What is "leakage error"?

Input of time signal is generally continuous signals which last infinitely. FFT processing is performed by using the finite time length T which is cut out from the time window length T.
In the FFT calculation, the time waveform is treated as that the finite time length T cut out from the real signal is repeated. So when T is an integral multiple of the input signal period, the repeated waveform becomes continuous and the correct spectrum is obtained.
However, if it is not, the waveform becomes discontinuous before and after the repetition point, causing distortion in the waveform, and spreading the distortion around the frequency in the spectrum. As a result, the magnitude of the peak of the spectrum is decreased compared to the true value, and the power corresponding to the decreases (equivalent to the magnitude) is leaked to both sides. Cutting out the finite time length T from the real signal is called applying time window (window), and the spread of this spectrum is called leakage error. The practical big problem caused by the error like this is that the small peak is hidden by the frequency component with large power nearby. So it is necessary to devise to reduce the leakage error as much as possible.


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