We study analytic forms in Fourier space of one-dimensional height-height correlation functions for self-affine rough surfaces. Comparisons with complex systems suggest three alternative models. However, only the model C1(k) ∝ (1 + a|k|ξ)^-(1+2H) permits analytic calculation of important surface roughness quantities (i.e. surface width) for roughness exponents in range 0 ≤ H ≤ 1. Furthermore, the implications of the results to experimental roughness studies by means of STM-AFM are discussed.