal oversampling ratio, appropriate design of the convolution kernel is important for maintaining high accuracy. We derive a simple equation for choosing the optimal Kaiser-Bessel convolution kernel for a given oversampling ratio and kernel width. As well, we evaluate the effect of presampling the kernel, a common technique used to reduce the computation time, and find that using linear interpolation between samples adds negligible error with far less samples than is necessary with nearest-neighbor interpolation. We also develop a new method for choosing the optimal presampled kernel. Using a minimal oversampling ratio and presampled kernel, we are able to perform a three-dimensional (3-D) reconstruction in one-eighth the time and requiring one-third the computer memory versus using an oversampling ratio of two and a Kaiser-Bessel convolution kernel, while maintaining the same level of accuracy.     

Frame analysis for biorthogonal cosine-modulated filterbanks

This paper addresses the efficient computation of frame bounds for cosine-modulated filterbanks. We derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype's polyphase components. The number of channels and the downsampling factor may be even or odd, and the oversampling factor is supposed to be an integer. The analysis of low-delay, biorthogonal filterbanks; shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior. Because the computational cost of determining the frame bounds with the proposed method is very low, we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds. Various design examples are presented.     

A Nyquist-rate delta-sigma A/D converter

This paper describes an analog-to-digital converter which combines multiple delta-sigma modulators in parallel so that time oversampling may be reduced or even eliminated. By doubling the number of Lth-order delta-sigma modulators, the resolution of this architecture is increased by approximately L bits. Thus, the resolution obtained by combining M delta-sigma modulators in parallel with no oversampling is similar to operating the same modulator with an oversampling rate of M. A parallel delta-sigma A/D converter implementation composed of two, four, and eight second-order delta-sigma modulators is described that does not require oversampling. Using this prototype, the design issues of the parallel delta-sigma A/D converter are explored and the theoretical performance with no oversampling and with low oversampling is verified. This architecture shows promise for obtaining high speed and resolution conversion since it retains much of the insensitivity to nonideal circuit behavior characteristic of the individual delta-sigma modulators     

基于盲源分离的单通道窄带干扰抑制算法

针对窄带干扰下通信系统性能恶化的问题,提出一种基于过采样与盲源分离技术的单通道窄带干扰抑制算法。该算法利用通信信号与窄带干扰的基带结构特征,通过过采样以及串并变换构造出源信号为信息序列的盲源分离模型,并利用快速独立成分分析法实现信息码元的恢复。仿真结果表明,该算法能有效对抗窄带干扰,抗干扰能力强。     

Design and Analysis of an Oversampling D/A Converter in DMT-ADSL Systems

Oversampling sigma-delta digital-to-analog converters are crucial building blocks for telecommunication applications. To reduce power consumption, lower oversampling ratios are preferred thus high-order digital sigma-delta modulators are needed to meet the dynamic performance requirements. This paper presents an oversampling DAC with 1.104 MHz signal bandwidth for DMT-ADSL application and focuses on the design issues of the high-order one-bit multiple feedback modulators (such as the stability problem, good inband SNDR performance, limit cycles, etc.). A new approach to obtain and optimize the stable feedback coefficients has been presented. From our analysis results it is found that the extra feedback coefficients and scaling coefficients in the modulator have non-negligible impact on the behavior of the limit cycles, and design guide for selecting the scaling coefficients is provided. Finally a 5th-order modulator with an oversampling ratio of 32 and 14-bit input has been implemented in a 0.6 m 3.3 V CMOS process and integrated into the whole DAC chip.     

