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| 1 | The structure of instantaneous frequencies of periodic analytic signals显示文摘In this paper, the structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one depending on the amplitude of the signal and another on the boundary value of an inner function. Based on this result, properties of the instantaneous frequencies of these two parts are studied, and it is found that negative instantaneous frequencies are caused by the amplitude of a signal. Finally, such conditions that an analytic signal is of positive instantaneous frequency are presented. | Tan LiHui Yang LiHua Huang DaRen | 2010 | Science China Mathematics2010，53，2： | 7 |
| 2 | Hilbert Transferin Applied to Separation of Waves显示文摘The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda's method and satisfactory results are obtained. | SUN Hequan(孙鹤泉) WANG Yongxue(王永学) PENG Jingping(彭静萍) | 2002 | China Ocean Engineering2002，17，2： | 7 |
| 3 | A distribution space for Hilbert transform and its applications显示文摘In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in DH. Finally, the applications of the extended Hilbert transform are discussed. | YANG LiHua School of Mathematics and Computing Science, Sun Yat-Sen University, Guangzhou 510275, China | 2008 | Science China Mathematics2008，51，12： | 3 |
| 4 | Anomalous SmKS induced by postcritical reflection and refraction at the core-mantle boundary显示文摘Earth’s outer core is generally thought to be a well-mixed liquid consisting mostly of iron and a small amount of lighter elements.Recent seismic studies using Sm KS waves show that the top a few hundred kilometers of the outer core possess a P-wave velocity slightly lower than the PREM model,which cannot be explained by self-compression of a chemically homogeneous outer core.We investigated the Sm KS waveforms of a deep earthquake occurring beneath South America recorded by a large and dense seismic array in China,and measured the differential arrival times of the Sm KS pairs.We found significant waveform distortion of the Sm KS caused by postcritical refraction and reflection at the core-mantle boundary.This waveform distortion can introduce significant bias to the measured differential times,leading to incorrect estimate of P-wave velocity of the outer core.Whether stable stratification is occurring in outer core or not requires further seismic investigations. | Liwei Wang Fenglin Niu | 2019 | Science Bulletin2019，64，21： | 2 |
| 5 | Simple proofs of the Bedrosian equality for the Hilbert transform显示文摘Two simple proofs of Bedrosian theorem are given. | WANG SiLei Department of Mathematics, Zhejiang University, Hangzhou 310027, China | 2009 | Science China Mathematics2009，52，3： | 1 |
| 6 | A METHOD FOR THE MEASUREMENT OF DYNAMIC TRANSMISSION ERROR OF PRECISION HOBBING MACHINES显示文摘In the paper,a new method for the measurement of the dynamic transmission crror of preci-sion hobbing machines using only one sensor is proposed.The dynamic transmission error i ob-tained by demodulating the phase-modulated signal according to the Hilbert transform priple.The results of dynamic testing show that the new method is effective. | 黄迪山 童忠钫 陆乃炎 | 1991 | Journal of China Textile University(English Edition)1991，9，4： | 0 |
| 7 | 希尔伯特-黄变换及其应用显示文摘近年来,基于时频变换理论、用于处理非平稳信号的一种新的变换方法——Hilbert—Huang变换(Hilbert—Huang Transform,HHT)在各个行业得到越来越广泛的应用。HHT方法能够对非线性、非平稳信号进行处理,不需事先确定基函数,是一种更具适应性的时频局部化分析方法。 | N.E.黄 牟文英 | 2007 | 国外科技新书评介2007，，6： | 0 |
| 8 | The Hilbert transform along the extended evil ladder curve显示文摘Let γ(t) be an even function extended by the evil ladder (tri-adic Cantor function)γ(t).Denote the curve L(t)=(t,(t))(-1≤t≤1). It is shown that the Hilbert transform along this curve L is bounded on L^2 (R^2). | Baoyi Wu Weiyi Su | 1999 | Chinese Science Bulletin1999，44，1： | 0 |
| 9 | Complex Semblance and Its Application显示文摘Semblance,a measure of multi-trace coherence,has been used extensively in seismic data processing and interpretation such as velocity analysis and fault detection. The traditional algorithm has a difficulty at zero-crossings of seismic recordings. This problem is alleviated by applying a smoothing window at the cost of losing vertical resolutions. In this paper,we improve the algorithm by computing semblance from complex traces. Our initial results show that the complex semblance is smooth at zero-crossings. Because the smoothing time window becomes unnecessary,the higher vertical resolution can be achieved by using small windows or none. Some geological features,like faults and unconformities,appear clearer and easier to identify with the complex semblance. As the advantages are obvious and the implementation is straight-forward with the Hilbert transform,this new algorithm may replace the traditional one in future applications. | Taikun Shi Shoudong Huo | 2019 | Journal of Earth Science2019，30，4： | 0 |
