Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and ...Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and practice of uniqueness of such frequency representation(decomposition)raise the related topics in approximation.During approximately the last two decades there has formulated a signal decomposition and reconstruction method rooted in harmonic and complex analysis giving rise to the desired signal representations.The method decomposes any signal into a few basic signals that possess positive instantaneous frequencies.The theory has profound relations to classical mathematics and can be generalized to signals defined in higher dimensional manifolds with vector and matrix values,and in particular,promotes kernel approximation for multi-variate functions.This article mainly serves as a survey.It also gives two important technical proofs of which one for a general convergence result(Theorem 3.4),and the other for necessity of multiple kernel(Lemma 3.7).Expositorily,for a given real-valued signal f one can associate it with a Hardy space function F whose real part coincides with f.Such function F has the form F=f+iHf,where H stands for the Hilbert transformation of the context.We develop fast converging expansions of F in orthogonal terms of the form F=∑k=1^(∞)c_(k)B_(k),where B_(k)'s are also Hardy space functions but with the additional properties B_(k)(t)=ρ_(k)(t)e^(iθ_(k)(t)),ρk≥0,θ′_(k)(t)≥0,a.e.The original real-valued function f is accordingly expanded f=∑k=1^(∞)ρ_(k)(t)cosθ_(k)(t)which,besides the properties ofρ_(k)andθ_(k)given above,also satisfies H(ρ_(k)cosθ_(k))(t)ρ_(k)(t)sinρ_(k)(t).Real-valued functions f(t)=ρ(t)cosθ(t)that satisfy the conditionρ≥0,θ′(t)≥0,H(ρcosθ)(t)=ρ(t)sinθ(t)are called mono-components.If f is a mono-component,then the phase derivativeθ′(t)is defined to be instantaneous frequency of f.The above described positive-instantaneous fre展开更多
Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components.The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent mot...Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components.The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions,and the small-scale one is obtained by subtracting the large-scale one from the total,which fully remove the outer influences.We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000,while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000.Therefore,a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000.The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number,and empirical fitting expressions are given in this work.展开更多
Two popular traditional join algorithms and their parallel versions are introduced. When designing join algorithms in serial computing environment, decomposing inner relation is considered as the right direction to sa...Two popular traditional join algorithms and their parallel versions are introduced. When designing join algorithms in serial computing environment, decomposing inner relation is considered as the right direction to save disk I/Os. However, two different decomposition algorithms are compared, such as inner vs. outer decomposition first algorithms for tuple-based and block-based nested loop joins, showing that the proposed approach is 20% better than general approach. Also lemmas are proved, when we have to use the outer decomposition first parallel join algorithms.展开更多
The outer-product decomposition algorithm(OPDA)performs well at blindly identifying system function.However,the direct use of the OPDA in systems using bandpass source will lead to errors.This study proposes an approa...The outer-product decomposition algorithm(OPDA)performs well at blindly identifying system function.However,the direct use of the OPDA in systems using bandpass source will lead to errors.This study proposes an approach to enhance the channel estimation quality of a bandpass source that uses OPDA.This approach performs frequency domain transformation on the received signal and obtains the optimal transformation parameter by minimizing the p-norm of an error matrix.Moreover,the proposed approach extends the application of OPDA from a white source to a bandpass white source or chirp signal.Theoretical formulas and simulation results show that the proposed approach not only reduces the estimation error but also accelerates the algorithm in a bandpass system,thus being highly feasible in practical blind system identification applications.展开更多
基金Macao University Multi-Year Research Grant(MYRG)MYRG2016-00053-FSTMacao Government Science and Technology Foundation FDCT 0123/2018/A3.
文摘Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and practice of uniqueness of such frequency representation(decomposition)raise the related topics in approximation.During approximately the last two decades there has formulated a signal decomposition and reconstruction method rooted in harmonic and complex analysis giving rise to the desired signal representations.The method decomposes any signal into a few basic signals that possess positive instantaneous frequencies.The theory has profound relations to classical mathematics and can be generalized to signals defined in higher dimensional manifolds with vector and matrix values,and in particular,promotes kernel approximation for multi-variate functions.This article mainly serves as a survey.It also gives two important technical proofs of which one for a general convergence result(Theorem 3.4),and the other for necessity of multiple kernel(Lemma 3.7).Expositorily,for a given real-valued signal f one can associate it with a Hardy space function F whose real part coincides with f.Such function F has the form F=f+iHf,where H stands for the Hilbert transformation of the context.We develop fast converging expansions of F in orthogonal terms of the form F=∑k=1^(∞)c_(k)B_(k),where B_(k)'s are also Hardy space functions but with the additional properties B_(k)(t)=ρ_(k)(t)e^(iθ_(k)(t)),ρk≥0,θ′_(k)(t)≥0,a.e.The original real-valued function f is accordingly expanded f=∑k=1^(∞)ρ_(k)(t)cosθ_(k)(t)which,besides the properties ofρ_(k)andθ_(k)given above,also satisfies H(ρ_(k)cosθ_(k))(t)ρ_(k)(t)sinρ_(k)(t).Real-valued functions f(t)=ρ(t)cosθ(t)that satisfy the conditionρ≥0,θ′(t)≥0,H(ρcosθ)(t)=ρ(t)sinθ(t)are called mono-components.If f is a mono-component,then the phase derivativeθ′(t)is defined to be instantaneous frequency of f.The above described positive-instantaneous fre
基金supports by grants from the National Natural Science Foundation of China(92052202 and 11972175).
文摘Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components.The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions,and the small-scale one is obtained by subtracting the large-scale one from the total,which fully remove the outer influences.We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000,while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000.Therefore,a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000.The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number,and empirical fitting expressions are given in this work.
基金supported by the National Research Foundation (NRF) of Korea through contract N-14-NMIR06
文摘Two popular traditional join algorithms and their parallel versions are introduced. When designing join algorithms in serial computing environment, decomposing inner relation is considered as the right direction to save disk I/Os. However, two different decomposition algorithms are compared, such as inner vs. outer decomposition first algorithms for tuple-based and block-based nested loop joins, showing that the proposed approach is 20% better than general approach. Also lemmas are proved, when we have to use the outer decomposition first parallel join algorithms.
基金This study is supported by the Natural Science Foundation of China(NSFC)under Grant Nos.11774073 and 51279033.
文摘The outer-product decomposition algorithm(OPDA)performs well at blindly identifying system function.However,the direct use of the OPDA in systems using bandpass source will lead to errors.This study proposes an approach to enhance the channel estimation quality of a bandpass source that uses OPDA.This approach performs frequency domain transformation on the received signal and obtains the optimal transformation parameter by minimizing the p-norm of an error matrix.Moreover,the proposed approach extends the application of OPDA from a white source to a bandpass white source or chirp signal.Theoretical formulas and simulation results show that the proposed approach not only reduces the estimation error but also accelerates the algorithm in a bandpass system,thus being highly feasible in practical blind system identification applications.
