Downhole characterization of formation pressure

A method includes operating a downhole acquisition tool in a wellbore in a geological formation and performing formation testing to determine at least one measurement associated within the formation, the wellbore, or both. The tool may include sensors to detect measurements including, for example, formation pressure and/or wellbore pressure. The tool may also include a processor to obtain at least one spectral characteristic associated with the measurement, which may include frequencies of oscillation. The processor may also determine one or more parameters, associated with an oscillation suppression process, based on the spectral characteristic and remove oscillations, including noise associated with fluctuations of a fluid level in the wellbore, in the measurement based on the parameters. Petrophysical parameters may be estimated based on the modified measurement.