Understanding the Hanning Window

Definition: What is a Hanning Window?

The Hanning window is a specific type of mathematical function applied to a block of time waveform data before it is processed by a Fast Fourier Transform (FFT). It is one of the most commonly used windowing functions in vibration analysis. The purpose of the Hanning window is to minimize an error known as spectral leakage.

The window has a smooth, bell-like shape. When multiplied with the time signal, it forces the signal to be zero at the very beginning and end of the time block and leaves the center of the signal unchanged. This tapering process ensures that the sample block does not contain sharp, artificial discontinuities at its boundaries.

Why is a Hanning Window Necessary? (Spectral Leakage)

The FFT algorithm fundamentally assumes that the finite block of time data it is analyzing represents one perfect, repeating cycle of the signal. This assumption is only true if a whole number of cycles of every frequency component fits exactly into the time block. In a real-world signal from a rotating machine, this is almost never the case.

When a non-integer number of cycles is captured, the end of the time block does not match up with the beginning. The FFT sees this mismatch as a sharp jump or discontinuity. This artificial discontinuity contains energy that is not part of the real signal, and this energy “leaks” out into the surrounding frequency bins in the FFT spectrum. This leakage can:

• Cause a single, sharp frequency peak to appear as a broad, smeared peak, making it difficult to pinpoint the exact frequency.
• Obscure low-amplitude signals that are close in frequency to high-amplitude signals.

How the Hanning Window Solves the Problem

By forcing the signal to zero at the boundaries of the time block, the Hanning window removes the artificial discontinuity. The FFT now sees a smoothly transitioning, periodic signal, which it can process much more accurately. The result is a significant reduction in spectral leakage, leading to:

• Improved Frequency Resolution: The smearing effect is reduced, and frequency peaks in the spectrum become sharper and more clearly defined.
• Improved Amplitude Accuracy: While the window slightly reduces the overall peak amplitude (a known correction factor is applied by the analyzer to compensate), the amplitude reading at the correct frequency bin is more accurate because less energy has leaked into adjacent bins.

When to Use a Hanning Window

The Hanning window is the default, general-purpose window for most steady-state machinery vibration analysis. It provides a very good compromise between frequency resolution (how well you can separate close-together frequencies) and amplitude accuracy. It should be used for the vast majority of routine FFT measurements on machines like motors, pumps, fans, and compressors.

Other windows, like the Flattop (for high amplitude accuracy) or Uniform (for transient events), are used for more specialized applications, but Hanning is the standard choice for general diagnostics.

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