The equivalent noise bandwidth (ENBW) for a window function is the bandwidth in bins of a brickwall filter that would result in the same noise power as the DFT "filter" (when viewing, appropriately, each bin of the DFT as a bandpass filter). The ENBW for the rectangular window (no further windowing) is 1 bin. The ENBW determined specifically from the following equation:

$$ENBW = N\frac{\sum (w[n])^2}{(\sum w[n])^2}$$

Where $ENBW$ is Equivalent Noise Bandwidth (in bins), and $w[n]$ is the window.

This is derived from $$\frac{\sigma_W+\mu_W^2}{\mu_W^2}$$

Where $\sigma_W$ is the variance of the window and $\mu_W$ is the mean of the window.

Further the processing gain of the window is given as

$$PG = -10\log_{10}(ENBW)$$

Which is the change in SNR due to using the window (always negative compared to the rectangular window). This is explained intuitively by the ENBW: Each bin is reporting the power in its own bin plus some or all of the adjacent bins due to the spectral widening from the window. Thus in the case of white noise where all the bins are at or close to the same power level, when you sum all the bins you will over-report that actual power since power in adjacent bins is getting double-counted. ENBW and PG are useful metrics when comparing window functions.


[![ENBW][1]][1]


 [1]: https://i.sstatic.net/zdR8L.png