Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion

Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/（Wp（R）） are determined up to a logarithmic factor.

A Velocity Dealiasing Scheme for C-band Weather Radar Systems

A dealiasing algorithm for radar radial velocity observed by C-band Doppler radars is presented as an extension of an existing S-band dealiasing algorithm. This has operational significance in that many portable and many commercial broadcast radars, as well as approximately one half of the Chinese weather radar network （CINRAD）, are C-band radars. With a wavelength of about 5 cm, the Nyquist interval of C-band radars is just about one half that of S-band radars （wavelength of about 10 cm） and thus has more velocity folding. The proposed algorithm includes seven modules to remove noisy data, find the starting radials, dealias velocities, and apply least squares error checking in both the radial and azimuth directions. The proposed velocity dealiasing method was applied to one widespread rain case and three strong convective cases from radars operating in China. It was found that, on average, 92.95% of the aliased radial velocity data could be correctly de-aliased by the algorithm, resulting in 96.65% of the data being valid.

On the aliasing error in a class of bidimensional wavelet subspaces

This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an

Anti-aliasing wavelet packet method for harmonic detection

A novel anti-aliasing wavelet packet transform method for harmonic detection is proposed. Aiming at the low measurement precision and poor robustness which exists in the former traditional wavelet methods for lack of the aliasing_reduction scheme, an optimal interpolation wavelet packet filter is designed according to new optimal criteria. First, the limitation of anti-aliasing on the traditional wavelet filter bank is analyzed. Second, the designed optimal interpolation filters axe denoted, and then the solution algorithm is given. This devised wavelet packet filter can seek a reasonable balance between signal preservation and aliasing reduction; it overcomes the inherent bug of traditional wavelet transforms, which rooted from just only concerning total aliasing cancellation but not aliasing-reduction in decomposition. Simulation and several comparative results indicate that the proposed method can effectively eliminate aliasing and precisely extract harmonic information.

Geotechnical engineering blasting:a new modal aliasing cancellation methodology of vibration signal de-noising

In the present study of peak particle velocity(PPV)and frequency,an improved algorithm(principal empirical mode decomposition,PEMD)based on principal component analysis(PCA)and empirical mode decomposition(EMD)is proposed,with the goal of addressing poor filtering de-noising effects caused by the occurrences of modal aliasing phenomena in EMD blasting vibration signal decomposition processes.Test results showed that frequency of intrinsic mode function(IMF)components decomposed by PEMD gradually decreases and that the main frequency is unique,which eliminates the phenomenon of modal aliasing.In the simulation experiment,the signal-to-noise(SNR)and root mean square errors(RMSE)ratio of the signal de-noised by PEMD are the largest when compared to EMD and ensemble empirical mode decomposition(EEMD).The main frequency of the de-noising signal through PEMD is 75 Hz,which is closest to the frequency of the noiseless simulation signal.In geotechnical engineering blasting experiments,compared to EMD and EEMD,the signal de-noised by PEMD has the lowest level of distortion,and the frequency band is distributed in a range of 0-64 Hz,which is closest to the frequency band of the blasting vibration signal.In addition,the proportion of noise energy was the lowest,at 1.8%.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.

Aliasing-free high resolution imaging of fast rotating targets with narrowband radar

Narrowband radar has been successfully used for high resolution imaging of fast rotating targets by exploiting their micro-motion features.In some practical situations,however,the target image may suffer from aliasing due to the fixed pulse repetition interval(PRI)of traditional radar scheme.In this work,the random PRI signal associated with compressed sensing(CS)theory was introduced for aliasing reduction to obtain high resolution images of fast rotating targets.To circumvent the large-scale dictionary and high computational complexity problem arising from direct application of CS theory,the low resolution image was firstly generated by applying a modified generalized Radon transform on the time-frequency domain,and then the dictionary was scaled down by random undersampling as well as the atoms extraction according to those strong scattering areas of the low resolution image.The scale-down-dictionary CS(SDD-CS)processing scheme was detailed and simulation results show that the SDD-CS scheme for narrowband radar can achieve preferable images with no aliasing as well as acceptable computational cost.

