# 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?

## 1 Answer

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\$$.

Describing it like this is necessary to mathematically capture the idea that if you measure something in arbitrarily small regions, the thing you observe converges to a density; in your case, for any continuous spectrum, the idea is that your "power in measurable (hence, non-infinitesimally-narrow) bandwidth" converges to "power spectral density".

• Thanks for the answer. So I can sample the output and then find this by digital methods/programs. If I use tools(like MATLAB) for noise's power spectral density; I have two sub questions. If the constant signal is 1V mean with random noise superimposed, should I first subtract the mean value from the signal and take the power spectral density? And secondly does that mean to analyse the nosie like that should our logged data be a constant voltage? – atmnt Jun 20 '19 at 12:55
• 1) depends on of what you want the PSD, 2) I don't understand. Please ask these as new questions instead of in a comment. – Marcus Müller Jun 20 '19 at 13:02
• Okay I will ask as separate question – atmnt Jun 20 '19 at 13:09