Power Spectral Density and Self-similarity (if present) are two essential features of a signal. The first one determines the power levels of the frequency components present in a signal. In contrast, the second one (if present) in a signal signifies the repetitions of its statistical properties from the microphase to the macro phase. In this respect, searching for the internal relationship between these two aspects is quite fascinating. Some study has already been made in this regard, revealing a linear relationship between the power index (which appears as the index of the power law relation between power spectral density and frequency) and the Hurst exponent (which appears as a scaling index of a self-similar signal). This paper explores the relationship between Power Spectral Density (PSD) and self-similarity in signals, highlighting their distinct roles. It questions the prevailing linear model linking the Power Index, which quantifies the PSD, and the Hurst Exponent, which quantifies the self-similarity. In the present work, we demonstrate that this conventional linear relationship does not hold well at certain levels. Alternatively, it has been experimentally found that a 4th order polynomial relationship fits better at all feasible proximities for Fractional Brownian Motion and Fractional Gaussian Noise and accordingly, an appropriate model has been obtained.