Spectral leakage

Spectral leakage is the spreading of a signal's power from its true frequency into neighbouring bins, caused by analysing a finite record. Truncating a signal to a window of length T is equivalent to multiplying by a rectangular window, which convolves the true spectrum with the window's Fourier transform, a sinc-like kernel with a narrow main lobe and slowly decaying side lobes (only about minus 13 dB for a rectangular window). Strong low-frequency or line-noise components then leak into weak high-frequency bands and can masquerade as physiological rhythms.

Tapering the segment with a smooth function such as a Hann, Hamming or Slepian window suppresses the side lobes at the cost of a wider main lobe, that is, worse frequency resolution. This resolution-versus-leakage tradeoff is unavoidable and underlies the design of every spectral estimator. The half-width of the main lobe sets the smallest frequency separation two peaks can have and still be resolved.