SIMPLE DERIVATION OF THE THERMAL NOISE FORMULA USING WINDOW-LIMITED FOURIER-TRANSFORMS AND OTHER CONUNDRUMS

A simple theoretical derivation for obtaining the Johnson thermal nois e formula using window-limited Fourier transforms is presented in deta il for the first time, utilizing the well-known energy theorems. In th e literature, a diverse range of alternative methods already exist, an d the pedagogical value of the Fourier transform approach illustrates useful mathematical principles, taught at the undergraduate level, nat urally highlighting a number of physical assumptions that are not alwa ys clearly dealt with. We also proceed to survey a number of misconcep tions, problems, surprises, and conundrums concerning thermal noise.