Windowing in Frequency Domain

In the previous post we dealt with the windowing technique in general. And if we remember windowing technique may be applied to both time domain data and frequency domain data.

However, in the frequency domain, a window acts like a filter. The amplitude of each frequency bin is determined by centering this filter on each bin and measuring how much of the signal falls within the filter. It just acts like a physical window through which we see the world outside our rooms. Through a window we can see directly what is across the window but would not be able to see much outside the frame of window if we stand behind a window at some distance.

So, if the filter or window is narrow, only frequencies near the bin will contribute to the bin. A narrow filter is called a selective window. It selects a small range of frequencies around each bin. However, since the filter is narrow, it falls off from center rapidly. This means that even frequencies close to the bin may be attenuated somewhat. This area is called the ‘skirt’ area of a window. It actually hides the frequencies falling in this area.

But if the filter is wide, frequencies far from the bin will contribute to the bin amplitude, but those close by will not be attenuated significantly. The net result of windowing is to reduce the amount of smearing in the spectrum from signals not exactly periodic with the time record. This is an important feature that we look for. Because smearing makes it difficult to see the phenomenon clearly in terms of amplitude and the frequencies that contribute to the amplitude.

There are different types of windows to select from. The different types of windows trade off selectivity, amplitude accuracy and noise floor. There are several window functions such as Uniform (none), Flattop, Hanning, BlackmanHarris and Kaiser, of which most analysts use the Hanning window.

The basic parameter that governs the selection of a window depends on the nature of analysis we want to do. For example, if we are interested to analyse machinery problems we generally use Hanning window. Whereas when we are interested to see transients, which do not fill the entire time record, we would use an Uniform window for the purpose. Similarly, when we are interested to observe the natural frequencies of a system through say “bump test” we would prefer a Flattop window.

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