The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT), which converts a signal from the time domain to the frequency domain. It is the fundamental computational tool for frequency-domain analysis in structural dynamics, SHM, and signal processing.
The Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence with dramatically reduced computational cost. The DFT of a sequence of N samples requires O(NΒ²) operations in its direct form; the FFT reduces this to O(N log N) β a difference that becomes enormous for large datasets. For N = 1 million, the DFT requires ~10ΒΉΒ² operations, while the FFT requires ~2 Γ 10β· β a factor of 50,000 improvement. This efficiency is what makes frequency-domain analysis practical for real-world signal processing, including the analysis of structural vibration data, seismic records, and SHM measurements.
The FFT is the fundamental tool for transforming vibration measurements into the frequency domain, where structural dynamics and modal properties become apparent. In structural dynamics, the FFT is used to compute the power spectral density (PSD) of a measured response, revealing the frequency content of the signal. Peaks in the PSD correspond to the structure's natural frequencies, and their widths provide information about damping. The FFT is the first step in most frequency-domain modal identification methods β including peak picking, frequency domain decomposition (FDD), and enhanced FDD (EFDD) β that are the foundation of operational modal analysis (OMA). In earthquake engineering, the FFT is used to compute response spectra, to characterize ground motion frequency content, and to analyze the effects of site conditions on ground motion. In SHM, FFT-based spectral analysis is used for damage detection (identifying changes in modal frequencies), for system identification, and for processing large volumes of continuous monitoring data.
The FFT is a numerical tool with important practical considerations. The choice of windowing function (Hanning, Hamming, Blackman, etc.) affects the spectral estimate and must be matched to the signal characteristics. The choice of FFT length (number of samples) determines the frequency resolution: longer records give finer frequency resolution but are more affected by non-stationarity. Zero-padding can improve the visual appearance of the spectrum but does not increase the true resolution. Leakage β the spreading of spectral energy to adjacent frequencies β is a common artifact that is mitigated by windowing. Modern practice typically uses the FFT as part of a more comprehensive spectral analysis framework β including averaging, overlapping segments (Welch's method), and appropriate preprocessing (detrending, filtering). The FFT is not the only spectral analysis tool: alternatives such as the chirp-Z transform, wavelet transform, and Hilbert-Huang transform are used for non-stationary or non-linear signals. In earthquake engineering, the wavelet transform in particular has become increasingly popular because ground motions and structural responses are inherently non-stationary (their frequency content evolves over time). In Iran, FFT and its derivatives are standard tools in structural dynamics research and practice, and are increasingly used as part of SHM systems for automated modal identification and damage detection.