Aliasing Error of Sampling Theorem

Let f∈Lpr（R）,1【p【∞,r∈N),the bound for aliasing of function fin Lp—metricesis given in[1].From embedding Theorem and Stein inequality,it follows,that if f∈Lpr（R）,1【p【∞,then f∈Lqr（R）,1【p【q≤∞ and f（k）∈Lp（R）∩Lq（R）,k=0,1,…,r-1.In this paper,we con-tinued Fang’s work in[1],and obtain the bound for aliasing error of function f∈Lpr（R）,1【p【∞,inLq-metrices（p≤q≤∞）.And the order is exact when 1【p≤q≤2.

The impact of frequency aliasing on spectral method of measuring T wave alternans

In this paper we investigate frequency aliasing in spectral method of measuring T wave alter-nans, which may lead a high false positive rate. Microvolt T wave alternans(TWA) has been evaluated as a means of predicting occurrence of ventricular tachyarrhythmia events and its association with the genesis of ventricular ar-rhythmias has been demonstrated. Nowadays, spectral method is one of the most widely used procedures for measurement of microvolt TWA. In our study, based on the sampling theory, the alternans frequency 0.5 cycles/beat, at which the power of the spectrum is used to calculated the Valt and K score (these two parameters indicate the TWA), is equal to the nyquist frequency. Thus this generates frequency aliasing which will make the power at the alternans frequency (P0.5) be two times of the real magnitude of the original spectrum amplitude. With the assump-tion that the noise spectrum follows the normal distribution, in spectral method of measuring T wave alternans, the measuring standard K score>3 to consider the T wave alternans sig-nificant is only with a p<0.133. By change the standard to K score>6 can solve this problem and make the p value to p<0.0027.

Cancellable Multi-Biometric Template Generation Based on Arnold Cat Map and Aliasing

The cancellable biometric transformations are designed to be computationally difficult to obtain the original biometric data.This paper presents a cancellable multi-biometric identification scheme that includes four stages:biometric data collection and processing,Arnold’s Cat Map encryption,decimation process to reduce the size,and finalmerging of the four biometrics in a single generated template.First,a 2D matrix of size 128×128 is created based on Arnold’s Cat Map(ACM).The purpose of this rearrangement is to break the correlation between pixels to hide the biometric patterns and merge these patterns together for more security.The decimation is performed to keep the dimensions of the overall cancellable template similar to those of a single template to avoid data redundancy.Moreover,some sort of aliasing occurs due to decimation,contributing to the intended distortion of biometric templates.The hybrid structure that comprises encryption,decimation,andmerging generates encrypted and distorted cancellable templates.The simulation results obtained for performance evaluation show that the system is safe,reliable,and feasible as it achieves high security in the presence of noise.

An Anti-aliasing Algorithm Suitable to Map Publishing Symbol

On the basis of analysis of various algorithms, an anti-aliasing algorithm called brush method was presented, which is suitable to map publishing symbol. Aftes introducing the basic principle and implementation of brush method in detail, the result and efficiency were evaluated through experiments.

AN ANTI-ALIASING FILTER FOR ∑△ ADC

An anti-aliasing filter for ∑△ ADCs using a combination of active RC and analog FIR filters is presented in this letter. The first order active RC filter is set at 100kHz to minimize the die size and variations of linear phase and gain in 0-4kHz passband. The 2-tap FIR filter provides more than -53dB attenuation at 2MHz ±4kHz frequency range. The proposed filter achieved more than -76dB attenuation at sampling frequency with ±0.01° phase linearity and ±0.02dB gain variation within 0-4kHz bandwidth. The active die area of the fully differential filter is 0.17mm2 in 0.5μm CMOS technology. The experimental and simulation results have been obtained and the feasibility of the proposed method is shown.

An efficient spatial anti-aliasing method for deferred shading

In recent years, image-based anti-aliasing techniques have been widely investigated in real-time computer graphics. Compared to traditional routine of anti-aliasing, image-based methods, which combined with deferred shading, can efficiently decouple anti-aliasing step from standard graphics pipeline. However, most of the existing image-based methods consume video memory, bandwidth and computation resources heavily. In this paper, we propose an optimized anti-aliasing method, which can efficiently reduce the multi-sampling rate by a multi-sampling mask. We carefully designed the rendering system to avoid serial execution on branch divergence, by utilizing both modern GPU’s features and latest shader model. Experimental results demonstrate that our method can achieve high-quality synthesized image with real-time performance.

