Vibroacoustic analysis of mechanical systems has an important role in the engineering discipline. This can be used as a monitoring tool to obtain insights about the condition of a system, identify its probable defects, and determine the time window that the maintenance should happen. This article introduces the basics of signal processing in time, frequency, and time-frequency domains. It focuses on statistical analysis of the time-domain data. Various measures of data distribution and variability are pointed out. Important signal-processing functions in the frequency domain are presented and explained with examples. The article discusses and clarifies the benefits of time-frequency domain based on short-time Fourier transform with some practical applications. The article presents the most frequently used statistical functions. It concludes with information on some real-world applications of vibroacoustic analysis.