MATLAB FFT Transformation from Acceleration Time History to Displacement

The article discusses using MATLAB's FFT (Fast Fourier Transform) for converting acceleration time history to displacement. To elaborate on this process, let's first explain that FFT is an algorithm for transforming time-domain signals into frequency-domain representations. Through FFT implementation, we can obtain spectral information for both acceleration time history and displacement data, which proves highly valuable for subsequent signal analysis and processing. In MATLAB implementation, the typical workflow involves: 1. Applying FFT to the acceleration signal using fft() function to obtain frequency components 2. Converting acceleration to displacement in frequency domain by dividing by (jω)² (where ω represents angular frequency) 3. Applying inverse FFT using ifft() function to transform back to time domain The key mathematical relationship utilized is: Displacement(ω) = Acceleration(ω) / (-ω²), which requires careful handling of DC components and proper phase management during the transformation process. Therefore, employing MATLAB's FFT for acceleration-to-displacement conversion represents a standard and effective methodology in signal processing applications, particularly in structural dynamics and vibration analysis. The approach requires proper windowing techniques and sampling frequency considerations to ensure accurate results.