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 the discrete and finite nature of viscoelastic functions obtained from experiments and discuss the impact of these characteristics on the frequency spectrum analysis. We derive equations for the Discrete-Time Fourier Transform (DTFT) of a discrete-finite stress relaxation signal corresponding to the relaxation of a generalized Maxwell model. Our analysis highlights the limitations of the traditional continuous -time framework in capturing the inherent features of real signals, which are discrete and finite in nature. This results in two phenomena: aliasing and spectral leakage. We present equations that consider these phenomena, allowing experimentalists to anticipate and account for aliasing and leakage when performing model fitting. The proposed discrete-finite approach provides a more accurate representation of real viscoelastic data, enabling researchers to make better-informed decisions in the analysis and interpretation of sample viscoelastic functions.