Spectral Leakage
Spectral Leakage is a phenomenon that occurs when applying spectral transformations to finite segments of an indefinite signal. It causes leaking frequency components that would not be present if the whole signal would be known.
Sampling¶
When [[Sampling]], the time signal is multiplied with a [[Dirac Comb]]. This the same as convoluting the frequency with a Dirac Comb of the inverse period length. The frequencies of the time signal (upper graph) are thus copied at each dirac of the Dirac Comb (middle graph). If the period of the Dirac Comb isn't at least two times the highest frequency of the time signal, the copies at each dirac overlap. These overlaps add up in the convoluted signal, leading to frequencies not present in the original signals, so called aliasing effects (lower graph, marked in red). This is an example of spectral leakage when sampling.
Windowing¶
For more information: https://youtu.be/L02Yq5nJdn0?si=_MlwmsRCHCmyWA-L&t=203.
When applying a window to a time signal and then a Spectral Transformation, frequencies leak over the whole spectrum. This is because the spectral transformation considers the windowed fragment as if it was an infinite, periodically extended signal. If the window doesn't perfectly line up with the underlying period of the time signal, there will be jumps at the cut-off points in the periodically extended signal. A jump is like a short impulse and as known from the [[Dirac]], such a short impulse will contribute energy over all frequencies in the spectral domain.