VNU Journal of Science, Mathematics - Physics 25 (2009) 21-38 Proper Orthogonal Decomposition and its Proper Transformations has been applied widely in many engineering topics including the wind engineering recently due to its advantage of optimum approximation of multi-variate random fields using the modal decomposition and limited number of dominantly orthogonal eigenvectors. This paper will present fundamentals of the Proper Orthogonal Decomposition and its Proper Transformations in both the time domain and the frequency domain based on both covariances matrix and cross spectral matrix branches. .
