A linear decomposition of stationary random processes into uncorrelated and completely correlated components
Gianfranco Cariolaro · IEEE Transactions on Information Theory · 1968
This paper deals with a decomposition of a set of stationary random processes:x_{1}, x_{2}, \cdots, x_{n}. The decomposition has the form:x_{1} = y_{11}, x_{2} = y_{21} + y_{22}, x_{3} = y_{31} + y_{32} + y_{33}, etc., where the componentsy_{ij}have the following properties: for a fixedi, they are completely correlated in pairs; for a fixedj, they are uncorrelated in pairs. Assuming the spectral matrix of thex_{i}'s as known, the spectral description of they_{ij}'s given by a lower triangular matrix, is determined. This is achieved by both an iterative and a direct method. In both methods regular and singular cases are considered.