A low oversampling ratio 14-b 500-kHz ΔΣ ADC with aself-calibrated multibit DAC

Delta-sigma (ΔΣ) analog-to-digital converters (ADC's) rely on oversampling to achieve high-resolution. By applying multibit quantization to overcome stability limitations, a circuit topology with greatly reduced oversampling requirements is developed. A 14-bit 500-kHz ΔΣ ADC is described that uses an oversampling ratio of only 16. A fourth-order embedded modulator, four-bit quantizer, and self-calibrated digital-to-analog converter (DAC) are used to achieve this performance. Although the high-order embedded architecture was previously thought to be unstable, it is shown that with proper design, a robust system can be obtained. Circuit design and implementation in a 1.2-μm CMOS process are presented. Experimental results give a dynamic range of 84 dB with a sampling rate of 8 MHz and oversampling ratio of 16. This is the lowest oversampling ratio for this resolution and bandwidth achieved to date     

Discrete multiwindow Gabor-type transforms

The discrete (finite) Gabor scheme is generalized by incorporating multiwindows. Two approaches are presented for the analysis of the multiwindow scheme: the signal domain approach and the Zak transform domain approach. Issues related to undersampling, critical sampling, and oversampling are considered. The analysis is based on the concept of frames and on generalized (Moore-Penrose) inverses. The approach based on representing the frame operator as a matrix-valued function is far less demanding from a computational complexity viewpoint than a straightforward matrix algebra in various operations such as the computation of the dual frame. DFT-based algorithms, including complexity analysis, are presented for the calculation of the expansion coefficients and for the reconstruction of the signal in both signal and transform domains. The scheme is further generalized and incorporates kernels other than the complex exponential. Representations other than those based on the dual frame and nonrectangular sampling of the combined space are considered as well. An example that illustrates the advantages of the multiwindow scheme over the single-window scheme is presented     

Linear prediction approach to oversampling parameter estimation for multiple complex sinusoids

The problem of oversampling parameter estimation for noisy sinusoidal signals is addressed. We first extend the weighted least squares (WLS) approach to the complex sinusoids. Then the oversampling weighted least squares (OSWLS) estimator is proposed based on data decimation. Estimation performance of the OSWLS method is analyzed via theoretical and simulation studies. Results are also compared to those of the WLS and decimative unitary ESPRIT methods as well as Cramér-Rao lower bound.     

基于三支决策的不平衡数据过采样方法

采样是解决不平衡数据分类问题的一个有效途径.文中结合三支决策理论，根据样本分布将样本划分成三个区域：正域、边界域和负域；在此基础上，分别对边界域和负域中的小类样本进行不同的过采样处理，提出了一种基于三支决策的不平衡数据过采样算法（TWD-IDOS算法）.实验结果表明，在C4.5、KNN和CART等分类器上，文中提出的算法能有效解决不平衡数据的二分类问题，在Recall、F-value、AUC等指标上优于文献中的过采样算法.     

Dual Gabor frames: theory and computational aspects

We consider a general method for constructing dual Gabor elements different from the canonical dual. Our approach is based on combining two Gabor frames such that the generated frame-type operator S/sub g,/spl gamma// is nonsingular. We provide necessary and sufficient conditions on the Gabor window functions g and /spl gamma/ such that S/sub g,/spl gamma// is nonsingular for rational oversampling, considering both the continuous-time and the discrete-time settings. In contrast to the frame operator, the operator S/sub g,/spl gamma// is, in general, not positive. Therefore, all results in Gabor analysis that are based on the positivity of the frame operator cannot be applied directly. The advantage of the proposed characterization is that the algebraic system for computing the Gabor dual elements preserves the high structure of usual Gabor frames, leading to computationally efficient algorithms. In particular, we consider examples in which both the condition number and the computational complexity in computing the proposed dual Gabor elements decrease in comparison to the canonical dual Gabor elements.     

