### Frequency analysis FFT

Frequency analysis, when properly applied, overcomes the limitations of time-domain analysis and serves as a valuable method for identifying emerging faults in specific components of the monitored machine through the analysis of vibration data.

By performing a complete frequency analysis, the amplitude and phase spectrum of the signal are obtained. The foundation of frequency analysis lies mainly in the Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT). The time-varying signal X(t) is acquired through measurements (e.g., acceleration of a vibrational motion) and further processed numerically. In the time domain, the signal is sampled using an analog-to-digital converter, meaning its values are determined at moments spaced by a typically regular sampling period.