基于Alias的自由曲面逆向造型设计

介绍了Alias逆向造型工具的特点和工作流程及其曲面造型技术.通过儿童安全座椅局部点云的反求设计,阐述运用Alias进行复杂曲面重建及造型的过程.通过曲面拓扑结构的合理划分,解决复杂曲面的重建很难用简单特征或特征曲线拟合的曲面来实现这一难题.研究表明,Alias直接建模的灵活性和高精确度,对于缩短产品开发周期、保证产品质量具有重大意义.

Alias与产品造型设计

论述了Alias区别于其它三维软件的特性,如模拟二维和三维素描设计,三维动态形态建模,照片真实感交互式可视化等,可以在设计过程中的任何阶段快速、方便地对模型形态进行修改并实时看到其渲染效果图。设计者可以在一个完整流程中创建、修改和再现自己的创意,集中精力在产品造型设计构思上而不是在设计工具上。

工程地质三维岩性网格模型体绘制的边界平滑方法

目的为了解决工程地质三维岩性网格模型体绘制过程中岩性属性在岩层分界处非连续过渡而产生锯齿的问题,方法提出一种三维岩性网格模型细分的边界线性平滑方法。基于岩层水平连续和纵向上空间叠置关系下老上新的特点,借鉴相邻钻孔岩层连接地质界面的思路,将岩性网格组织为横向上规则划分、纵向上记录岩层段顶底高程值的形式,类似规则分布的虚拟孔(称为垂直柱Pillar),并基于此种形式在光线投射过程中利用采样点周围4个岩层段形成属性计算单元,再定义相邻柱Pillar上岩层连接规则和16种空间单元细分模板,实现模型空间内任意点的岩性属性线性计算。结果通过WebGL2.0在GPU中实现与验证,得出可以明显平滑纵向上的岩层分界,解决了体绘制岩性边界的锯齿问题,最终实现采样点岩性属性的计算并得到平滑后的效果。结论结果表明,将岩层特点与体绘制光线投射算法空间采样过程结合,针对水平连续假设的工程地质岩层具有较好的平滑效果,可为工程地质岩性网格可视化的抗锯齿处理提供一种新思路。但是,因岩层间没有明确清晰的层序关系,因此不能处理含断层的模型,也不能处理大倾角岩层横向不连通的情况。

考虑频响函数混叠误差的阻尼比识别效果研究

通过实测频响函数识别阻尼比时,识别准确性受到频谱混叠现象的影响,因此建立了考虑频响函数混叠误差的阻尼比识别有效性判断方法.首先,根据傅里叶变换原理进行理论推导,证明了采样频率不足时频响函数会发生混叠现象;然后,根据频响函数混叠原理和模态叠加原理,建立了多自由度结构的基准频响混叠误差拟合公式,进而给出考虑频响函数混叠误差的阻尼比识别结果有效性判断的步骤.通过对两自由度理论频响函数模型设置不同的等效柔度比和固有频率比,表明其对两阶模态计算频响混叠误差有显著影响;通过对比四层框架结构基准模型的响应在设置不同采样频率时对阻尼比的识别结果,验证了所提方法的可行性.

基于Alias的自由曲面汽车造型设计

在传统的汽车造型设计中,对设计方案的改进往往耗时耗力,生产效率因此受到制约。文章介绍了传统造型设计的流程,提出了理想的纯数字化研发流程及基于Alias的曲面造型原理,以某款车为例,对其中的正向汽车造型设计进行了描述,并用showcase软件对其进行渲染。结果表明,Alias直接建模具有灵活性和高精度的特点,Alias在汽车造型设计中的使用对于缩短产品开发周期,保证产品质量具有重大意义。

基于多次滑动均值滤波的混合储能功率分配与定容研究

为了解决混合储能系统功率分配时因模态混叠导致功率分配不精确、储能系统成本过高的问题,提出一种多次滑动均值滤波(MMAF)的功率分配方法用于削弱模态混叠现象,降低混合储能成本。首先,获取满足平抑要求的混合储能最小总功率指令,采用MMAF算法对其进行滤波,获得蓄电池与超级电容各自的功率指令,引入Pearson相关系数量化模态混叠现象,作为判断滤波次数和每次滤波滑窗大小的指标,将蓄电池和超级电容各自的功率指令作为储能定容的可行域,考虑电池荷电状态约束求取储能适配的最小额定功率和额定容量;然后,基于等效运行时间建立蓄电池全寿命周期量化模型,为经济性分析提供依据;最后,以改进的混合储能全寿命周期成本模型验证了该文方法可以有效地限制模态混叠,降低混合储能系统成本。