Welch Took 3.4x Longer Than FFT — But Found the Fault
I ran the same 10-second vibration signal through FFT, Welch's method, and STFT to see which could catch a bearing fault while staying under 100ms latency. FFT finished in 0.8ms. Welch needed 2.7ms. STFT with 256-sample windows hit 5.1ms.
But here's the twist: FFT's spectrum was so noisy I couldn't tell inner race fault peaks from background rumble. Welch smoothed it just enough to see the 162 Hz BPFI modulation riding on a 3600 RPM shaft. STFT showed me when the fault amplitude spiked during load changes — something the other two couldn't.
This isn't an academic comparison. It's what happens when you wire up a MEMS accelerometer to a $40 bearing test rig, sample at 10 kHz, and try to ship a fault detector that runs on a Raspberry Pi 4 without choking.
Why Speed Matters in Vibration Monitoring
Most PHM textbooks skip the compute budget conversation. They show you gorgeous spectrograms from MATLAB, then you try to run the same analysis in a PLC loop and blow your 50ms cycle time.
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