Leakage

In a Fourier Transform the signal is assumed to be periodic.

Therefore, a continuous sine wave

pure sine wave in the time domain

will transform to a single spectral line in the frequency domain

single spectral line in the frequency domain

However, in the case of the Discrete Fourier Transform a finite section of the time history is transformed. If a pure sine wave does not repeat exactly within the time window, it is truncated.

windowed section of time history

the windowed section of the time history is assumed to repeat

repeated windowed section of the time history

This truncation will lead to the frequency domain resultant being smeared (leakage) and not a single frequency.

smeared result in the frequency domain

This phenomenon is called leakage; the signal energy essentially "leaks" from a single FFT line to adjacent lines. Leakage reduces the accuracy of the measured levels of peaks in the spectrum, and reduces the effective frequency resolution of the analysis.

Leakage is worst for continuous signals and rectangular window, and it is greatly reduced by use of the Hanning window, which forces the signal level to zero at the ends of the data block.

See also: Bohman Window, Discrete Fourier Transform, Fast Fourier Transform, Fourier Transform, Hamming Window, Hanning Window, Windowing.

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Subjects: Noise & Vibration Signal Processing