基于过采样的混合滤波器组性能优化

模拟误差是制约混合滤波器组信号重构精度的主要原因,如何降低由模拟误差导致的分解滤波器组系数误差成为了首要问题。引入过采样技术,研究在不同过采样率下8通道混合滤波器组的性能,寻找到过采样率最优值约等于7%。在不同模拟误差下对基于过采样的混合滤波器组的性能进行仿真,结果表明,原型结构和双阶型结构的混叠值相近,但后者对模拟误差的敏感度比前者大。信号重构阶段,在最小二乘法的基础上采用频带加权法进行误差校准。在1%模拟误差内,采用7%过采样率的原型混合滤波器组相比无过采样,平均混叠值下降了约50 dB,最大混叠值下降了约94 dB。仿真验证了引入过采样的有效性。     

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     

基于数字锁相相关计算结构的优化算法

为了兼顾数字锁相检测的速度和精度,提高信号检测系统的综合性能,该文提出了一种基于数字锁相相关计算结构的高速算法并结合过采样对算法性能优化。该方法在过采样的基础上将采样频率还原为4倍于原信号的频率,快速数字锁相算法对下抽样后q个周期的4q个采样点进行加减法运算即可实现,与传统数字锁相算法相比几乎消除了所有的乘法运算,大幅度地提高了数字锁相算法实现的速度。同时引入修正因子改善了由于降采样所带来的误差。实验结果表明,该方法既有过采样和锁相检测的高精度,能够检测到较低信噪比的信号,又具备较高的速度,使得该算法对微弱信号的实时检测在普通微处理器上的实现成为可能。     

Multiloop sigma-delta quantization

It is shown that, for a multiloop sigma-delta modulator driven by a DC input, the statistical behavior (described by long-term time averages) of the error process from an inner (multibit) quantizer is consistent with that of a signal-independent. white. uniform noise. The same result also holds for sinusoidal inputs, provided that the modulator has three or more loops. This behavior is exploited to obtain trade-offs between asymptotic system performances and oversampling ratios, for several sigma-delta modulator/decoding filter pairs. For an L-loop modulator with a simple sinc^L+1 decoding filter, it is shown that doubling the oversampling ratio can result in an improvement of 3.01(2L+1) dB in the signal-to-quantization-noise ratio     

A second-order extension of the edge-selection algorithm for a ΣΔ-DAC architecture insensitive to oversampling clock jitter

In this paper we propose a ΣΔ-digital-to-analogue converter (DAC) architecture using a clock from an all-digital fractional programmable clock generator as an oversampling clock. Although this method is attractive in respect of implementation issues, it has not been widely used because the clock generated by this method contains a significant amount of jitter. The proposed architecture uses an edge-selection algorithm to suppress the in-band noise caused by the oversampling clock jitter. The improvement of the algorithm over the previous work is mainly achieved by adopting a second-order four-way edge selection. Simulation results show that the improved algorithm achieves a signal-to-noise distortion ratio of around 100 dB when applied to a 1-bit ΣΔ-DAC for a voiceband codec and that the performance degradation due to the clock jitter has been kept within 3 dB.     

基于子带脉冲压缩的雷达宽带接收方法

宽带信号的大容量高速数据率,使宽带信号实时处理受到软硬件各方面的限制。本文详细研究了宽带信号的子带脉冲压缩处理方法,给出了过采样子带脉冲压缩系统的基本结构,并对该方法的详细性能进行仿真分析,有效地解决了宽带信号的实时处理问题。将该系统应用于实际工程中,对实测数据的处理结果证明了系统的正确性和有效性。     

A 50-MHz multibit sigma-delta modulator for 12-b 2-MHz A/Dconversion

The authors examine the application of oversampling techniques to analog-to-digital conversion at rates exceeding 1 MHz. A cascaded multibit sigma-delta (ΣΔ) modulator that substantially reduces the oversampling ratio required for 12-b conversion while avoiding stringent component matching requirements is introduced. Issues concerning the design and implementation of the modulator are presented. At a sampling rate of 50 MHz and an oversampling ratio of 24, an implementation of the modulator in a 1-μm CMOS technology achieves a dynamic range of 74 dB at a Nyquist conversion rate of 2.1 MHz. The experimental modulator is a fully differential circuit that operates from a single 5-V power supply and does not require calibration or component trimming