Window Function Characteristics

November 8, 2018

The following are several characteristics used to describe a window function.

Window Function Characteristics

Main Lobe Width

The measure of the main lobe width at -3dB or -6dB below the main lobe peak. When the main lobe width decreases, the remaining energy spreads out to the side lobes and thereby increases spectral leakage/decreases amplitude accuracy (“detection” ability). A compromise is needed to find the balance between detection and resolution fitting for a given application.

Side Lobes

Side lobes occur at either side of the main lobe. They approach zero at integral multiples of Fs/N where Fs=sampling frequency and N is the length of N-point FFT/DFT. Side lobes directly affect the extent to which the adjacent frequency components leak into the adjacent frequency bins.

Side Lobe Height

The side lobe height is usually measured for the side lobe with the maximum peak compared to other side lobes. It is measured in decibels relative to the peak of the main lobe.

window function characteristics graph

Side Lobe Roll-off Rate

The asymptotic decay rate in decibels per decade of the frequency of the side lobes’ peaks.

Note: Main lobe width and side lobe levels can be evaluated by visual inspection of the windows’ frequency response.

In an ideal window function the:

  • Main lobe width is small (high-frequency resolution)
  • Side lobe level is high (good noise suppression, high detection ability)
  • Side lobe roll-off rate is high

Equivalent Noise Bandwidth (ENBW)

The equivalent width of a rectangular filter that passes the same amount of white noise as the window.