What an FFT actually sees

A vibration signal from a machine looks like a mess in the time domain. But most of that mess is a handful of sine waves stacked on top of each other: running speed, its harmonics, blade pass, gear mesh. The FFT's job is to pull those sine waves apart and tell you how big each one is.

Below is a signal built from two components plus random noise. Change them and watch both views update. A few things to try:

• Push the noise up until the time waveform is unreadable. The peaks in the spectrum stay clear long after the waveform stops making sense.
• Set a frequency that doesn't land exactly on a bin, then toggle the Hann window. Without a window, energy smears into the neighbouring bins (leakage).
• Move the two frequencies close together. When they're closer than the bin spacing, the FFT can no longer separate them.

The idea in one line

The FFT compares your signal against a sine wave at every bin frequency. Where the signal and the sine line up, the comparison gives a big number; where they don't, it averages out to nearly zero. Noise is random, so it doesn't line up with anything for long, which is why it spreads thinly across all bins instead of forming peaks.

Why it matters in the field

The bin spacing is the sample rate divided by the number of samples, so resolution costs measurement time. Separating two close frequencies (say running speed and line frequency on a 2-pole motor) means a longer capture, not a faster one. And without a window, a peak that falls between bins reads lower than it really is, which can make a real defect look smaller than it is.

Downloads

• fft_demo.py · the same experiment in Python (NumPy + Matplotlib)