Mathematical tools, including the Fast Fourier Transform (FFT), the Short-Time Fourier Transform (STFT), the Continuous Wavelet Transform (CWT), and spectrograms, were applied to analyze engine vibrations under various operating conditions. These methods allow both visual and quantitative evaluation of signals, with parameters such as standard deviation (SD) and peak values serving as indicators of vibrational behavior. The FFT enabled the transformation of time-domain signals into the frequency domain, revealing the correlation between motor speed and amplitude, which peaked at 2500 rpm due to increased fuel demand. However, to capture transient events and non-stationary signals, complementary tools were required. STFT spectrograms provided time–frequency insights but were limited in distinguishing noise sources, while CWT spectrograms, especially on a logarithmic frequency scale, proved more effective in identifying combustion events and piston knock. Two- and three-dimensional spectrograms highlighted distinct vibrational phenomena: combustion peaks between 1400 and 1600 Hz, unwanted signals at 200–400 Hz, and the characteristic sequence of peaks associated with the combustion cycle, exhaust release, and intake-compression stages. Quantitative analysis showed that SD and peak values are reliable indicators of operational stability and filter condition, with SD increasing by up to 50% between 1500 and 2500 rpm under efficient operation. Moreover, using well-maintained filters improved efficiency, reducing fuel consumption by 40.78% and decreasing HC and NOx emissions by 68.58% and 22.25%, respectively. These results demonstrate that vibrational analysis, through advanced signal-processing techniques, can serve as a non-invasive tool for performance optimization and preventive maintenance.