A note on the capacity of the band-limited Gaussian channel

In this paper we reexamine results of a previous paper¹ in which the capacity of the continuous-time channel with bandwidth W, average signal power P<inf>0</inf>, and additive gaussian noise with flat spectral density N<inf>0</inf> was shown to be approximately W In (1 + P<inf>0</inf>/N<inf>0</inf>W) under a number of physically consistent assumptions. When one of the models in Ref. 1 is modified by techniques suggested by Slepian in his 1974 Shannon Lecture,² the channel capacity turns out to be exactly W In (1 + P<inf>0</inf>/N<inf>0</inf>W).