Digital signal processing

spectral leakage

Spectral leakage is what happens when a single pure tone, analyzed by a DFT, refuses to stay in a single frequency bin and instead 'leaks' a halo of energy into all the bins around it. Picture spilling a drop of ink that should make one clean dot but instead bleeds into a fuzzy blotch. The cause is that the DFT silently assumes your finite recording loops seamlessly — and if the tone doesn't complete a whole number of cycles inside the window, the join is a sudden jump that masquerades as extra frequencies.

The damage is practical: leakage from a strong signal can completely hide a weak one sitting at a nearby frequency, ruining the measurement. Two cures exist. The first is windowing — taper the ends so the wrap-around discontinuity disappears. The second, where you control the source, is to pick the record length so the tone lands exactly on a bin (coherent sampling), making the leakage vanish entirely.

A tone falling between bins leaks across the spectrum.

A related artifact is scalloping loss: even a perfectly windowed tone landing between two bins reads a few dB lower in amplitude than one landing dead-centre, because the bins sample the window's frequency response at fixed points.

Also called
frequency leakage頻率洩漏