You are drawing AWGN wrong (or How to simulate physical noise)
by [Fran]If you need to draw AWGN you will surely do something like:
I'm afraid to tell you that it is wrong!
This would be more truthful:
That's right! Everything blue. Improving it will require infinite blue paint for your entire wall, house, city, planet, galaxy until you fill the entire universe.
# Why?
Because AWGN is a fractal. You can zoom in all you want and you will forever find infinite more "samples".
You may be thinking: "OK... That explains the horizontal spread but... what about the vertical one?"
Remember every sample is the sum of infinite randomized frequency components that will cover all possible values.
- The more you try to be truthful, the more detail, more sampling, more bandwidth, more components adding up to each sample.
# Story time!
When I was a student of "Digital and Analog Communications I" in 2010 I wanted to check by simulation the solutions to the "pen & paper" excercises.
Many of those mentioned the parameter N0
# Philosophy time!
- Every physical measue implies an interaction, during a certain amount of time, with energy flowing. So we are always "low pass filtering". There is always a bandwidth.
- Intuition: more sampling rate --> wider filter --> more noise
# Misc
- revisando mi cuaderno viejo, encuentro que hay ambiguedad de unidades