The FFT implicitly assumes that its input is periodic. In reality this is almost never the case – we cut a finite section out of a continuous signal. This cut creates a jump at the frame edges, which shows up as the leakage effect: sharp frequency lines become broad, smeared mountains.
Leakage in concrete terms
Example: pure 1 kHz sinusoid sampled at fs = 51.2 kHz, N = 8,192. Resolution Δf = 6.25 Hz. If the 1 kHz line falls exactly on a bin, you see a clean peak. If it falls between bins (e.g. 1,003 Hz), the energy smears over 5–10 bins. A weaker nearby line drowns in leakage noise.
The cure: smooth roll-off
The window function smoothly tapers the frame to zero at both ends so no jump remains. Price: signal weighted more in the middle, frequency resolution broadens.
The most important windows
Rectangle: no window. Narrowest main lobe, strong side lobes (−13 dB). Only useful for naturally periodic signals.
Hann: w(n) = 0.5 · (1 − cos(2π n / (N−1))). Classic for general spectral analysis. Main lobe 1.5× wider, side lobes −31 dB.
Hamming: w(n) = 0.54 − 0.46 · cos(2π n / (N−1)). Side lobes −43 dB.
Blackman-Harris: very strong side lobe attenuation (< −90 dB), main lobe 4× wider.
Flat-Top: optimised for amplitude measurement. Main lobe 5× wider, amplitude error < 0.01 dB.
Comparison matrix
| Window | Main lobe | Highest side lobe | Amplitude error | Use |
|---|---|---|---|---|
| Rectangle | 1.0 | −13 dB | 3.9 dB max | periodic signals |
| Hann | 1.5 | −31 dB | 1.5 dB max | NVH default |
| Hamming | 1.4 | −43 dB | 1.7 dB max | communications |
| Blackman-Harris | 4.0 | −92 dB | 0.8 dB max | weak next to strong |
| Flat-Top | 5.0 | −70 dB | < 0.01 dB | amplitude measurement |
Decision guide
- Resonance detection: Hann or Blackman-Harris.
- Order analysis on motors: Hann (default).
- Calibration / level measurement: Flat-Top.
- Triggered hammer excitation: Rectangle (signal naturally decays).
