The objective of this paper is to exhibit the construction of compactly supported orthonormal symmetric scaling functions with scaling factor a=4 and the three corresponding compactly supported orthonormal wavelets,on...The objective of this paper is to exhibit the construction of compactly supported orthonormal symmetric scaling functions with scaling factor a=4 and the three corresponding compactly supported orthonormal wavelets,one of which is symmetric and the others are antisymmetric. The orthonormal wavelets of L2(R) isn’t unique. It is possible to choose "good" base from a lot of wavelets base. Examples of scaling functions and wavelets are given.展开更多
In this paper,we displayed one-dimensional climate signals,such as global temperature variation,Southern Oscillation Index and variation of external forcing factors,on a two- dimensional time-scale plane using compact...In this paper,we displayed one-dimensional climate signals,such as global temperature variation,Southern Oscillation Index and variation of external forcing factors,on a two- dimensional time-scale plane using compactly supported wavelet decomposition.Using the lag- correlation analysis method,and interpretative variance analysis method,and phase comparison method to the wavelet analysis result,we not only gained the variation on different scales to the global temperature and El Nino signals,the location of the jump point and intrinsic scale of these series,but also indicated the magnitude,extent and time of the effect of external forcing factors on them.We also put forward reasonable explanation to the main variation of recent 140 years.展开更多
文摘The objective of this paper is to exhibit the construction of compactly supported orthonormal symmetric scaling functions with scaling factor a=4 and the three corresponding compactly supported orthonormal wavelets,one of which is symmetric and the others are antisymmetric. The orthonormal wavelets of L2(R) isn’t unique. It is possible to choose "good" base from a lot of wavelets base. Examples of scaling functions and wavelets are given.
文摘In this paper,we displayed one-dimensional climate signals,such as global temperature variation,Southern Oscillation Index and variation of external forcing factors,on a two- dimensional time-scale plane using compactly supported wavelet decomposition.Using the lag- correlation analysis method,and interpretative variance analysis method,and phase comparison method to the wavelet analysis result,we not only gained the variation on different scales to the global temperature and El Nino signals,the location of the jump point and intrinsic scale of these series,but also indicated the magnitude,extent and time of the effect of external forcing factors on them.We also put forward reasonable explanation to the main variation of recent 140 years.
