in Practice
A pure tone should be a single bin. It rarely is — its energy smears across the neighbours. This lesson is about what leakage does to a measurement, and how to control it.
A finite window convolves every spectral line with the window’s own spectrum. Reading a peak, you must ask why it looks the way it does:
- Genuinely weak — or buried under a neighbour’s leakage?
- On a bin — or scalloped low between two?
- A real noise floor — or the window’s sidelobes?
Land the tone exactly on a bin and every other bin sits on a zero of the window spectrum — zero leakage. Works only when you control the signal.
A tone between bins is measured on the main lobe’s skirt, so it reads low — a predictable bias, not noise. A flatter window scallops less.
Each bin passes a band of noise. ENBW is the ideal rectangular width passing the same power — the factor that calibrates a windowed DFT into a PSD in W/Hz.
Harris (1978): taper harder and the sidelobes plunge, but the main lobe widens and the ENBW grows.
- Rectangular — sidelobes −13 dB, ENBW 1.00
- Hann — −32 dB, ENBW 1.50
- Blackman — −58 dB, ENBW 1.73
- Blackman-Harris — −92 dB, ENBW 2.00 (a tone 90 dB down becomes visible)
- Control the source? Sample coherently — leakage gone, no penalty
- Need amplitude? Flat-top window (<0.1 dB scalloping)
- Weak tone beside a strong one? Blackman-Harris / high-β Kaiser
- Absolute levels? Correct for coherent gain (Σw) and ENBW
- Leakage = finite window: one line becomes a copy of the window’s spectrum
- Coherent sampling (f₀ = k·f_s/N) → zero leakage, if you control the signal
- Scalloping loss: 3.92 dB (rectangular) down to <0.1 dB (flat-top)
- ENBW calibrates a windowed DFT into a PSD in W/Hz
- A window trades resolution against sidelobes and amplitude accuracy