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. Moreover, the most recent topics and applications of the Proper Orthogonal Decomposition and its Proper Transformation in the wind engineering will be emphasized and discussed in this paper as follows: (1) Analysis and synthesis, identification of the multi-variate dynamic pressure fields; (2) Digital simulation of the multi-variate random turbulent wind fields and (3) Stochastic response prediction of structures due to the turbulent wind flows. All applications of the Proper Orthogonal Decomposition and its Proper Transformations will be investigated under numerical examples, especially will be formulated in both time domain and the frequency domain.
