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In this paper, we present a new approach to derive series expansions for someGaussian processes based on harmonic analysis of their covariance function. Inparticular, we propose a new simple rate-optimal series expansion forfractional Brownian motion. The convergence of the latter series holds in meansquare and uniformly almost surely, with a rate-optimal decay of the remainderof the series. We also develop a general framework of convergent seriesexpansions for certain classes of Gaussian processes with stationarity.Finally, an application to optimal functional quantization is described.

Harmonic analysis meets stationarity: A general framework for series expansions of special Gaussian processes