| 10 | IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES显示文摘The nonlinear behavior varying with the instantaneous response was analyzed through the joint time_frequency analysis method for a class of S.D.O.F nonlinear system. A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time_varying linear one, called the generalized skeleton linear system(GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non_linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time_ frequency filtering technique. | 王丽丽 张景绘 | 2001 | Applied Mathematics and Mechanics(English Edition)2001，22，2： | 0 |
| 11 | ITERATIVE ALGORITHM FOR HILBERT TRANSFORM WITH LESS LEAKAGE显示文摘An iterative algorithm is developed for the Hilbert transform based on FFT using the phase in-formation of modulated signal.The feature of this iterative algorithm is frequency shifting on apart of non-integral frequency in a modulated signal,and the final result of the orthogonal signalwith less pollution caused by the leakage phenomenon is obtained.The algorithm has been appliedto estimate envelope,center frequency and initial phase,including simulation and engineering ex-amples. | 黄迪山 童忠钫 | 1993 | Journal of China Textile University(English Edition)1993，10，1： | 0 |
| 12 | THREE-DIMENSIONAL FILTERING USING HILBERT TRANSFORM显示文摘It takes a long computer time for 3-D convolution to accomplish 3-D ideal band-pass filtering according to conventional method. The author proposed that 2-D fan filtering or directional filtering can be accomplished by using Hilbert transform. This note introduces accomplishment of some kinds of ideal band-pass filtering by Hilbert transform, and then the 3-D convolution becomes a finite number of 1-D convolution series-parallel connected. | 王天禧 | 1990 | Chinese Science Bulletin1990，35，2： | 0 |
| 13 | IDENTIFICATION OF PHASE ERROR BY MULTI-SAMPLING DIGITAL TANLOCKED LOOP(MS-DTL)显示文摘IntroductionThemainfeatureoftheC-DTListhatithasaphaseerrordetectorwithlinearcharacteristics,whichmeansthatithasawiderlock-inr... | 哈迪 李文舜 李介谷 | 1999 | Journal of Shanghai Jiaotong university(Science)1999，4，1： | 0 |
| 14 | Oscillatory hyper Hilbert transforms along variable curves显示文摘For n = 2 or 3 and x ∈ Rn, we study the oscillatory hyper Hilbert transform Tα,β f(x)=∫Rf(x-Г(t,x))e^-i|t|-β|t|^-1-α dt along an appropriate variable curveГ(t, x) in R^n (namely,Г(t, x) is a curve in R^n for each fixed x), where α〉β〉0. We obtain some LP boundedness theorems of Tα,β, under some suitable conditions on α and β. These results are extensions of some earlier theorems. However, Tα,β f(x) is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems. | Jiecheng CHEN Dashan FAN Meng WANG | 2019 | Frontiers of Mathematics in China2019，14，4： | 0 |
| 15 | A Practical Algorithm for Analysis of AM-FM Signals显示文摘The demodulation algorithm for AM-FM sinusoids proposed in reference[1]canonly deal with complex exponential sequences.In real applications,one needs to con-struct an analytic signal from real samples.Influenced by the Hilbert Transformation,thecomplex noise in the analytic signal is colored.This paper analyzes the colored noise andthe disadvantage caused by the noise in the estimations of the instantaneous frequencyand amplitude factor using the algorithm in[1]and formulates a practical algorithm. | 孙圣和 吴岩巍 | 1997 | Journal of Harbin Institute of Technology(New Series)1997，4，3： | 0 |
| 16 | Measurement of Moment of Inertia Based on Hilbert Transform显示文摘A measurement model based on torsion pendulum was established,in which nonlinear damping and nonlinear restoring force were considered.The calculation method of the moment of inertia was based on Hilbert transform.The motion of torsion pendulum showed the time-frequency characteristics due to the nonlinear factors,which were validated by the experimental data.The analytical signal was formed by Hilbert transform of the angular displacement signal of the test object.The moment of inertia can be computed by the instantaneous undamped natural frequency with Hilbert transform.Prior to the implementation of Hilbert transform,the empirical mode decomposition was used to filter the experimental signal.The moment of inertia of the test object was measured by the torsion pendulum system.The experimental results show that the relative measurement error of the moment of inertia was within 0.7%,which indicated the validity of the measurement method. | 赵岩 张晓琳 王军 唐文彦 | 2013 | Transactions of Tianjin University2013，19，3： | 0 |
| 17 | Testing Jitter on PLL Clocks Based on Analysis of Instantaneous Phase显示文摘A novel method based on the analysis of instantaneous phase is proposed to extract the jitter on phase-locked loops output clock. The method utilizes the Hilbert transform to extend the real signal of PLLs output into an analytic signal, and the implementation of Hilbert transform is based on the Fourier transform windowed with Hamming window. Then, the jitter of clock is extracted from the instantaneous phase of analytic signal. The experimental results of simulations validate that the proposed method can effectively extract the jitter on PLL clock, and it has better performance by comparing the sinusoidal jitter extraction results with the other methods. | 朱彦卿 何怡刚 方葛丰 阳辉 齐绍忠 刘惠 | 2007 | Tsinghua Science and Technology2007，12，S1： | 0 |
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