I came across to Shannon’s formula for calculating channel capacity and I don’t quite understand why we calculate average signal power… “over bandwidth”. Why over that "domain of interest"?
Here is my interpretation why but I’m not sure if I understood it right.
Imagine we are sending some signal f(t) from point A to point B. We take FT (Fourier transform) of signal f(t) at point A, and we get ourselves all the sinusoid components of that signal. For every component of that signal in frequency domain we have particular value of amplitude. Now, I’m not sure if this can be done but here is my interpretation of “power over bandwidth”: “Inside frequency domain” we calculate avg. power of signal in such fashion that we calculate power of every component of signal and by doing some manipulations with all those calculated “powers” (sum of them equals power of signal in time domain?) we can calculate average power of the signal in frequency domain.
So we have avg. power of “clear/undistorted signal” of value for example 40[W] “over bandwidth” that interest us (bandwidth of our signal).
Signal traveling from point A to receiver side B gets distorted. At point B we take FT of that distorted signal. Now, maybe we have some components of signal that are added within our signal, so all those components represent “noise signal”. We “separate” noise components and our signal components (in our head). Since signal is distorted maybe some of the amplitudes of signal’s components are now changed, so we again calculate (in a same fashion as one above) average power of that components and get… maybe some different average power which for example might be less than one at point A.
So, based on this interpretation do we by that mean average signal power “over bandwidth” (“over bandwidth of something that interests us, over our signal bandwidth to see if something has changed”)?