Signals and Telecommunication Journal Hsing-Cheng Liu 15 2 2026 https://doi.org/10.6025/stj/2026/15/2/45-63 https://www.dline.info/stj/fulltext/v15n2/stjv15n2_1.pdf Characterizing long range dependence (LRD) and statistical self similarity in complex systems relies heavily on accurately estimating the scaling parameters of fractional Gaussian noise (fGn). However, empirical observations are inherently finite, and short observation windows severely constrain frequency resolution, introducing spectral leakage and estimation variance that obscure intrinsic fractal scaling. This study systematically investigates the finite sample effects on the spectral characterization and power law convergence of fGn. We developed a controlled, scalable benchmark using synthetic fGn realizations across four dyadic lengths (N = 64 to 65,536). By employing dual spectral estimators Welch’s averaged periodogram and the raw Fast Fourier Transform we tracked the evolution of the spectral exponent, goodness of fit, and confidence intervals. Our results demonstrate a non-linear transition from noise dominated, white like spectra in short records to asymptotic power law scaling in longer sequences. For the shortest realizations, estimation variance dominates, yielding statistically fragile exponents. Conversely, as sample size increases to N  4096, the spectral exponents stabilize near 0.68 (corresponding to a persistent Hurst exponent of ~0.84), with R² values exceeding 0.75 and significantly narrowed confidence intervals. The concordance between smoothed and unsmoothed spectral representations confirms the robustness of this convergence. Ultimately, this work quantifies the minimum observational requirements necessary to reliably distinguish true fractal scaling from finite data artifacts, providing a rigorous reference framework for the spectral analysis of longmemory stochastic processes in complex systems.