# Window Function Choices

November 8, 2018

Mathematicians and data scientists have developed a range of window functions. Users should select the function that best fits their application or the purpose of their analysis.

### Common Window Selection Choices

If the goal is to display the exact amplitude of a signal, the optimal choice is the flat top window as it exhibits the best amplitude resolution.

If analysis involves searching for the exact frequency of the peaks of a signal, and if the signal has the length needed to avoid discontinuities, then the rectangular window is ideal.

For general purpose analysis, the BlackmanHamming, and Hanning windows perform well. Each has advantages and disadvantages in relation to the others.

For example, Hamming has a superior side lobe height to the Hanning, but an inferior side lobe roll-off rate. The Blackman has a superior side lobe roll-off rate to the Hanning and a superior side lobe height to both Hanning and Hamming. As a result, it has a wider main lobe width than both.

### Examples of Using Selection Criteria

#### Signals Close in the Frequency Domain

If two signals are very close in the frequency domain (ex. 50Hz and 51Hz), then the analysis is best served by a window function with a narrow main lobe width. This will deliver better selectivity for finding closely spaced signals. In addition, a lower side lobe height will be more important than a superior side lobe roll-off rate. For this example, the Blackman is ruled out because it has a wider main lobe width. Between the Hamming and Hanning, the Hamming is preferable because it has the lower side lobe height.

#### Signals Far in the Frequency Domain

If analysis involves two signals that are far apart (ex. 50Hz and 1000Hz), the main lobe width is least important, and the side lobe roll-off rate is more important than the side lobe height. In this example, Blackman is the best choice because it has a superior side lobe roll-off rate and side lobe height (detection capability). This is, however, at the cost of its somewhat inferior main lobe width (frequency resolution).

### Other Window Options

While Blackman, Hanning, and Hamming are the most commonly used window functions, there are over 40 other options in the VibrationVIEW and ObserVIEW software tools. The next lesson, Tables of Window Function Details, provides more information on all these functions.