EOFs of harmonizable cyclostationary processes
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While approximate cyclostationary processes are commonly found in climatic and geophysical studies, one great disincentive for using cyclostationary empirical orthogonal functions is their computational burden. This is especially so for the three-dimensional, space-time case. This paper discusses a simple method of computing approximate cyclostationary empirical orthogonal functions based on the theory of harmonizable cyclostationary processes. The new method is computationally much more efficient than that of Kim et al. In the new method, cyclostationary empirical orthogonal functions are easier to understand. Namely, they are naturally defined as the products of Bloch functions (inner modes) and Fourier functions (outer modes), which otherwise are the result of the factorization theorem. Bloch functions are simply the principal components (PC) of the multivariate coefficient time series, which are generally correlated. They represent the normal modes of the nested fluctuations of harmonizable cyclostationary processes. Under the assumption of independent PC time series, Bloch functions are computed independently of the outer modes, which results in a tremendous speedup in computation.
