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.

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%.

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.

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.

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

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.

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.

Whittaker-Kotelnikov-Shannov type sampling theory and the estimates of aliasing error

Let E be a finite interval or real axis R and denote by Lp（E）, 1≤p≤∞, the classical Lebesque space with usual norm. Let r∈N and denote by Lpr（R）, 1≤p≤∞, the subspace of functions f in Lp（R） for which the （r-1）-th derivative exists and is locally absolutely continuous on R and ||ff||P（R） is finite. Further

Aliasing Errors in Parallel Signature Analyzers

A Linear Feedback Shift Register (LFSR)can be used to compress test response data as a Signature Analyzer(SA). Parallel Signature Analyzers (PSAs) implemented as multiple input LFSRs are faster and re- quire less hardware overhead than Serial Signature Analyzers (SSAs)for compacting test response data for Built-In Serf-Test (BIST)in IC or hoard-testing environments. However, the SAs are prone to aliasing errors because of some specific types of error patterns. An alias is a faulty output signature that is identical to the fault-free signature. A penetrating analysis of detecting capability of SAs depends strongly on mathematical manipulations, instead of being aware of some special cases or examples. In addition , the analysis should not be restricted to a particular structure of LFSR, but be appropriate for various structures of LFSRs. This pa- per presents necessary and sufficient conditions for aliasing errors based on a complete mathematical descrip- tion of various types of SAs. An LFSR reconfiguration scheme is suggested which will prevent any aliasing double errors. Such a prevention cannot be obtained by any extension of an LFSR.

Roll Eccentricity Compensation Based on Anti-Aliasing Wavelet Analysis Method

Roll eccentricity is an important factor causing thickness variations during hot strip rolling and might define the limit of strip thickness control accuracy. An improved multi-resolution wavelet transform algorithm was proposed to compensate for the roll eccentricity. The wavelet transform method had good localization characteristics in both the time and frequency domains for signal analysis; however, the wavelet method had a frequency-aliasing problem owing to the less than ideal cut-off frequency characteristics of wavelets. This made its component reconstruction of an inaccurate signal. To eliminate inherent frequency aliases in the wavelet transform, fast Fourier transform （FFT） and inverse fast Fourier transform （IFFT） were combined with the Mallat algorithm. This synthesis was described in detail. Then, the roll eccentricity component was extracted from rolling force signal. An automatic gauge control （AGC） system added with a multi-resolution wavelet analyzer was designed. Experimental results showed that the anti-aliasing method could greatly restrain the inverse effect of eccentricity and the thickness control accuracy was improved from ±40 μm to ±15 μm.

Comb-Based Filter Design Using Sharpening Technique and Certain Palindromic Polynomial

This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening technique. As a result, aliasing rejection and the passband characteristic are improved. The method is illustrated with various examples and compared with the methods from the literature. .

混叠和抗混叠技术

操作Photoshop或其它图像处理软件时经常要对是否启用Anti-aliasing这一功能作出选择。Aliasing一词指数字图像信号的频率混叠现象,它可能因原稿数字化时采样间隔过大而产生,也可能产生于图像的重新采样操作(比如放大或缩小图像,选择部分图像后的裁剪或粘贴操作)。此外。

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。

Optimization of the End Effect of Hilbert-Huang transform(HHT)

In fault diagnosis of rotating machinery, Hil- bert-Huang transform （HHT） is often used to extract the fault characteristic signal and analyze decomposition results in time-frequency domain. However, end effect occurs in HHT, which leads to a series of problems such as modal aliasing and false IMF （Intrinsic Mode Func- tion）. To counter such problems in HHT, a new method is put forward to process signal by combining the general- ized regression neural network （GRNN） with the bound- ary local characteristic-scale continuation （BLCC）. Firstly, the improved EMD （Empirical Mode Decompo- sition） method is used to inhibit the end effect problem that appeared in conventional EMD. Secondly, the gen- erated IMF components are used in HHT. Simulation and measurement experiment for the cases of time domain, frequency domain and related parameters of Hilbert- Huang spectrum show that the method described here can restrain the end effect compared with the results obtained through mirror continuation, as the absolute percentage of the maximum mean of the beginning end point offset and the terminal point offset are reduced from 30.113% and 27.603% to 0.510% and 6.039% respectively, thus reducing the modal aliasing, and eliminating the false IMF components of HHT. The proposed method caneffectively inhibit end effect, reduce modal aliasing and false IMF components, and show the real structure of signal components accuratelX.

基于NURBS的自由曲面在陶瓷造型设计中的实践性研究

NURBS功能可帮助在计算机中表达设计思维与创意,实现陶瓷的三维造型。本文主要在探讨NURBS曲面造型方法的基础上,研究如何通过计算机对陶瓷的造型进行辅助设计,同时对陶瓷造型中的曲面形态加以关注,以实际应用案例作为参照和类比。

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。

NOVEL APPROACH BASED ON DERAMPING TECHNIQUE FOR SQUINTED SLIDING SPOTLIGHT SAR IMAGING

This paper investigates a novel approach based on the deramping technique for squinted sliding spotlight Synthetic Aperture Radar (SAR) imaging to resolve the azimuth spectrum aliasing problem. First of all, the properties of the azimuth spectrum and the squint angle impacts on the azimuth spectrum aliasing problem are analyzed. Based on the analysis result, an operation of filtering is added to the azimuth preprocessing step of traditional Two-Step Focusing Approach (TSPA) to resolve the azimuth folding problem and remove the influence of the squint angle on the azimuth spectrum aliasing problem. Then, a modified Range Migration Algorithm (RMA) is performed to obtain the precise focused image. Furthermore, the focused SAR image folding problem of traditional TSPA is illuminated in this paper. An azimuth post-processing step is proposed to unfold the aliased SAR image. Simulation experiment results prove that the proposed approach can solve the spectrum aliasing problem and process squinted sliding spotlight data efficiently.

随机抽样中的Alias算法及其改进

为减少随机数的使用次数和降低抽样时间,基于等概化思路(或古典概型思路),对著名的Alias抽样方法进行了改进.以存储空间的少量增加为代价,使改进后的抽样方法A_Ⅰ和A_Ⅱ随机数的平均使用次数为Alias方法的75%和62.5%,平均抽样时间大约为Alias方法的80%和70%.