# How to determine waveform of thermal (white) noise?

Here, the mean power of thermal noise is given by:

$$P = 4kT$$ ($$T$$ = temperature, $$k$$ = Boltzmann’s constant)

And the voltage in the instrument is, of course, thus given by:

$$V^2/R = 4kT$$

The thermal noise, and therefore the voltage, is distributed as a Gaussian around this mean, with RMS given by:

RMS = $$4RkTB$$ ($$B$$ = bandwidth)

The idea of plotting a function only really makes sense for something that is continuous (at enough points to draw). The waveform for $$\delta$$-correlated Gaussian noise is continuous nowhere and infinite everywhere, so you can't really draw it. However, you can plot the discrete-time equivalent, which is an independent, normally-distributed random number associated to each point in time.
• Just to add to that, generating Gaussian random variables, if it is not supported by your random number generator library for your programming language natively, can be done with the en.wikipedia.org/wiki/Box%E2%80%93Muller_transform, or in Google Sheets you can do =NORMINV(RAND(),0,1) which is a trick called sampling the inverse CDF. – CR Drost Aug 29 at 21:57