Advanced DSP - FFT windows: equivalet noise bandwidth

A given FFT bin contains contributions from other frequency component including broadband noise:

The shape of the window function's kernel can be thought of as a filter's frequency response. Noise will contribute to the measured value at the FFT bin proportionally to the filter's frequency response.

To detect a narrow band signal in the presence of broadband noise, we want to narrow the bandwidth from which noise contributions are significant. This can be done by narrowing the window function's kernel.

Equivalent Noise Bandwidth measures the noise performance of the window function:

Equivalent Noise Bandwidth is the width of an ideal rectangular filter which would accumulate the same noise power from white noise as the window function's kernel with the same peak power gain. This is a fruitful concept, and quite easy to visualise.