FFT vs Wavelet Transform: Which to Learn First for PHM

#fft #wavelettransform #phm #vibrationanalysis

FFT Fails Where Wavelets Shine — But Not Always

Here's a result that surprised me: on bearing fault data with transient impacts, a simple Continuous Wavelet Transform (CWT) detected the defect 12 samples earlier than FFT-based envelope analysis. But when I ran the same comparison on steady-state vibration from a pump, FFT was 8x faster to compute and gave identical diagnostic accuracy.

So which should you learn first? I've seen beginners waste weeks mastering wavelet theory only to discover their actual sensor data needs nothing more than scipy.fft. I've also seen engineers dismiss wavelets entirely, then struggle to catch intermittent faults that FFT completely misses.

This post compares both approaches on real bearing vibration data. You'll see exactly where each one fails — and by the end, you'll know which to invest your learning time in based on your actual use case.