Technological advances in instrumentation have led to an exponential increase in exoplanet detection and scrutiny of stellar features such as spots and faculae. While the spots and faculae enable us to understand the stellar dynamics, exoplanets provide us with a glimpse into stellar evolution. While the ubiquity of noise (e.g., telluric, instrumental, or photonic) is unavoidable, combining this with increased spectrographic resolution compounds technological challenges. To account for these noise sources and resolution issues, we use a temporal multifractal framework to study data from the Spot Oscillation And Planet 2.0 tool, which simulates a stellar spectrum in the presence of a spot, a facula or a planet. Given these controlled simulations, we vary the resolution as well as the signal-to-noise ratio (S/N) to obtain a lower limit on the resolution and S/N required to robustly detect features. We show that a spot and a facula with a 1% coverage of the stellar disk can be robustly detected for a S/N (per pixel) of 35 and 60, respectively, for any spectral resolution above 20,000, while a planet with a radial velocity of 10 m s(-1) can be detected for a S/N (per pixel) of 600. Rather than viewing noise as an impediment, our approach uses noise as a source of information.