# Confusion with applying incremental bandwidth to measure noise power spectral density

From a text, regarding the following paragraph about random noise:

Being not very informed on this topic, I don't understand what meant by the following statement:

"If such a measurement is made over a specific incremental bandwidth Δf at a specific center frequency fk, the output noise voltage can be expressed in terms of..."

Does that mean a band-pass filter applied for each Δf? And is so will it be applied at the input or output? And how is this done by analog way in reality? Or is it more convenient to measure the entire signal and apply digital methods?

The sentence you're referring to describes a mathematical model; so, no, there's no bandpass filter for each $$\\Delta f\$$; that would be impossible, since $$\\Delta f \to 0\$$.