Understanding Spectral Leakage

Definition: What is Spectral Leakage?

Spectral leakage is a form of measurement error that occurs during the Fast Fourier Transform (FFT) analysis of a signal. It is the “smearing” or spreading of energy from a single, discrete frequency peak into adjacent frequency bins. This leakage can distort the amplitude and frequency of the true vibration signal, potentially masking smaller signals or leading to an inaccurate diagnosis.

The Root Cause: Discontinuity

Spectral leakage is caused by a violation of the FFT’s fundamental assumption. The FFT algorithm assumes that the finite block of time waveform data it analyzes is a single, perfectly repeating cycle of a periodic signal. To be perfectly periodic, the signal’s value at the very end of the time block must be identical to its value at the very beginning.

In practice, when analyzing a real-world vibration signal, it is almost impossible to capture a time block that contains an exact integer number of cycles for every frequency component. This results in a discontinuity where the end of the signal does not match the beginning. The FFT algorithm interprets this sharp jump as a high-frequency transient event, similar to an impact. This artificial transient contains energy that is not part of the original signal, and it is this energy that “leaks” out across a wide range of frequencies in the resulting spectrum.

The Effects of Spectral Leakage

The smearing of energy caused by spectral leakage has two main negative effects:

1. Reduced Amplitude Accuracy: The energy that should have been concentrated in a single frequency bin is now spread out among many. This causes the amplitude of the main peak to be lower than its true value, while the amplitudes of the adjacent “sidelobe” bins are artificially raised.
2. Reduced Frequency Resolution: The leakage can be so severe that it completely hides smaller, nearby frequency peaks. A small signal from a bearing fault, for example, could be completely lost in the “skirt” of the leakage from a large 1X unbalance peak.

The Solution: Windowing

Spectral leakage is controlled by using windowing functions. A window is a mathematical function that is multiplied with the time waveform data *before* it is sent to the FFT.

The most common window used for this purpose is the Hanning window. The Hanning window has a smooth, bell shape that tapers the signal down to zero at both the beginning and the end of the time block. This tapering action forces the ends of the signal to match, effectively eliminating the artificial discontinuity.

By presenting the FFT with a smoothly periodic signal, the windowing function dramatically reduces spectral leakage. This results in a much cleaner spectrum with sharper peaks and a lower noise floor, allowing for more accurate and sensitive analysis.

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