Abstract: For multi-dimensional temporal-spatial data, EEMD is applied to time series of each spatial location to obtain IMF-like components of different time scales. All the ith IMF-like components of all the time series of all spatial locations are arranged to obtain ith temporal-spatial multi-dimensional IMF-like component. For two-dimensional spatial data or images, the two-dimensional spatial data or images are consider as a collection of one-dimensional series in first direction along locations in second direction. The same approach to the one used in temporal-spatial data decomposition is used to obtain the resulting two-dimensional IMF-like components. Each of the resulted IMF-like components are taken as the new two-dimensional data for further decomposition, but the data is considered as a collection of one-dimensional series in second-direction along locations in first-direction.

Abstract: A degree of nonlinearity based on intra-wave frequency modulation is proposed here with the value substantially between 0 and 1. The degree of nonlinearity is used for obtaining the state rather than a system. The data required for defining the degree of nonlinearity is the state of the motion or the observed data. For a complicate state with more than one IMF containing prominent energy density, the degree of nonlinearity has also considered the amplitude variations. The combination of the intra-wave frequency modulation and the amplitude variation gives the Combined Degree of nonlinearity. With the definitions of degree of nonlinearity, the nonlinearity characteristic can be quantified, and the discussion of nonlinear effects could be conducted more precisely.

Abstract: A degree of nonlinearity based on intra-wave frequency modulation is proposed here with the value substantially between 0 and 1. The degree of nonlinearity is used for obtaining the state rather than a system. The data required for defining the degree of nonlinearity is the state of the motion or the observed data. For a complicate state with more than one IMF containing prominent energy density, the degree of nonlinearity has also considered the amplitude variations. The combination of the intra-wave frequency modulation and the amplitude variation gives the Combined Degree of nonlinearity. With the definitions of degree of nonlinearity, the nonlinearity characteristic can be quantified, and the discussion of nonlinear effects could be conducted more precisely.

Abstract: For multi-dimensional temporal-spatial data, EEMD is applied to time series of each spatial location to obtain IMF-like components of different time scales. All the ith IMF-like components of all the time series of all spatial locations are arranged to obtain ith temporal-spatial multi-dimensional IMF-like component. For two-dimensional spatial data or images, the two-dimensional spatial data or images are consider as a collection of one-dimensional series in first direction along locations in second direction. The same approach to the one used in temporal-spatial data decomposition is used to obtain the resulting two-dimensional IMF-like components. Each of the resulted IMF-like components are taken as the new two-dimensional data for further decomposition, but the data is considered as a collection of one-dimensional series in second-direction along locations in first-direction.