Insights about aliasing and spectral leakage when analyzing discrete-time finite viscoelastic functions

Material property viscoelastic inversion studies often rely on the continuous -time framework for Fourier analysis, which may not accurately represent real experimentally collected data. In this paper, we address discrete and finite nature of functions obtained from experiments discuss impact these characteristics frequency spectrum analysis. We derive equations Discrete-Time Transform (DTFT) a discrete-finite stress relaxation signal corresponding to generalized Maxwell model. Our analysis highlights limitations traditional in capturing inherent features signals, are nature. This results two phenomena: aliasing spectral leakage. present that consider phenomena, allowing experimentalists anticipate account leakage when performing model fitting. The proposed approach provides more accurate representation data, enabling researchers make better-informed decisions interpretation sample functions.